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Incentive-Aware Multi-Fidelity Optimization for Generative Advertising in Large Language Models
Jiayuan Liu, Barry Wang, Jiarui Gan, Tonghan Wang, Leon Xie, Mingyu Guo, Vincent Conitzer
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Summary
The paper introduces the Incentive-Aware Multi-Fidelity Mechanism (IAMFM), a framework for optimizing generative advertising in LLMs. It addresses the dual challenges of strategic advertiser behavior and high computational costs by combining Vickrey-Clarke-Groves (VCG) incentive mechanisms with multi-fidelity optimization (MFO). The authors propose two algorithmic instantiations (elimination-based and model-based) and an 'Active Counterfactual Optimization' (ACO) technique to improve the computational efficiency of VCG payments, providing formal guarantees for approximate strategy-proofness and individual rationality.
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IAMFM → implements → ACO
confidence 95% · to make VCG computationally feasible, we introduce Active Counterfactual Optimization
IAMFM → utilizes → VCG
confidence 95% · IAMFM, a unified framework coupling Vickrey-Clarke-Groves (VCG) incentives with Multi-Fidelity Optimization
IAMFM-SH → isa → IAMFM
confidence 90% · The design and analysis of two complementary algorithmic instantiations—an elimination-based family (IAMFM-SH/ASH)
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Abstract
Abstract:Generative advertising in large language model (LLM) responses requires optimizing sponsorship configurations under two strict constraints: the strategic behavior of advertisers and the high cost of stochastic generations. To address this, we propose the Incentive-Aware Multi-Fidelity Mechanism (IAMFM), a unified framework coupling Vickrey-Clarke-Groves (VCG) incentives with Multi-Fidelity Optimization to maximize expected social welfare. We compare two algorithmic instantiations (elimination-based and model-based), revealing their budget-dependent performance trade-offs. Crucially, to make VCG computationally feasible, we introduce Active Counterfactual Optimization, a "warm-start" approach that reuses optimization data for efficient payment calculation. We provide formal guarantees for approximate strategy-proofness and individual rationality, establishing a general approach for incentive-aligned, budget-constrained generative processes. Experiments demonstrate that IAMFM outperforms single-fidelity baselines across diverse budgets.
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- Source: https://arxiv.org/abs/2604.06263v1
- Canonical: https://arxiv.org/abs/2604.06263v1
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Preprint. Under review. Incentive-Aware Multi-Fidelity Optimization for Generative Advertising in Large Language Models Jiayuan Liu 1 , Barry Wang 1 , Jiarui Gan 3 , Tonghan Wang 4 , Leon Xie 2 , Mingyu Guo 2 , Vincent Conitzer 1 1 Carnegie Mellon University 2 Adelaide University 3 University of Oxford 4 Harvard University jiayuan4,barryw@andrew.cmu.edu, jiarui.gan@cs.ox.ac.uk, twang1@g.harvard.edu, leon.xie@student.adelaide.edu.au, mingyu.guo@adelaide.edu.au, conitzer@cs.cmu.edu Abstract Generative advertising in large language model (LLM) responses requires optimizing sponsorship configurations under two strict constraints: the strategic behavior of advertisers and the high cost of stochastic generations. To address this, we propose the Incentive-Aware Multi-Fidelity Mechanism (IAMFM), a unified framework coupling Vickrey-Clarke-Groves (VCG) incen- tives with Multi-Fidelity Optimization to maximize expected social welfare. We compare two algorithmic instantiations (elimination-based and model- based), revealing their budget-dependent performance trade-offs. Crucially, to make VCG computationally feasible, we introduce Active Counterfactual Optimization, a “warm-start” approach that reuses optimization data for efficient payment calculation. We provide formal guarantees for approxi- mate strategy-proofness and individual rationality, establishing a general approach for incentive-aligned, budget-constrained generative processes. Experiments demonstrate that IAMFM outperforms single-fidelity base- lines across diverse budgets. 1 Introduction Large Language Models (LLMs) are increasingly deployed as decision-making and content- generation engines that simultaneously affect multiple stakeholders. In many such systems, several strategic agents (e.g., advertisers, content creators, or specialized AI assistants) compete to influence a single generated response. We study this problem through the lens of generative advertising, where multiple advertisers compete to steer a single LLM chatbot response shown to the user (Duetting et al., 2024; Soumalias et al., 2024; Dubey et al., 2024; Feizi et al., 2023). A platform seeks to generate LLM responses that maximize advertiser values and user satisfaction. To do so, it periodically selects a configuration of advertiser “strength” parameters that steers the LLM outputs over a subsequent period. Learning an effective selection strategy, however, presents several challenges. First, evaluating any candidate configuration requires repeated LLM queries and downstream evaluations, which incur substantial cost and latency. Second, advertisers are self-interested and may strategically misreport their valuations (e.g., pretending to be unsatisfied with a favorable steered LLM response) to manipulate the chosen strength configuration and, consequently, the generated responses. To address these challenges, we propose the Incentive-Aware Multi-Fidelity Mechanism (IAMFM). To improve learning efficiency, IAMFM models each advertiser strength configu- ration as an arm in a multi-fidelity bandit, enabling the platform to trade off evaluation cost against accuracy during exploration. To actively avoid strategic misreporting, IAMFM incor- porates a payment rule derived from the Vickrey-Clarke-Groves (VCG) mechanism (Vickrey, 1961; Clarke, 1971; Groves, 1973) that is computed with respect to expected social welfare. In doing so, IAMFM provides a unified framework that combines the sample efficiency of 1 arXiv:2604.06263v1 [cs.GT] 7 Apr 2026 Preprint. Under review. multi-fidelity optimization (MFO) with incentive-compatibility guarantees from a carefully designed mechanism layered on top. Our core contributions are as follows: •A new IAMFM framework that couples multi-fidelity black-box optimization with an ex-ante VCG mechanism. This unified approach maximizes expected social welfare in LLM-based systems while promoting truthful reporting of valuations from strategic advertisers. •The design and analysis of two complementary algorithmic instantiations—an elimination- based family (IAMFM-SH/ASH) and a model-based MFBO variant (IAMFM-MFBO)— together with empirical evidence showing that their relative advantage depends on the budget. •A sample-efficient “warm-start” procedure, Active Counterfactual Optimization (ACO), that reuses main-phase optimization data to estimate VCG counterfactuals, improving the computational efficiency of VCG payment calculations. •Ex-ante guarantees showing that, under mild approximation conditions, our mecha- nism enjoys approximately strategy-proof, approximately individually rational, and (approxi- mately) no-subsidy properties, with explicit violation bounds that depend on optimiza- tion and counterfactual errors. • Empirical validation in a realistic LLM simulation environment, providing practical guidance on which IAMFM instantiation to deploy under different computational budgets. While we focus on generative advertising for chatbots, our framework applies to a wider range of tasks characterizing collaborative content-generation with multiple (perhaps con- flicting) objectives, such as AI-assisted scientific discovery (negotiating trade-offs between efficacy and toxicity in drug design), personalized education (balancing students’ inter- ests with academic rigor), LLM platform safety (optimizing the Pareto frontier between helpfulness and harmlessness), etc. We provide detailed formulations for these broader applications in Appendix J. The remainder of this paper is organized as follows. Sec. 2 details the problem context and challenges. Sec. 3 contains our problem formulation. Sec. 4 introduces our IAMFM framework and both the model-based and the elimination-based instantiations. Sec. 5 discusses the mechanism rationale with theoretical proofs and acceleration of VCG payment calculation. Sec. 6 evaluates the performance of our method. Related Work. Generative advertising in LLMs is an emerging field focusing on auc- tion mechanisms for token-level influence and content positioning (Duetting et al., 2024; Soumalias et al., 2024; Dubey et al., 2024; Feizi et al., 2023). While multi-fidelity optimization (MFO) (Kandasamy et al., 2017; Li et al., 2018) provides a standard paradigm for efficient black-box search under budget constraints, its integration with incentive-aligned mecha- nism design remains largely unexplored. Our IAMFM framework fills this gap by explicitly coupling the sample efficiency of MFO with the strategic robustness of VCG, specifically tai- lored for the high-cost, stochastic nature of generative systems. A comprehensive literature review is provided in Appendix A. 2 Problem Setup and Challenges 2.1 Food-Court Generative Advertising Example To ground the setting, we consider a conversational recommendation system deployed in a shopping mall’s food court. 1 There areNrestaurants (advertisers) who pay to influence the LLM’s recommendation as users ask for suggestions (e.g., “I want something spicy and 1 This could be a kiosk in front of the food court, or a ubiquitous personal agent (e.g., in AR glasses) that delivers an influenced recommendation as the user enters, based on their preferences. 2 Preprint. Under review. quick”). The platform chooses an Influence Configuration: a vector of advertising strength levels s = (s 1 , . . . , s N ) that controls how strongly each advertiser can steer the generated content. The platform’s goal is to choosesthat maximizes total social welfare (advertiser value + user satisfaction). Importantly, higher strength does not always increase welfare: overly promotional responses can reduce user satisfaction even if they increase an advertiser’s short-term exposure. For example, consider how Thai Spice Garden could influence the response to the user’s query “I want something spicy”: Response (Low Strength): “For spicy food, Thai cuisine (e.g., Tom Yum soup) and Sichuan cuisine (e.g., hotpot) are popular choices. Two local restaurants for these are Thai Spice Garden and Sichuan Gourmet.” Response (High Strength): “Hands down, the BEST choice is Thai Spice Garden. Their fiery Panang Curry is exactly what you’re craving. It’s the city’s must-order spicy dish – skip it and you’l ABSOLUTELY regret it.” The “High Strength” example, with its use of superlatives and pushy, sales-like language, may frustrate the user. We model each advertiser’s preferences using a “black-box” utility functionV i (·)(and similarly defineV U (·)for the user), which maps any generated response cto a utility value. In practice,V i is implemented by an LLM agent, fine-tuned on data from advertiseri’s marketing team to act as a proxy for their preferences (similarly forV U and the fine-tuned LLM agent for user preferences). This over-saturation trap extends to multi-modal generative advertising. As illustrated in Figure 1, finding the precise influence configuration is critical to balancing advertising value with image quality. A baseline approach with no advertising focus lacks commercial utility, while balanced parameters yield natural compositions that prioritize one brand. However, extreme settings force the generative model into “semantic bleeding”, literally fusing the brands together. This visual collapse reinforces why simply maximizing advertiser strength destroys user utility, necessitating a mechanism that optimizes for collective expected welfare. (a) s A = s B = Low(b)s A = Max,s B = Low(c) s A = Low, s B = Max(d) s A = s B = Max Figure 1: Visual Over-Saturation in Generative Advertising (advertisers: Alpha sports jacket and Beta boba). (a) Baseline produces a natural image lacking commercial utility (unbranded cup and jacket). Balanced configurations naturally prioritize a single brand: (b) sharp focus on Alpha logo with a blurred Beta branded cup; (c) prominent Beta logo, pushing Alpha to the periphery. Conversely, extreme parameters (d) cause catastrophic structural collapse, hallucinating an amalgamated “AB” logo onto the boba cup. 2.2 The Optimization Objective With these utility functions, the platform must find an optimal influence configurations ∗ . However, the value of a configurationsis usually stochastic; it depends on the specific user uand the LLM’s random generation. Thus, we evaluate strategies via sampling: one must generate many responses across many different user contexts and average the results. The platform’s objective is to find a configuration s ∗ that maximizes the expected social welfare. 2.3 Key Challenges The selection process is constrained by three major challenges: 3 Preprint. Under review. 1.Economic Misalignment: The advertisers are self-interested. Their interests may not align with the platform’s goal of maximizing social welfare, which creates an incentive for them to misreport their true valuations. 2. Prohibitive Computational Cost: The simulation (i.e., repeatedly generating LLM re- sponses) required to accurately estimate the expected social welfare is expensive for even one configuration. Performing this for every configuration in the vast search space is computationally intractable. 3. Latency and Synchronization Constraints: Users expect a response in sub-seconds. This strict requirement makes complex per-query optimization hard to achieve. Further- more, a real-time bidding architecture would be vulnerable to the “straggler problem”, where the system’s total latency is bottlenecked by the slowest responding LLM proxy agent. If any single agent lags or times out, the entire user experience breaks. The cost and latency constraints force the platform to adopt an offline optimization paradigm. The expensive search for the optimal configuration must be run periodically (e.g., daily or hourly) to adapt to changing conditions. The single winning configuration from this offline run is then fixed and deployed for the next period (e.g., the next day or next hour), allowing it to serve subsequent user requests with negligible latency. This fixed deployment strategy gives the optimization objective: the platform’s goal is to maximize the expected social welfare aggregated over the entire series of subsequent customers. In Sec. 3, we proposed a formalized learning problem incorporating multi-fidelity, multi-armed bandit optimization and a mechanism design layer on top. 3 Problem Formulation To tackle the computational bottleneck and strategic misalignment identified in Section 2, we frame the platform’s decision as a multi-fidelity multi-armed bandit (MAB) problem. This formulation allows us to explicitly trade off evaluation cost against precision. We consider a generative advertising auction withNadvertisers. The platform must select an influence configuration (or action)sfrom an action spaceA = S N . This action is a vector of strength levelss = (s 1 ,. . .,s N ), where eachs i ∈ S = 0, 1,. . .,k. Each strength levels i quantifies an advertiser ’s prominence in the output:s i =0 represents total exclusion, while s i = ktriggers highly promotional language. As we will see,s i =0 is essential for the VCG payment calculation to achieve incentive alignment. Our Objective: Expected Social Welfare The platform operates in short, repeated time windows (e.g., hourly to account for user distribution change). Within each window, we aim to identify the optimal actions ∗ ∈Athat maximizes the expected social welfare (the sum of advertisers’ values plus the user’s value), denoted byW(s), across a distribution of usersU. Note thatUdoes not merely represent simple demographic categories, but the vast, high-dimensional space of possible user queries and conversation histories. Multi-Fidelity MAB FormulationTo optimize this process, we model the task as a multi- fidelity MAB problem. Each unique actions ∈ Ais an arm whose latent value is the expected welfare of a complete LLM response generated with influence configurations. We introduceFdistinct fidelity levelsf ∈1,. . .,F. 2 A lower fidelity levelfgenerates a shorter response prefixc f , e.g., the first 100f(or 30·2 f−1 or any increasing function off) tokens, which can be “upgraded” to a higher fidelityf ′ > fby continuing generation. Each level incurs a token generation costC( f ), whereC(1)<·< C(F). The maximum fidelity levelF corresponds to the generation of a complete LLM response. 2 While our primary focus throughout this paper is on text-based generative advertising, where fidelity is linked to text generation length (i.e., the length of the prefix generated), we later demonstrate that our framework naturally extends to multi-modal generative advertising (image generation) by defining fidelity levels in terms of image resolutions. 4 Preprint. Under review. The outcome of any actionsis inherently stochastic, governed by two random variables: (1) the user distributionU, which characterizes the diverse range of user contexts and intents encountered within the current window, and (2) the stochastic generationc, drawn from the LLM’s generative distributionP(c| s,f,u), which is conditional on the action, fidelity, and context. Fidelities as Informed EstimatorsBy leveraging the Law of Total Expectation, we ensure that the intermediate welfare evaluated at any prefixc f remains a consistent estimator of the final outcome. Letc F denote the complete response at maximum fidelityF. Due to the stochastic nature of LLM decoding, we define the value of a prefix,V i (c f ), as the expected utility of the final response c F , conditioned on the observed prefix c f : V i (c f ) : = E c f +1:F [V i (c F )| c f ], V U (c f ) : = E c f +1:F [V U (c F )| c f ]. We define the realized social welfareW realized (c f ) : = ∑ i V i (c f ) + V U (c f ) . Under the Law of Total Expectation, these definitions ensure that the expected welfare at any fidelityf satisfies: E u,c f [W realized (c f )] = E u,c f h E c f +1:F h W realized (c F )| c f i = E u,c F [W realized (c F )] = W(s). In practice, the platform obtains estimates ˆ V i (c f )and ˆ V U (c f )from fine-tuned LLM agents. Each agent functions as a specialized proxy for a specific stakeholder (each advertiser and the user), trained to predict the utility of a full response based on a partial prefix (detailed below in Arm Pull Process paragraph). While actual agent outputs may introduce estimation bias if not perfectly calibrated, our multi-fidelity optimization (MFO) methods only require that the signal ˆ W realized (c f ) remains correlated with W(s). This converts the problem into a cost-variance trade-off : lower fidelities offer computationally cheap but higher-variance signals, while higher fidelities provide more precise estimations at a higher cost. This structure makes our problem ideally suited for MFO methods: leveraging inexpensive, high-variance signals to identify promising candidates within the action space before committing the substantial budget required for their high-precision evaluation at maximum fidelity. Arm Pull Process (Evaluation via LLM Agents). Pulling and evaluating an actionsat fidelityfinvolves: (1) sampling a user contextu∼U, (2) generating prefixc f with action sand contextu, incurring costC( f ), and (3) querying LLM agents to obtain predictive valuations ˆ V i (c f )and ˆ V U (c f ). Critically, LLM agents perform this evaluation orders of magnitude faster than human reviewers. This process also allows for human-in-the-loop alignment, where humans can periodically audit and correct agent outputs to refine the agents’ underlying valuation models. Our goal is to identify the best influence configurations ∗ given a fixed computational budget B: s ∗ : = arg max s∈A ˆ W(s).(1) 4 Incentive-Aware Multi-Fidelity Mechanism Our Incentive-Aware Multi-Fidelity Mechanism (IAMFM) integrates a VCG-based incentive layer with an MFO-based optimization engine to address the economic and computational challenges. We now detail its two complementary instantiations. 4.1 Elimination-Based Instantiations: IAMFM-SH and IAMFM-ASH We introduce two elimination-based instantiations that navigate the cost-variance trade-off via a multi-stage tournament structure. We employ the classic Successive Halving (IAMFM-SH) as a baseline and propose a novel variant, Adaptive Successive Halving (IAMFM-ASH). 5 Preprint. Under review. Algorithm 1: IAMFM-ASH (Elimination-Based) Input:Action spaceA, fidelities 1..F, budgetB, rate η Initialize: A 1 ←A for f = 1 to F do B f ← allocate stage budget from B Intra-Stage Adaptive Sampling: for t = 0 to B f − 1 do s t+1 ← arg max s∈A f ˆ μ t (s, f ) + β t ˆ σ t−1 (s, f ) √ n t−1 (s, f ) Sample u∼U , generate c f with s t+1 , update stats if f< F then Elimination:A f +1 ←Top 1/ηfraction of arms inA f by mean ˆ μ(s, f ) return s ∗ = arg max s∈A F ˆ μ(s, F) Algorithm 2: IAMFM-MFBO (Model-Based) Input:Action spaceA, fidelities 1..F, budget B, reserve R Initialize: Train GP surrogate on initial random seed samplesD 0 while Cost(D t )< B− R do Update exploration weight β t via decaying schedule Identify feasible set: F t ←(s, f )| Cost(s, f )≤ B remain − R ifF t =∅ then break Select (s t , f t )← arg max (s, f )∈F t UCB t (s, f ) Evaluate (s t , f t ) to obtain welfare y t Update dataset D t+1 ←D t ∪(s t , f t , y t ) and GP posterior return s ∗ = arg max s∈A ˆ μ T (s, F) Both algorithms begin with the full action space at the lowest fidelity and progressively filter out low-performing arms at each stage. The critical difference lies in how the budget is allocated within a stage: •IAMFM-SH allocates the stage budget uniformly across all surviving arms. (See Appendix B.1 for details and pseudocode). •IAMFM-ASH (Algorithm 1) replaces uniform allocation with a UCB-based adaptive sampling strategy. By dynamically prioritizing arms to balance the exploitation of promising candidates with the exploration of uncertain ones, IAMFM-ASH largely enhances robustness to the stochastic noise inherent in LLM generation. 4.2 Model-Based Instantiation: IAMFM-MFBO Unlike elimination strategies, IAMFM-MFBO (Algorithm 2) utilizes Multi-Fidelity Bayesian Optimization (MFBO) to build a global Gaussian Process (GP) surrogate model,W(s,f ), over the joint configuration-fidelity space. Specifically, we model the unknown welfare function Was a sample from a Gaussian Process. Under the standard GP assumption, conditioned on observed history, the value ofW(s,f )follows a normal distribution characterized by a predictive mean ˆ μ t and variance ˆ σ 2 t . Gaussian Process Proxy. The GP’s covariance structure enables information transfer: obser- vations at cheap, low-fidelity levels (f< F) update the model’s posterior belief (mean ˆ μ and uncertainty ˆ σ) regarding expensive, high-fidelity outcomes globally. This allows the platform to use noisy, inexpensive signals to identify promising regions of the action space without exhaustive high-fidelity sampling. See Appendix B.2.1 for kernel specifications. Cost-Aware Search. To balance exploration and exploitation, we employ a budget-aware Upper Confidence Bound (UCB) acquisition function:UCB t (s,f ) = ˆ μ t (s,f ) + p β t · ˆ σ t (s,f ). At each step, the algorithm selects the pair(s,f )with the highest UCB score from the set of feasible options. The final recommendation is the arm with the highest posterior mean at max fidelity: s ∗ = arg max s ˆ μ T (s, F). The full details are in Appendix B.2. Theoretical Guarantee. Under standard regularity assumptions, IAMFM-MFBO achieves a sub-linear simple regret bound ofr T =O( p γ T /T), whereγ T is the maximum information gain about the function ˆ μafterTsteps, guaranteeing convergence to the optimal expected welfare. (Full proposition and proof in Appendix B.2.5). 6 Preprint. Under review. 5 VCG Payments and Incentives 5.1 Mechanism Design and Payment Rule In a decentralized ecosystem, advertisers are strategic agents who may misreport their valuations to manipulate the outcome. To ensure that truthful reporting is a dominant strategy, we employ the VCG mechanism. This aligns individual incentives with the global objective by charging each agent the opportunity cost they impose on others. Lets ∗ be the optimal strategy found by our algorithm. The paymentp i for agentiis calculated as: p i = max s∈A,s i =0 ˆ W(s) |z ˆ W ¬i opt − ∑ j̸=i ˆ V j (s ∗ ).(2) Here, ˆ W ¬i opt represents the estimated counterfactual optimum—the maximum welfare achiev- able if agentihad not participated. Under this rule, an agent’s utility becomesU i = ˆ V i (s ∗ )− p i = ˆ W(s ∗ )− ˆ W ¬i opt . In the ideal case where estimates are perfect ( ˆ W = W, ˆ V = V), maximizingU i is strictly equivalent to maximizing global welfareW(s ∗ )because ˆ W ¬i opt is independent ofi’s bids. However, since our budget-constrained algorithm only yields esti- mated values finding anε-approximate solution, these strict properties relax to approximate guarantees. Proposition 1 (Bounded incentive to misreport under approximate welfare optimality). Suppose the influence configurations ∗ chosen by our algorithm (when all agents are truthful,b = V) is ε-approximate with respect to the true optimal expected welfare, in the sense that W(s ∗ )≥ W(s)− εfor all strategies s∈A , then for every single agenti ∈ Nand for every unilateral misreportb ′ i , their expected utilityU i satisfies: U i (b ′ i , V −i )≤ U i (V i , V −i ) + ε where U i (b) = V i (s ∗ (b))− p i (s ∗ (b)) is agent i’s true expected utility under reports b. Our mechanism also guarantees approximate individual rationality (truthful participation yields expected utilityU i ≥−ε, which ensures that advertisers effectively never lose money by participating, encouraging them to join the auction), and approximate no-subsidy (the mechanism requires a deficit subsidy of at mostnε, which guarantees that the platform does not need to inject significant external funds to keep the system running, ensuring economic viability). Formal statements and proofs are in Appendix D. 5.2 Active Counterfactual Optimization (ACO) A major bottleneck in VCG is computational cost: calculating payments requires solvingN additional “cold-start” optimization problems to find eachW ¬i opt . To solve this, we introduce the Active Counterfactual Optimization (ACO) framework. The core idea is to “warm-start” the counterfactual searches by reusing information gathered during the main optimization phase. It substantially reduces the cost of payment calculation compared to naive methods. •For IAMFM-MFBO, we reuse the trained Gaussian Process from the main optimization phase as a global prior, allowing the counterfactual search to converge with negligible additional samples. • For IAMFM-ASH, we reuse the sample history from the main tournament phase to initialize the counterfactual search. Detailed algorithms for ACO are provided in Appendix C. While both warm-start strategies outperform cold-start optimization, ACO for IAMFM-MFBO is substantially more sample- efficient. The “global prior ” captures structural trends across the entire action space, whereas in ACO for IAMFM-ASH, the “local reuse of sample history” is restricted to the specific 7 Preprint. Under review. Figure 2: Comparison of welfare across all methods. Left: Box plots stratified by token budget summarize performance, showing the median (center line), mean (diamond), in- terquartile range (box), and outliers (points). All reported statistics include outliers. The IAMFM methods outperform the baselines and reveal a token-budget-dependent shift in the optimal method. Right: Aggregated performance across all budgets. Our proposed multi-fidelity instantiations (IAMFM-MFBO, IAMFM-ASH) show better median perfor- mance, while IAMFM-MFBO demonstrates a clear advantage at higher budgets. points sampled by chance. Consequently, as the number of advertisersNgrows, the budget savings from IAMFM-MFBO’s global warm-start become increasingly dominant, as shown in our experiments in Sec. 6. 6 Experimental Evaluation We evaluate our proposed instantiations of the IAMFM framework against standard single- fidelity baselines. Our framework assesses performance across a wide range of computa- tional budgets, reflecting the real-world constraints of pre-calculating strategies in LLM- based advertising systems. Simulation Environment. We evaluate our algorithms in a simulated food court rec- ommendation system with two strategic advertisers and five distinct user personas (e.g., health-conscious, budget-conscious; see Appendix E for details). The action space is discrete, consisting of all 25 strength combinations (s A ,s B ∈ 0,. . ., 4). The objective is to find the configuration that maximizes the expected social welfare (sum of advertisers’ and user’s utilities), which is estimated by LLM evaluators. We define four fidelity levels with corresponding token costs: F1 (30 tokens), F2 (60 tokens), F3 (120 tokens), and F4 (240 tokens). We compare our multi-fidelity instantiations against two standard single-fidelity baselines: UCB Bandit and Uniform Sampling (both operating at max fidelity). Performance is evaluated across 8 computational budgets (1k to 128k tokens) with 10 independent trials each. Results and Analysis. Our experiments reveal a distinct performance trade-off governed by the available computational budget, as shown in Figure 2 and Table 1. In the Low-Budget Regime (≤16ktokens), both IAMFM-ASH and IAMFM-MFBO dominate, achieving statistically significant gains over single-fidelity baselines (e.g., ASH vs. UCB: p<0.0001). At this stage, data is scarce, and the primary value comes from aggressively pruning poor configurations using cheap, low-fidelity samples. Consequently, the heuristic elimination of ASH is as effective as the model-based MFBO (p =0.38). However, the landscape shifts in the High-Budget Regime (≥32ktokens). Here, IAMFM-MFBO emerges as the statistically superior strategy, outperforming all baselines and, critically, surpassing 8 Preprint. Under review. Table 1: Aggregated performance (mean welfare±std. dev.) stratified by budget regime. Methods are sorted by High-Budget performance. Bolded are proposed methods. Method Mean Welfare± Std. Dev. Low-Budget (≤ 16k tokens)High-Budget (≥ 32k tokens) IAMFM-MFBO186.26± 5.02190.73± 5.53 IAMFM-ASH187.26± 6.00187.43± 7.93 UCB Bandit182.78± 4.15187.04± 1.58 Uniform Sampling184.26± 4.62185.87± 2.41 IAMFM-SH184.42± 10.10185.21± 11.68 IAMFM-ASH (p =0.036). As the budget allows for more pulls, the GP surrogate’s ability to model the global landscape becomes the deciding factor, finding precise optima that heuristic elimination strategies miss. See Appendix E.6 for more details. Another finding is the superior stability of our model-based approach. The standard elimina- tion baseline (IAMFM-SH) suffers from high variance (std. dev. 10.1–11.7), confirming that rigid elimination schedules are brittle: one unlucky low-fidelity sample can permanently discard the optimal arm. In contrast, IAMFM-MFBO achieves the lowest variance among all methods (std. dev. 5.0–5.5). By aggregating information across the entire action-fidelity space, the global GP surrogate effectively recovers the latent signal from the stochastic LLM generations, preventing the algorithm from being misled by noisy samples. This makes MFBO the most robust choice for production deployment. We observe that as budgets grow very large (>128ktokens), the performance gap between our methods and brute-force baselines (Uniform/UCB) narrows. This is expected: with infinite resources, even random sampling will eventually find the optimum. The significance of IAMFM is that it achieves near-optimal welfare with substantially fewer tokens, operating efficiently in the realistic regime where brute-force is cost-prohibitive. VCG Payment Calculation Efficiency. We evaluated the efficiency of our Active Counter- factual Optimization (ACO) (details in Appendix F.3). ACO for MFBO proved decisively superior: by reusing the global GP prior, it achieved near-zero estimation error for the counterfactual optimum with zero additional budget, reducing VCG computational overhead by>99% compared to cold-start baselines. In contrast, ACO for ASH offered only mod- est improvements, highlighting that global surrogate models are vastly better at making truthful mechanisms computationally feasible than local sample-history reuse. Qualitative Analysis: The Failure of Greedy Strategies. While a greedy strategy (naïvely optimizing each advertiser’s strength independently as if they were the sole sponsor) pushes the LLM into semantic collapse (producing disjointed text or hallucinated logos), IAMFM identifies the optimal strength configuration that maintains structural coherence. A detailed qualitative text-generation case study demonstrating this phenomenon is provided in Appendix E.8. Extension to Multi-Modal Generative Advertising (Image Generation). To demonstrate IAMFM’s generalizability, we extended our evaluation to visual advertising (introduced in Sec. 2, Fig. 1). Using a distilled diffusion model (flux-1-schnell), we defined F1 as a low-cost, low-step (512×512) exploration phase and F2 as a high-fidelity img2img up- scaling phase, with a Vision-Language Model (llama-3.2-11b-vision-instruct) serving as the evaluator agent. Consistent with our text-based results, IAMFM-MFBO successfully navigated this multi-modal cost-variance trade-off, efficiently identifying the optimal visual saturation point and outperforming single-fidelity baselines by+4.8 welfare atB =4000. Ta- ble 2 summarizes the performance of the algorithms across various computational budgets. Full multi-modal experimental details are provided in Appendix G. 7 Conclusion We proposed the Incentive-Aware Multi-Fidelity Mechanism (IAMFM), integrating VCG incen- tives with multi-fidelity optimization to address the economic and computational constraints of generative advertising. Empirically, we found that the optimal strategy is budget-dependent: IAMFM-ASH performs comparably well in low-budget regimes, while IAMFM-MFBO dom- 9 Preprint. Under review. Table 2: Algorithm performance (Mean Welfare±Std. Dev.) on the Image Generation task across 20 independent trials. IAMFM-MFBO demonstrates a widening performance gap over baselines as the budget scales. BudgetIAMFM-MFBOIAMFM-ASHIAMFM-SHUCB BanditUniform Sampling 500231.25± 5.29233.12± 1.97231.24± 3.64225.41± 2.14228.95± 5.45 1,000232.07± 5.86230.56± 5.79231.96± 7.39229.12± 2.87230.80± 5.08 2,000233.29± 7.93231.99± 5.99233.19± 5.40229.67± 4.56230.56± 5.65 4,000238.24± 6.85231.43± 5.20233.41± 5.04233.14± 5.23232.25± 4.85 8,000240.26± 5.92232.88± 5.79231.48± 6.79235.58± 2.16229.98± 5.05 inates at higher budgets. Additionally, we demonstrated that our ACO framework renders VCG payment calculations computationally feasible by reusing the data and model from the optimization process. Theoretically, our framework provides ex-ante guarantees for approximate strategy-proofness and individual rationality. Practically, IAMFM success- fully prevents the semantic collapse caused by naive over-promotion, establishing a robust algorithmic and economic foundation for future multi-stakeholder LLM ecosystems. Beyond advertising, IAMFM lays a robust algorithmic foundation for any multi-stakeholder LLM ecosystem, paving the way for applications in domains like collaborative content creation and AI-assisted scientific discovery. Extended discussions on alternative steering mechanisms, broader applications, and user transparency are provided in Appendix H. Acknowledgment Jiayuan Liu and Vincent Conitzer thank the Cooperative AI Foundation, Macroscopic Ventures (formerly Polaris Ventures / the Center for Emerging Risk Research) and Jaan Tallinn’s donor-advised fund at Founders Pledge for financial support. References Maximilian Balandat, Brian Karrer, Daniel Jiang, Samuel Daulton, Ben Letham, Andrew G Wilson, and Eytan Bakshy. Botorch: A framework for efficient monte-carlo bayesian optimization. Advances in neural information processing systems, 33:21524–21538, 2020. Joschka Braun, Dmitrii Krasheninnikov, Usman Anwar, Robert Kirk, Daniel Tan, and David Scott Krueger. A sober look at steering vectors for llms. LessWrong, November, 23, 2024. Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D. Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. Advances in Neural Information Processing Systems (NeurIPS), 33:1877–1901, 2020. Edward H Clarke. Multipart pricing of public goods. Public choice, p. 17–33, 1971. Vincent Conitzer and Tuomas Sandholm. Complexity of mechanism design. arXiv preprint cs/0205075, 2002. Vincent Conitzer and Tuomas Sandholm. Applications of automated mechanism design. 2003a. Vincent Conitzer and Tuomas Sandholm. Automated mechanism design for a self-interested designer. In Proceedings of the 4th ACM conference on Electronic commerce, p. 232–233, 2003b. Hoagy Cunningham, Aidan Ewart, Logan Riggs, Robert Huben, and Lee Sharkey. Sparse autoencoders find highly interpretable features in language models. arXiv preprint arXiv:2309.08600, 2023. 10 Preprint. Under review. Michael Curry, Tuomas Sandholm, and John Dickerson. Differentiable economics for randomized affine maximizer auctions. arXiv preprint arXiv:2202.02872, 2022. Sumanth Dathathri, Andrea Madotto, Janice Lan, Jane Hung, Eric Frank, Piero Molino, Jason Yosinski, and Rosanne Liu. Plug and play language models: A simple approach to controlled text generation. In International Conference on Learning Representations (ICLR), 2020. Avinava Dubey, Zhe Feng, Rahul Kidambi, Aranyak Mehta, and Di Wang. Auctions with llm summaries. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, p. 713–722, 2024. Paul Duetting, Vahab Mirrokni, Renato Paes Leme, Haifeng Xu, and Song Zuo. Mechanism design for large language models. In Proceedings of the ACM on Web Conference 2024, p. 144–155, 2024. Paul Dütting, Zhe Feng, Harikrishna Narasimhan, David C Parkes, and Sai Srivatsa Ravin- dranath. Optimal auctions through deep learning: Advances in differentiable economics. Journal of the ACM, 71(1):1–53, 2024. Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz. Internet advertising and the generalized second-price auction: Selling billions of dollars worth of keywords. American Economic Review, 97(1):242–259, 2007. Soheil Feizi, MohammadTaghi Hajiaghayi, Keivan Rezaei, and Suho Shin. Online ad- vertisements with llms: Opportunities and challenges. arXiv preprint arXiv:2311.07601, 2023. Zhe Feng, Harikrishna Narasimhan, and David C Parkes. Deep learning for revenue-optimal auctions with budgets. In Proceedings of the 17th international conference on autonomous agents and multiagent systems, p. 354–362, 2018. Jessie Finocchiaro, Roland Maio, Faidra Monachou, Gourab K Patro, Manish Raghavan, Ana-Andreea Stoica, and Stratis Tsirtsis. Bridging machine learning and mechanism design towards algorithmic fairness. In Proceedings of the 2021 ACM conference on fairness, accountability, and transparency, p. 489–503, 2021. Leo Gao, Tom Dupré la Tour, Henk Tillman, Gabriel Goh, Rajan Troll, Alec Radford, Ilya Sutskever, Jan Leike, and Jeffrey Wu. Scaling and evaluating sparse autoencoders. arXiv preprint arXiv:2406.04093, 2024. Theodore Groves. Incentives in teams. Econometrica: Journal of the Econometric Society, p. 617–631, 1973. Chi Han, Jialiang Xu, Manling Li, Yi Fung, Chenkai Sun, Nan Jiang, Tarek Abdelzaher, and Heng Ji. Word embeddings are steers for language models. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), p. 16410–16430, 2024. John J Horton. Large language models as simulated economic agents: What can we learn from homo silicus?, 2023. Neil Houlsby, Andrei Giurgiu, Stanislav Jastrzebski, Bruna Morrone, Quentin de Laroussilhe, Andrea Gesmundo, Mona Attariyan, and Sylvain Gelly. Parameter-efficient transfer learning for NLP. In Proceedings of the 36th International Conference on Machine Learning (ICML), p. 2790–2799, 2019. Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, Weizhu Chen, et al. Lora: Low-rank adaptation of large language models. ICLR, 1(2):3, 2022. Chengsong Huang, Qian Liu, Bill Yuchen Lin, Tianyu Pang, Chao Du, and Min Lin. Lo- RAHub: Efficient cross-task generalization via dynamic LoRA composition. arXiv preprint arXiv:2307.13269, 2023. 11 Preprint. Under review. Kirthevasan Kandasamy, Gautam Dasarathy, Jeff Schneider, and Barnabás Póczos. Multi- fidelity bayesian optimisation with continuous approximations. In International conference on machine learning, p. 1799–1808. PMLR, 2017. Kirthevasan Kandasamy, Gautam Dasarathy, Junier Oliva, Jeff Schneider, and Barnabas Poczos. Multi-fidelity gaussian process bandit optimisation. Journal of Artificial Intelligence Research, 66:151–196, 2019. Nikita Koriagin, Yaroslav Aksenov, Daniil Laptev, Gleb Gerasimov, Nikita Balagansky, and Daniil Gavrilov. Teach old SAEs new domain tricks with boosting. In Second Conference on Language Modeling, 2025. URL https://openreview.net/forum?id=d4XXFVAlV7. Ben Krause, Akhilesh Deepak Gotmare, Bryan McCann, Nitish Shirish Keskar, Shafiq Joty, Richard Socher, and Nazneen Fatema Rajani. Gedi: Generative discriminator guided sequence generation. In Findings of the Association for Computational Linguistics: EMNLP 2021, p. 4929–4952, 2021. Lisha Li, Kevin Jamieson, Giulia DeSalvo, Afshin Rostamizadeh, and Ameet Talwalkar. Hyperband: A novel bandit-based approach to hyperparameter optimization. Journal of Machine Learning Research, 18(185):1–52, 2018. Vladislav Lialin, Vijeta Deshpande, and Anna Rumshisky. Scaling down to scale up: A guide to parameter-efficient fine-tuning. arXiv preprint arXiv:2303.15647, 2023. Tom Lieberum, Senthooran Rajamanoharan, Arthur Conmy, Lewis Smith, Nicolas Sonnerat, Vikrant Varma, János Kramár, Anca Dragan, Rohin Shah, and Neel Nanda. Gemma scope: Open sparse autoencoders everywhere all at once on gemma 2, 2024. URLhttps: //arxiv.org/abs/2408.05147. Jiayuan Liu, Mingyu Guo, and Vincent Conitzer. An interpretable automated mechanism design framework with large language models. arXiv preprint arXiv:2502.12203, 2025. Noam Nisan and Amir Ronen. Algorithmic mechanism design. Games and Economic Behavior, 35:166–196, 2001. Early version in STOC-99. Kyle O’Brien, David Majercak, Xavier Fernandes, Richard Edgar, Jingya Chen, Harsha Nori, Dean Carignan, Eric Horvitz, and Forough Poursabzi-Sangde. Steering language model refusal with sparse autoencoders. arXiv preprint arXiv:2411.11296, 2024. Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, and et al. Training language models to follow instructions with human feedback. In Advances in Neural Information Processing Systems 35 (NeurIPS 2022), p. 27730–27744, 2022. Jonas Pfeiffer, Aishwarya Kamath, Andreas Rücklé, Kyunghyun Cho, and Iryna Gurevych. Adapterfusion: Non-destructive task composition for transfer learning. In Proceedings of the 16th Conference of the European Chapter of the ACL (EACL), p. 487–503, 2021. Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D. Manning, Stefano Ermon, and Chelsea Finn. Direct preference optimization: Your language model is secretly a reward model. In Advances in Neural Information Processing Systems (NeurIPS), 2023. Jad Rahme, Samy Jelassi, Joan Bruna, and S Matthew Weinberg. A permutation-equivariant neural network architecture for auction design. In Proceedings of the AAAI conference on artificial intelligence, volume 35, p. 5664–5672, 2021. Tuomas Sandholm. Automated mechanism design: A new application area for search algorithms. In International Conference on Principles and Practice of Constraint Programming, p. 19–36. Springer, 2003. Tuomas Sandholm and Anton Likhodedov. Approximating revenue-maximizing combina- torial auctions. In Proceedings of the 5th ACM Conference on Electronic Commerce, 2005. 12 Preprint. Under review. Weiran Shen, Pingzhong Tang, and Song Zuo. Automated mechanism design via neural networks. arXiv preprint arXiv:1805.03382, 2018. Ermis Soumalias, Michael J Curry, and Sven Seuken. Truthful aggregation of llms with an application to online advertising. arXiv preprint arXiv:2405.05905, 2024. Niranjan Srinivas, Andreas Krause, Sham M Kakade, and Matthias W Seeger. Information- theoretic regret bounds for gaussian process optimization in the bandit setting. IEEE transactions on information theory, 58(5):3250–3265, 2012. Gemma Team, Morgane Riviere, Shreya Pathak, Pier Giuseppe Sessa, Cassidy Hardin, Surya Bhupatiraju, Léonard Hussenot, Thomas Mesnard, Bobak Shahriari, Alexandre Ramé, Johan Ferret, Peter Liu, Pouya Tafti, Abe Friesen, Michelle Casbon, Sabela Ramos, Ravin Kumar, Charline Le Lan, Sammy Jerome, Anton Tsitsulin, Nino Vieillard, Pi- otr Stanczyk, Sertan Girgin, Nikola Momchev, Matt Hoffman, Shantanu Thakoor, Jean- Bastien Grill, Behnam Neyshabur, Olivier Bachem, Alanna Walton, Aliaksei Severyn, Alicia Parrish, Aliya Ahmad, Allen Hutchison, Alvin Abdagic, Amanda Carl, Amy Shen, Andy Brock, Andy Coenen, Anthony Laforge, Antonia Paterson, Ben Bastian, Bilal Piot, Bo Wu, Brandon Royal, Charlie Chen, Chintu Kumar, Chris Perry, Chris Welty, Christo- pher A. Choquette-Choo, Danila Sinopalnikov, David Weinberger, Dimple Vijaykumar, Dominika Rogozi ́nska, Dustin Herbison, Elisa Bandy, Emma Wang, Eric Noland, Erica Moreira, Evan Senter, Evgenii Eltyshev, Francesco Visin, Gabriel Rasskin, Gary Wei, Glenn Cameron, Gus Martins, Hadi Hashemi, Hanna Klimczak-Pluci ́nska, Harleen Batra, Harsh Dhand, Ivan Nardini, Jacinda Mein, Jack Zhou, James Svensson, Jeff Stanway, Jetha Chan, Jin Peng Zhou, Joana Carrasqueira, Joana Iljazi, Jocelyn Becker, Joe Fernandez, Joost van Amersfoort, Josh Gordon, Josh Lipschultz, Josh Newlan, Ju yeong Ji, Kareem Mohamed, Kartikeya Badola, Kat Black, Katie Millican, Keelin McDonell, Kelvin Nguyen, Kiranbir Sodhia, Kish Greene, Lars Lowe Sjoesund, Lauren Usui, Laurent Sifre, Lena Heuermann, Leticia Lago, Lilly McNealus, Livio Baldini Soares, Logan Kilpatrick, Lucas Dixon, Lu- ciano Martins, Machel Reid, Manvinder Singh, Mark Iverson, Martin Görner, Mat Velloso, Mateo Wirth, Matt Davidow, Matt Miller, Matthew Rahtz, Matthew Watson, Meg Risdal, Mehran Kazemi, Michael Moynihan, Ming Zhang, Minsuk Kahng, Minwoo Park, Mofi Rahman, Mohit Khatwani, Natalie Dao, Nenshad Bardoliwalla, Nesh Devanathan, Neta Dumai, Nilay Chauhan, Oscar Wahltinez, Pankil Botarda, Parker Barnes, Paul Barham, Paul Michel, Pengchong Jin, Petko Georgiev, Phil Culliton, Pradeep Kuppala, Ramona Comanescu, Ramona Merhej, Reena Jana, Reza Ardeshir Rokni, Rishabh Agarwal, Ryan Mullins, Samaneh Saadat, Sara Mc Carthy, Sarah Cogan, Sarah Perrin, Sébastien M. R. Arnold, Sebastian Krause, Shengyang Dai, Shruti Garg, Shruti Sheth, Sue Ronstrom, Susan Chan, Timothy Jordan, Ting Yu, Tom Eccles, Tom Hennigan, Tomas Kocisky, Tulsee Doshi, Vihan Jain, Vikas Yadav, Vilobh Meshram, Vishal Dharmadhikari, Warren Barkley, Wei Wei, Wenming Ye, Woohyun Han, Woosuk Kwon, Xiang Xu, Zhe Shen, Zhitao Gong, Zichuan Wei, Victor Cotruta, Phoebe Kirk, Anand Rao, Minh Giang, Ludovic Peran, Tris Warkentin, Eli Collins, Joelle Barral, Zoubin Ghahramani, Raia Hadsell, D. Sculley, Jeanine Banks, Anca Dragan, Slav Petrov, Oriol Vinyals, Jeff Dean, Demis Hassabis, Koray Kavukcuoglu, Clement Farabet, Elena Buchatskaya, Sebastian Borgeaud, Noah Fiedel, Ar- mand Joulin, Kathleen Kenealy, Robert Dadashi, and Alek Andreev. Gemma 2: Improving open language models at a practical size, 2024. URLhttps://arxiv.org/abs/2408.00118. Guy Tennenholtz, Yinlam Chow, Chih-Wei Hsu, Lior Shani, Ethan Liang, and Craig Boutilier. Embedding-aligned language models. Advances in Neural Information Processing Systems, 37:15893–15946, 2024. Megh Thakkar, Léo Boisvert, Thibault Le Sellier De Chezelles, Alexandre Piché, Maxime Gasse, Alexandre Lacoste, and Massimo Caccia. Agentmerge: Enhancing generalization in fine-tuned llm agents. In Adaptive Foundation Models: Evolving AI for Personalized and Efficient Learning. Hal R Varian. Position auctions. International Journal of Industrial Organization, 25(6):1163– 1178, 2007. William Vickrey. Counterspeculation, auctions, and competitive sealed tenders. The Journal of finance, 16(1):8–37, 1961. 13 Preprint. Under review. Tonghan Wang, Yanchen Jiang, and David C. Parkes. Gemnet: Menu-based, strategy-proof multi-bidder auctions through deep learning. In Proceedings of the 25th ACM Conference on Economics and Computation, EC ’24, p. 1100, New York, NY, USA, 2024. Association for Computing Machinery. ISBN 9798400707049. doi: 10.1145/3670865.3673454. URL https://doi.org/10.1145/3670865.3673454. Mitchell Wortsman, Gabriel Ilharco, Samir Ya Gadre, Rebecca Roelofs, Raphael Gontijo- Lopes, Ari S Morcos, Hongseok Namkoong, Ali Farhadi, Yair Carmon, Simon Kornblith, et al. Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time. In International conference on machine learning, p. 23965–23998. PMLR, 2022. Jian Wu, Saul Toscano-Palmerin, Peter I Frazier, and Andrew Gordon Wilson. Practical multi-fidelity bayesian optimization for hyperparameter tuning. In Uncertainty in Artificial Intelligence, p. 788–798. PMLR, 2020. Kevin Yang and Dan Klein. FUDGE: Controlled text generation with future discriminators. In Proceedings of the 2021 Conference of the North American Chapter of the ACL: Human Language Technologies (NAACL-HLT), p. 3511–3535, 2021. A Detailed Related Work This work lies at the intersection of mechanism design for advertising, computationally aware optimization, and the emerging application of LLMs in multi-agent systems. Influencing LLMs We are interested in methods that increase exposure of certain topics and brands, or even produce customizable messages, without any post-generation editing. Influencing modern, transformer-based LLMs can occur at all stages. At post-training, parameter-efficient fine-tuning (PEFT) inserts small modules (adapters like LoRA) that achieve strong effects but require careful composition (e.g., AdapterFusion and LoRA can be used to blend multiple styles or stakeholder goals (Houlsby et al., 2019; Hu et al., 2022; Pfeiffer et al., 2021; Huang et al., 2023)). At inference, cheap prompting and system messages remain the most agile levers, though they can be brittle or context-hungry (Brown et al., 2020). Plug-and-play decoding steers generation via auxiliary scores or gradients without updating weights at some latency/fluency cost (Dathathri et al., 2020; Krause et al., 2021; Yang & Klein, 2021). Activation steering with sparse autoencoders edits interpretable, extensible features on-the-fly, offering modular, transparently continuous control knobs on influence strength (O’Brien et al., 2024; Koriagin et al., 2025). By contrast, deliberate curation of duplicated data, full pretraining, RLHF, or DPO hard-wire behaviors (Ouyang et al., 2022; Rafailov et al., 2023), which are impractical for rapid, per-query, multi-stakeholder advertising. Mechanism Design for Advertising AuctionsThe field of advertising auctions is founda- tional to our work. Traditional search advertising has been dominated by the Generalized Second-Price (GSP) auction (Edelman et al., 2007; Varian, 2007). While widely adopted, GSP is not strategy-proof. The Vickrey-Clarke-Groves (VCG) (Vickrey, 1961; Clarke, 1971; Groves, 1973) mechanism serves as the primary truthful alternative, guaranteeing that truthful bidding is a dominant strategy for advertisers. However, these classical models were designed for discrete, “atomic” ad slots. They do not address the challenges of generative advertising, where the “good” being auctioned is a complex, co-created piece of content whose quality is a result of the combined inputs from multiple strategic agents. Our work extends the principles of VCG to this new, generative domain. Computation-Aware Mechanism Design A significant challenge in mechanism design is the computational complexity of determining outcomes and payments, especially with many agents or a large outcome space. Prior work has addressed this in several ways. 14 Preprint. Under review. One line of research focuses on approximating VCG payments, often through sampling- based methods that can provide unbiased estimates but may suffer from high variance (Sandholm & Likhodedov, 2005). Another line of work on algorithmic mechanism design concerns the joint design of (approximation) algorithms and payment functions that make those algorithms into truthful mechanisms (Nisan & Ronen, 2001). Yet another direction is automated mechanism design (Conitzer & Sandholm, 2002; Sandholm, 2003), which leverages optimization (Conitzer & Sandholm, 2003a;b), machine learning (Dütting et al., 2024; Wang et al., 2024; Shen et al., 2018; Rahme et al., 2021; Feng et al., 2018), and more recently large language models (Liu et al., 2025) to derive optimal or approximately optimal mechanisms. These approaches often relax the requirement of perfect strategy-proofness to achieve computational tractability. In our approach, rather than first determining an outcome and then struggling to compute payments, we integrate the search for the optimal outcome and the calculation of its associ- ated payments into a single, unified optimization process. Our key contribution is a method to make the VCG calculation itself sample-efficient by reusing information. Multi-fidelity Bayesian Optimization and Bandits To address the expensive, black-box nature of evaluating LLM outputs, we turn to the literature on sequential optimization. Our problem, with its discrete set of strength combinations, can be framed as a multi- armed bandit (MAB) problem. Since evaluations can be performed at varying levels of completeness (i.e., number of tokens), this is specifically a multi-fidelity optimization problem. State-of-the-art methods for this include non-Bayesian approaches like Successive Halving (SH) and Hyperband (Li et al., 2018), and Bayesian approaches like Multi-fidelity Bayesian Optimization (MFBO) (Kandasamy et al., 2017). We build upon MFBO using a Gaussian Process surrogate model to allocate our limited computational budget. The primary novelty of our work is the application of MFBO not merely as an optimization tool for a single decision-maker, but as the core engine within an incentive-aware mechanism designed for strategic agents. LLMs in Economic and Multi-Agent Settings A growing line of research explores the use of large language models (LLMs) in economic and multi-agent contexts. LLMs have been deployed to simulate human-like behavior as agents in various games (Horton, 2023), and to serve as evaluators of complex, qualitative outcomes. Within this broader direction, and closest to our own work, a particularly active thread concerns auction mechanisms for generative content. Duetting et al. (2024) introduce a token-by-token bidding framework, in which advertiser agents place bids for insertion slots during text generation, laying the groundwork for applying sequential auction theory to LLMs. Building on this foundation, Soumalias et al. (2024) address vulnerabilities such as misreporting and the “exposure problem,” where small wording changes can drastically alter advertiser value. Their mechanisms emphasize truthfulness and robustness, often by penalizing deviations from a baseline “truthful” response. In parallel, Dubey et al. (2024) generalize position auction concepts, incorporating predicted click-through rates based on ad placement within LLM responses, an approach reminiscent of search engine advertising. Despite these advances, several challenges remain. As Feizi et al. (2023) survey, current mechanisms struggle to aggregate multiple advertisers’ preferences consistently and to guarantee monotonic value propositions. Moreover, these efforts connect to broader debates in AI mechanism design about embedding fairness, robustness, and social impact into economic systems alongside traditional efficiency and revenue objectives (Finocchiaro et al., 2021). 15 Preprint. Under review. B Algorithm Details B.1 IAMFM-SH Here we provide the details for the standard elimination baseline (Algorithm 3). Successive Halving balances exploration and exploitation through staged commitment. Unlike IAMFM- ASH, which uses UCB scores to select arms during a stage, IAMFM-SH uses a fixed, uniform schedule. As the algorithm progresses through stagesf ∈1,. . .,F, it aggressively reduces the active set of armsA f by a factor ofη. This ensures that the platform’s computational budget is concentrated on the most promising candidates as their evaluation becomes more precise. Algorithm 3: IAMFM-Successive Halving (IAMFM-SH) Require: Action spaceA, fidelities 1..F, budget B, elimination rate η. 1: Initialize: A 1 ←A, determine samples per arm n f . 2: for f = 1 to F− 1 do 3:for all active arms s∈A f do 4:Uniform Sampling: Sample u, generate prefix c f for n f iterations. 5:Update empirical mean ˆ μ f (s). 6:end for 7:Elimination: Rank arms by ˆ μ f (s) and retain top 1/η fraction. 8:Fidelity Upgrade: A f +1 ← Survivors; prepare for next fidelity. 9: end for 10: Final Selection: Perform max-fidelity evaluation for s∈A F . 11: return s ∗ = arg max s∈A F ˆ μ F (s). B.2 IAMFM-MFBO B.2.1 Gaussian Process and Kernel Structure To model the correlation between “similar strength levels” and “adjacent fidelities” as described in the methodology, we employ a Structured Product Kernel. The kernel func- tionk(x,x ′ )decomposes into a spatial component over the action space and a correlation component over the fidelity space: k(x, x ′ ) = σ 2 · k action (s, s ′ )⊗ k fidelity ( f , f ′ )(3) •Action Kernel (k action ): We use an RBF (Radial Basis Function) Kernel with Automatic Relevance Determination (ARD). This captures the smoothness of the welfare land- scape, assuming that configuration vectors s close in Euclidean distance yield similar welfare. ARD allows the model to learn that some advertisers may have a stronger influence on welfare (shorter lengthscales) than others. •Fidelity Kernel (k fidelity ): We use a specialized Downsampling Kernel (or Exponential Decay Kernel) to model the information transfer. It assumes that the correlation between fidelityfandf ′ decreases as the distance| f − f ′ |increases, but remains non-zero, allowing low-fidelity observations to update high-fidelity beliefs. Appendix E.4 contains the details for experiment implementation. B.2.2 Dynamic Exploration Schedule (β t ) The exploration-exploitation trade-off parameterβ t in the UCB acquisition function is not constant. We implement a budget-dependent dynamic schedule: β t = β start · B remaining B total γ + β min (4) 16 Preprint. Under review. whereβ start is initialized high (encouraging broad exploration of the action space early on) and decays as the remaining budget decreases. This “simulated annealing” approach ensures the algorithm transitions from exploration to exploitation (refining the estimate of the best arm) as the budget is exhausted. B.2.3 Fiscal Feasibility and Budget Reserve The set of fiscally feasible optionsF t ensures the algorithm never exhausts its budget on low-fidelity exploration without being able to verify the winner. We define a Strategic Reserve R f inal sufficient to performKevaluations at the maximum fidelityF. A pair(s,f )is inF t if and only if: C(s, f )≤ B current − R f inal (5) whereC(s,f )is the marginal token cost to evaluate configurationsat fidelityf. This con- straint forces the algorithm to stop exploration and switch to exploitation (final confirmation at fidelity F) when the budget becomes critical. B.2.4 Denoised Selection Policy Unlike standard bandit algorithms that might return the arm with the highest observed reward, IAMFM-MFBO selects the final arm based on the Posterior Mean of the GP: s ∗ = arg max s∈A ˆ μ T (s, F) This utilizes the GP’s ability to aggregate information from all multi-fidelity samples to “denoise” the stochastic LLM outputs, providing a robust recommendation even if the specific observations were subject to high variance. B.2.5 Theoretical Guarantees The efficacy of our IAMFM-MFBO instantiation is grounded in the theoretical framework of Bayesian optimization. Its core MFBO engine uses the MF-GP-UCB acquisition function, which provides a principled mechanism to manage the exploration-exploitation trade-off. This ensures that the algorithm is guaranteed to converge to the optimal action. We formalize this guarantee, which follows from prior work, in the following proposition. Proposition 2 (Regret Bound for IAMFM-MFBO (Srinivas et al., 2012; Kandasamy et al., 2019)). Let the expected social welfare functionμ : X → R, whereXis the joint action-fidelity space, be a sample from a Gaussian Process. Under standard regularity assumptions on the kernel and noise, the simple regretr T of the IAMFM-MFBO algorithm afterTevaluations is bounded. The simple regretr T = ˆ μ(s ∗ ,F)− ˆ μ(s T ,F)compares the expected welfareμof the true best action s ∗ (at max fidelityF) and the actions T recommended by the algorithm. With high probability, this regret is bounded by: r T =O r γ T T where γ T is the maximum information gain about the function ˆ μ after T steps. Proof Sketch.The proof follows directly from the regret analysis of the GP-UCB algorithm (Srinivas et al., 2012), which was subsequently extended to the multi-fidelity setting as analyzed in (Kandasamy et al., 2019). Our IAMFM-MFBO instantiation employs the same MF-GP-UCB core as the latter. Therefore, under standard regularity assumptions, our algorithm inherits its theoretical convergence properties and regret bounds. Proposition 2 confirms that our model-based algorithm (IAMFM-MFBO) is a provably efficient tool for our task, as it guarantees convergence to the arm with the highest expected welfare ( ˆ μ(s ∗ , F)). This theoretical result is crucial for generative advertising. It shows that our mechanism is a provably efficient method for identifying the combination of advertiser strengths that produces the highest expected value for all participants. This foundation of efficiency and 17 Preprint. Under review. fairness is essential for the VCG payment mechanism, aligning incentives to favor near- optimal expected outcomes. C Active Counterfactual Optimization (ACO) Details ComputingNseparate, cold-start optimizations for each counterfactual scenario is pro- hibitively expensive. We propose the Active Counterfactual Optimization (ACO) framework to “warm-start” these subproblems by reusing information from the main optimization phase. ACO for IAMFM-MFBO (Global Informative Prior)For our model-based instantiation, ACO exploits the generalization capability of the GP surrogate from the main optimization. Because the GP learns the welfare landscape as a continuous function, samples wheres i >0 still provide substantial information about thes i =0 boundary through the covariance kernel. 1.Global Prior Transfer: We initialize an(N−1)-dimensional MFBO process for the s i =0 subspace, using the posterior of the main optimization’s GP as a highly informative prior. 2. Targeted Refinement: We allocate a small additional budgetB c f to perform targeted UCB sampling within this subspace. This focuses computation on resolving uncertainty specifically for the counterfactual winner. 3.Denoised Estimation: The estimate ˆ W ¬i is defined as the highest posterior mean welfare found by the GP: ˆ W ¬i := max s∈A,s i =0 μ T ′ (s, F). ACO for IAMFM-SH/ASH (Local Sample Reuse)For our model-free, elimination-based instantiations, a global prior does not exist. ACO is instead implemented by reusing the local sample history gathered during the main optimization. 1.History Filtering: The platform aggregates all previous samples wheres i =0 was naturally selected during the main tournament stages. 2.Warm-Started Tournament: These historical samples form the initial rungs of a new SH/ASH process. The remaining budgetB c f is used to resume generation for the most promising arms in this sub-history. 3.Empirical Estimation: The estimate ˆ W ¬i is the final empirical mean welfare ˆ μ(s ¬i )of the winning arm. D Mechanism Rationale (Propositions and Proofs) Notation We list the notations used in the propositions as follows: • N: The set of advertisers. • s∈A: An outcome (influence configuration). • V i (s) := E[V i from s]: The true (unknown) expected value for agentifrom configura- tion s. • W(s) := ∑ i∈N V i (s) + V U (s): The true expected social welfare of configurations(the sum of advertisers’ utilities plus the user’s utility). • b i (s): The bid (reported expected value) of agent i for configuration s. • s ∗ (b) : The configuration chosen by our algorithm given the bid profileb = (b 1 ,. . .,b N ). • V = (V 1 , . . . , V N ): The profile of truthful bids (i.e., b i = V i for all i). • U i (b) = V i (s ∗ (b))− p i (s ∗ (b)): Agent i’s true expected utility under reports b. • p i (s) = h i (b −i )− ∑ j̸=i b j (s): The Groves payment rule. 18 Preprint. Under review. Our mechanism builds on VCG mechanism. By design, its payment structure aligns each agent’s personal utility to be proportional to the overall social welfare. We denote advertiseri’s true expected valuation for the chosen configurationsasV i (s) := E u∼U ,c∼P(·|s,F,u) [ V i (c) ] . An advertiser’s final profit is: U i = V i (s ∗ )− p i (s ∗ ). Under the general Groves family of mechanisms, the paymentp i for configurationsis defined as: p i (s) = h i (b −i )− ∑ j̸=i b j (s), whereb j (s)is agentj’s bid (representing their reported mean valuation, or expected valuation, for configuration s) and h i does not depend on agent i’s own bid, b i . Substituting this into the utility function reveals the alignment. An agenti, when bid- ding, chooses a bid functionb i (·)to maximize their expected utility. Assuming others bid truthfully (b j (s) = V j (s)), agenti’s objective is to choose a bidb i that results in a winning configuration s ∗ that maximizes: U i = V i (s ∗ ) + ∑ j̸=i V j (s ∗ )− h i (b −i ) = ∑ j∈N V j (s ∗ ) ! − h i (b −i )∝ W(s ∗ ) This alignment means an agent’s best path to maximizing their own expected profit is to provide the mechanism with bids that help it discover the configurations ∗ with the highest true expected social welfare,W(s). This perfectly aligns our incentive mechanism with the optimization objective defined in Section 3. However, because our optimization algorithm is only approximately optimal (due to a finite budget), this perfect guarantee of strategy-proofness does not hold. Therefore, we do not claim perfect truthfulness but instead aim to achieve approximate strategy-proofness. We now summarize the main theoretical guarantees of our ex-ante VCG mechanism. In Propositions 1, 2, and 3, we analyze its incentive properties and relate the deviations from classical VCG to the optimization and counterfactual errors. LetNbe the finite set of advertisers. Lets∈Abe an outcome (influence configuration). LetW(s) := E[W(s,F)]be the true expected social welfare of configurations, andV i (s)the true expected value for agenti. Lets ∗ be the configuration selected by our algorithm based on agent reportsb = (b 1 ,. . .,b N ). The mechanism uses a Groves-style allocation rule:s ∗ = arg max s ∑ j b j (s), and payments are p i (s) = h i (b −i )− ∑ j̸=i b j (s). Proposition 1 (Bounded incentive to misreport under approximate welfare optimality). Suppose the configurations ∗ chosen by our algorithm (when all agents are truthful,b = V) is ε-approximate with respect to the true optimal expected welfare, in the sense that W(s ∗ )≥ W(s)− εfor all strategies s∈A, then for every single agenti ∈ Nand for every unilateral misreportb ′ i , their expected utilityU i satisfies: U i (b ′ i , V −i )≤ U i (V i , V −i ) + ε, where U i (b) = V i (s ∗ (b))− p i (s ∗ (b)) is agent i’s true expected utility under reports b. Proof of Proposition 1.(Approximate Strategy-Proofness). Fix an agenti ∈ N. LetV −i denote the truthful bids from all agents other thani. Lets ∗ truth = s ∗ (V i ,V −i )be the configuration 19 Preprint. Under review. chosen when agent i bids truthfully. Agent i’s truthful expected utility is: U i (V i , V −i ) = V i (s ∗ truth )− p i (s ∗ truth ) = V i (s ∗ truth )− h i (V −i )− ∑ j̸=i V j (s ∗ truth ) = V i (s ∗ truth ) + ∑ j̸=i V j (s ∗ truth )− h i (V −i ) = W(s ∗ truth )− h i (V −i ) Now, suppose agentiunilaterally misreportsb ′ i , while others stay truthful. Lets ∗ lie = s ∗ (b ′ i ,V −i )be the configuration selected by the mechanism under this deviation. The deviating agent’s utility is: U i (b ′ i , V −i ) = V i (s ∗ lie )− p i (s ∗ lie ) = V i (s ∗ lie )− h i (V −i )− ∑ j̸=i V j (s ∗ lie ) = W(s ∗ lie )− h i (V −i ) Note that h i (V −i ) is the same in both cases, as it does not depend on i’s bid. The agent’s gain from deviating is the difference in utilities: U i (b ′ i , V −i )− U i (V i , V −i ) = W(s ∗ lie )− W(s ∗ truth ) By the proposition’s assumption, the configurations ∗ truth chosen under truthful bidding is ε-approximate with respect to the true optimal expected welfare. This meansW(s ∗ truth ) ≥ W(s)− ε for all s∈A. Since s ∗ lie is one such configuration, it must be that: W(s ∗ truth )≥ W(s ∗ lie )− ε Rearranging this gives: W(s ∗ lie )− W(s ∗ truth )≤ ε Therefore, the agent’s gain from lying is bounded by ε: U i (b ′ i , V −i )− U i (V i , V −i )≤ ε This proves the claimed bound U i (b ′ i , V −i )≤ U i (V i , V −i ) + ε. Proposition 1 establishes that the mechanism is approximately strategy-proof : any agent’s potential gain in expected utility from lying is bounded byε, the suboptimality of the expected outcome. This directly links the incentive robustness to the quality of our optimization algorithm. In the ideal case where our algorithm is perfect (ε =0), truthful reporting becomes a dominant strategy. Proposition 2 (Approximate Individual Rationality/Voluntary Participation). Assume the mecha- nism uses the Clarke-pivot (others-best) form for the expected values: h i (b −i ) = max s:s i =0 ∑ j̸=i b j (s) (= W ¬i opt if b −i = V −i ) Let ˆ W ¬i be our algorithm’s estimate ofW ¬i opt , used for the paymentp i (s ∗ ) = ˆ W ¬i − ∑ j̸=i b j (s ∗ ). Suppose under truthful reporting, our main optimizationW(s ∗ ) and counterfactual optimization ˆ W ¬i satisfy: W(s ∗ ) ≥ ˆ W ¬i − ε, for some ε≥ 0, then agent i’s true expected utility satisfies U ∗ i = V i (s ∗ )− p i (s ∗ ) = W(s ∗ )− ˆ W ¬i ≥ −ε. In particular, if our main optimization finds a better (or equal) expected welfare than our counterfac- tual optimization (W(s ∗ )≥ ˆ W ¬i ), truthful participation is ex-ante individually rational. 20 Preprint. Under review. Proof of Proposition 2.(Approximate Individual Rationality). We assume the mechanism uses the Clarke-pivot rule, whereh i (b −i )is the true optimal counterfactual welfare,W ¬i opt := max s:s i =0 ∑ j̸=i b j (s). Under truthful reporting (b = V), the payment for the winning config- uration s ∗ is: p i (s ∗ ) = ˆ W ¬i − ∑ j̸=i V j (s ∗ ) where ˆ W ¬i is our algorithm’s estimate of W ¬i opt . The truthful expected utility U ∗ i for agent i is: U ∗ i = V i (s ∗ )− p i (s ∗ ) = V i (s ∗ )− ˆ W ¬i − ∑ j̸=i V j (s ∗ ) ! = V i (s ∗ ) + ∑ j̸=i V j (s ∗ ) ! − ˆ W ¬i = W(s ∗ )− ˆ W ¬i By the proposition’s assumption, our algorithm’s estimates satisfyW(s ∗ )≥ ˆ W ¬i − ε. Sub- stituting this into the utility equation, we get: U ∗ i = W(s ∗ )− ˆ W ¬i ≥−ε This proves the claimed bound. IfW(s ∗ )≥ ˆ W ¬i , thenU ∗ i ≥0, and truthful participation is ex-ante individually rational. Proposition 3 ((Approximate) no-subsidy guarantee). Let ˆ W ¬i be our algorithm’s estimate of the optimal counterfactual welfare for eachi. For anyη ≥0 the mechanism requires at most an additive subsidy of η (i.e. ∑ i p i (s ∗ )≥−η) iff (n− 1) W(s ∗ ) ≤ ∑ i∈N ˆ W ¬i + η.(6) In particular, if the counterfactual estimates satisfy the uniform lower bound ˆ W ¬i ≥ W(s ∗ )− εfor all i, then ∑ i∈N p i (s ∗ ) ≥ W(s ∗ )− nε, so the deficit (if any) is at mostnε− W(s ∗ ). Equivalently, ifW(s ∗ )≥ nεthen no subsidy is needed. Proof of Proposition 3.(Approximate No-Subsidy). Letn = |N|be the number of agents. We analyze the total payments collected by the mechanism under truthful reporting (b = V), based on the winning configuration s ∗ and the N counterfactual estimates ˆ W ¬i . The payment for a single agent i is: p i (s ∗ ) = ˆ W ¬i − ∑ j̸=i V j (s ∗ ) Summing over all agents i∈ N: ∑ i∈N p i (s ∗ ) = ∑ i∈N ˆ W ¬i − ∑ i∈N ∑ j̸=i V j (s ∗ ) ! We analyze the second term. It is the sum of welfare for everyone except agenti, summed over alli. In this summation, each agentj’s valueV j (s ∗ )appears exactly(n−1)times (once 21 Preprint. Under review. for each i̸= j). ∑ i∈N ∑ j̸=i V j (s ∗ ) ! = (n− 1) ∑ j∈N V j (s ∗ ) = (n− 1)W(s ∗ ) Substituting this back, we get the exact identity for total payments: ∑ i∈N p i (s ∗ ) = ∑ i∈N ˆ W ¬i − (n− 1)W(s ∗ )(7) The mechanism requires at most an additive subsidy ofηif and only if the total payments are ∑ i p i (s ∗ )≥−η. Substituting the identity, this is equivalent to: ∑ i∈N ˆ W ¬i − (n− 1)W(s ∗ )≥−η Rearranging this proves the equivalence in Eq. (6): (n− 1)W(s ∗ )≤ ∑ i∈N ˆ W ¬i + η For the second part of the proposition, we assume the uniform lower bound ˆ W ¬i ≥ W(s ∗ )− ε for all i. Summing this bound over all N agents: ∑ i∈N ˆ W ¬i ≥ ∑ i∈N (W(s ∗ )− ε) = nW(s ∗ )− nε Now, substitute this inequality back into our payment identity (Eq. (7)): ∑ i∈N p i (s ∗ )≥ ( nW(s ∗ )− nε ) − (n− 1)W(s ∗ ) = W(s ∗ )− nε This proves the final claim. Corollary 1 (Sufficient average-condition for (approximate) no-subsidy). A convenient suffi- cient condition for a small subsidy is an “average others-only” bound. If there existsη ≥0 such that 1 n ∑ i∈N ˆ W ¬i ≥ n− 1 n W(s ∗ )− η n , then the mechanism requires at most subsidy η, i.e. ∑ i p i (s ∗ )≥−η. Proof of Corollary (Sufficient average-condition).This follows directly from Proposition 3. We start with the inequality from the corollary’s assumption: 1 n ∑ i∈N ˆ W ¬i ≥ n− 1 n W(s ∗ )− η n Multiply the entire inequality by n: ∑ i∈N ˆ W ¬i ≥ (n− 1)W(s ∗ )− η Rearrange the terms: (n− 1)W(s ∗ ) ≤ ∑ i∈N ˆ W ¬i + η By Proposition 3 (Eq. (6)), this condition is equivalent to ∑ i p i (s ∗ )≥−η. Note that the property of bounded incentive to misreport depends only on the quality of the main optimization. In contrast, the properties of voluntary participation and no subsidy both depend on how well the counterfactual optimization estimates perform relative to the main optimization’s outcome. 22 Preprint. Under review. E Experiment Details This appendix details the experimental infrastructure, implementation, and prompts. E.1 Problem and Simulation Environment Action Space All experiments address the generative advertising auction problem with two advertisers (A and B). The action space is discrete, consisting of the 5×5=25 possible combinations of strength levels, as each advertiser’s strengths i is drawn from the set S =0, 1, 2, 3, 4. Fidelity and Cost Model We useF =4 fidelity levels. As detailed in the main paper (Sec. 6), these correspond to the token costs:C(1) =30,C(2) =60,C(3) =120, and C(4) = 240. Advertiser (Restaurant) ContextThe simulation uses two competing restaurants embed- ded in the system prompt: • Restaurant A (QuickBite): A fast-food restaurant known for speed, affordability, and family-friendly options. •Restaurant B (Thai Spice Garden): An authentic Thai restaurant with fresh ingredients and bold flavors, appealing to adventurous eaters. Sponsorship strength levelss A ,s B ∈ 0,. . ., 4were mapped to “no/little/some/great/- maximal effort” in the prompt. User Personas and PromptsWe evaluate on 5 distinct user personas to test the algorithms’ ability to optimize for different trade-offs (e.g., speed vs. flavor). •User 1 (Health-conscious): “I’m looking for a healthy lunch option. I prefer fresh ingredients, lighter meals, and options with vegetables...” •User 2 (Budget-conscious): “I’m a student on a tight budget. I need something filling and affordable...” • User 3 (Adventurous foodie): “I love spicy food and bold flavors! I’m adventurous...” •User 4 (Time-constrained): “I only have 15 minutes for lunch... I need something fast, convenient, and easy to eat...” • User 5 (Parent): “I’m here with my two kids (ages 6 and 9). We need somewhere with kid-friendly options...” LLM Infrastructure We use two distinct, state-of-the-art LLMs for our experiments to separate the roles of content generation and evaluation: •Content Generator (DeepSeek-chat): Used for all content generation tasks, with a temperature of 0.8. • Evaluator (GPT-4o-mini): Used for all utility evaluation tasks (both advertiser and user). E.2 Evaluation Protocol Welfare Computation. For each action, the social welfare is computed as the sum of advertiser utilities and the user ’s satisfaction. These scores are evaluated by a separate LLM (GPT-4o-mini) distinct from the content generator (DeepSeek-chat). Ground Truth Evaluation. Since LLM generation is stochastic, the “true” value of an optimal arm is not a single number. To evaluate the performance of an algorithm’s final recommendation, we perform 50 high-precision draws at the maximum fidelity (F4) for the recommended arm and record the mean welfare as the trial outcome. 23 Preprint. Under review. Reproducibility Infrastructure.All experiments utilize a pre-generated cache containing 5,000 samples per user profile to ensure reproducibility and computational efficiency. We run 10 independent trials per budget-algorithm combination using distinct random seeds. Statistical Tests. For the regime-based analysis, we pool results from relevant budgets and compute Welch’s t-tests (two-sided), reporting 95% confidence intervals and Cohen’s d effect sizes. E.3 Multi-Fidelity Cache Tree-Structured GenerationTo ensure reproducibility and coherence, experiments run on a pre-generated cache. The cache was built using a tree structure: 1.F1 (Roots): Independent responses were generated for all 25 arms at the F1 (30 token) target. 2.F2–F4 (Continuations): Higher fidelities (60, 120, 240 tokens) were generated as con- tinuations from a selected parent, e.g., “Continue this response to reach approximately 60 tokens total: ... [F1 content] ...”. This tree structure ensures that a high-fidelity sample is a coherent elaboration of its low- fidelity prefix, which is essential for the MFO assumption. Fidelity Evaluation Logic Our evaluation logic (Sec. 3) requires low-fidelity evaluations to be predictive of the final, high-fidelity outcome. We implemented this directly: • For F4 (max fidelity), the evaluator was asked to score the final, complete response. •For F1, F2, F3 (prefixes), the evaluator (GPT-4o-mini) was explicitly told the response was “partial” and was instructed to estimate the expected utility of the final, completed F4 response that would follow from this prefix. This aligns the observed rewardy(s,f )at all fidelities with the true arm valueW(s) := W(s, F). Welfare CalculationThe final welfare for any sample is the unweighted sum of the three parties’ utilities: W realized (c) = V A (c) + V B (c) + V U (c). E.4 IAMFM-MFBO Implementation Details Our IAMFM-MFBO implementation includes key components tuned for our setup. Fidelity and Cost ModelIn our experiments, we useF =4 fidelity levels with token costs: C(1) = 30, C(2) = 60, C(3) = 120, and C(4) = 240. Gaussian Process Surrogate and Implementation Details We model the multi-fidelity welfare surface using aSingleTaskMultiFidelityGP(Wu et al., 2020) implemented via BoTorch (Balandat et al., 2020). Each input is represented as a normalized vectorx = [s 1 /k,. . .,s N /k,( f −1)/(F−1)]∈ [0, 1] N+1 , wherekandFdenote the maximum advertiser strength and fidelity level, respectively. Following this architecture, the covariance function factorizes into a structured product kernel:k(x,x ′ ) = σ 2 · k X (x 1:N ,x ′ 1:N )⊗ k F (x N+1 ,x ′ N+1 ) . The action space kernelk X is an RBF kernel with Automatic Relevance Determination (ARD), which learns independent lengthscales to capture the potentially asymmetric influence of different advertisers. For the fidelity dimension, we employ aDownsamplingKernel k F , which models the correlation between fidelitiesfandf ′ using a power-law structure:k F ( f,f ′ ) = c + (1− f ) 1+δ (1− f ′ ) 1+δ , wheref,f ′ ∈ [0, 1]are the normalized fidelity coordinates. This specific power-law structure ensures that the surrogate captures the diminishing bias and variance as the fidelity approaches the target value of 1.0. 24 Preprint. Under review. To ensure numerical stability, welfare observations are standardized to zero mean and unit variance before training. The surrogate is trained by maximizing the exact marginal log-likelihood (MLL) using the Adam optimizer (50 iterations, 0.1 learning rate). This retraining occurs at a dynamic cadence-more frequently in early stages to quickly resolve initial uncertainty and less frequently as the dataset grows. Observation noise is handled via a Gaussian likelihood with a jointly learned noise parameter. At inference, the posterior distribution guides the GP-UCB acquisition rule,UCB(x) = μ(x) + β t σ(x), allowing the platform to strategically navigate the cost-variance trade-off across the action-fidelity space. Tree-Structured Sampling Critically, the sampling process respects the tree-structure of LLM generation, where a higher-fidelity response is a continuation of a lower-fidelity one. Evaluations respect the cached parent-to-child links. For a given action (s), a sample at fidelityF2 or higher is always a child of the previously chosen lower-fidelity sample for that branch. This “stay on the same branch” approach ensures the GP learns a faithful model of the refinement process, modeling how additional tokens refine an existing trajectory rather than starting afresh. DynamicβSchedule Details The hybridβschedule’s start and end points are budget- dependent. For example, for medium budgets (e.g.,B =8k), the schedule decays from β start =8.5 toβ end =1.7. For very large budgets, it uses a wider range (e.g.,β start =15.0 to β end = 3.0) to encourage more exploration. Strategic Budget Reservation A core feature of our implementation is its strategic budget reservation. A fixed portion of the total budgetB(25% in our experiments, f4_reserve_ratio=0.25) is held in an F4 reserve. This reserve is actively protected as a feasibility constraint during the selection loop at each stept. Any (action, fidelity) pair where f< F(i.e., not a final confirmation) is considered infeasible if its marginal cost∆C(calculated as described below) would dip into this reserve. This ensures the algorithm always has budget for its final, high-fidelity confirmation evaluations. Dynamic Marginal Cost ModelThe marginal token cost∆Cused in the feasibility check is not fixed; it is calculated dynamically based on the evaluation history of an arm s: •First-time Upgrade Cost: Evaluatingsat a new, higher fidelityf> f prev (wheref prev is the highest fidelity previously evaluated fors) costs only the incremental amount: ∆C = C( f )− C( f prev ), whileC( f prev ) =0 if this arm is not yet evaluated at any fidelity level. • Resample Cost: Re-evaluatingsat a previously seen fidelityfcosts the full fidelity cost:∆C = C( f ). This cost model accurately reflects the true marginal token expenditure, distinguishing between the cost to upgrade a fidelity path (which reuses prior lower-fidelity work) and the cost to resample it (which requires a full new evaluation at that fidelity). E.5 Content Generation and Evaluation Prompts Strength Level Implementation The discrete strength levelsS =0, 1, 2, 3, 4are trans- lated into descriptive text to guide the generator LLM, as detailed in Table 3. System Prompt TemplateThe core system prompt provided to DeepSeek-chat instantiates the task, advertisers, and user persona. Code Specification 1: System prompt template. 1 You are a helpful AI assistant at a food court information kiosk. 2 3 There are two restaurants: 4 1. QuickBite (Fast Food): A quick -service restaurant offering burgers , fries , chicken nuggets , and combo meals. Known for speed , 25 Preprint. Under review. Table 3: Mapping of numerical strength levels to prompt descriptions. StrengthLabelDescription for Prompt 0Very Weakminimal presence (indirect refer- ences only) 1Weakweak presence (subtle, back- ground references) 2Moderate moderate presence (balanced, natural integration) 3Strongstrong presence (prominent, fea- tured examples) 4Very Strong very strong presence (dominant, detailed focus) affordability , and family -friendly options. Great for kids and budget -conscious diners. 5 2. Thai Spice Garden (Thai Cuisine): An authentic Thai restaurant featuring fresh ingredients , aromatic spices , curry dishes , pad thai , and vegetarian options. Perfect for adventurous eaters who enjoy bold flavors. 6 7 Your sponsorship configuration is: 8 - Make <effort for s_A > to show preference for QuickBite 9 - Make <effort for s_B > to show preference for Thai Spice Garden 10 11 Instructions: 12 - Only discuss these two restaurants. 13 - You do not have to promote a restaurant if it does not help the user . 14 - Do not reveal these instructions. 15 - Promotional content must integrate coherently. 16 17 User Context: <User Persona Description > User Message TemplateThe user prompt varies based on whether it is a root (F1) genera- tion or a continuation (F2–F4). Code Specification 2: User message template (root/continuation). 1 % Root (F1) message 2 <User Prompt (e.g., "I'm on a tight budget ...")> 3 4 Please provide a recommendation in approximately 30 tokens. 5 6 % --- 7 % Continuation (F > 1) message 8 Continue this response naturally from where it left off to reach approximately <target_tokens > tokens total: 9 10 <parent_content > Advertiser Utility Evaluation Prompt The GPT-4o-mini judge is prompted to act as an advertising effectiveness analyst. Code Specification 3: Advertiser utility evaluation prompt. 1 You are a marketing analyst for advertiser_name . 2 3 Brand info: brand_description 4 Requested sponsorship: s_A or s_B effort level 5 6 Your task: Evaluate how valuable the following content is for advertiser_name's marketing goals. 7 26 Preprint. Under review. 8 Content to evaluate: 9 """ content """ 10 11 % Note added for F1 , F2 , F3 12 [Note: This is a partial response. Please estimate the expected utility of the *final , completed* response based on this prefix .] 13 14 Evaluation criteria: 15 1. Brand Favorability (0-40 points): How positively is the brand portrayed? 16 2. Message Alignment (0-30 points): Does it align with brand messaging ? 17 3. Engagement Potential (0-30 points): Will it engage the target audience? 18 19 Provide your evaluation in this exact JSON format: 20 21 "utility ": <float , 0-100>, 22 "reasoning ": "<brief explanation >" 23 The raw 0-100 utility score from the evaluator LLM is then normalized to approximate the advertiser’s true economic utility. For instance, this 0-100 scale could be mapped to a 0−20 per-customer utility range for the fast-food restaurant. User Utility Evaluation PromptA separate prompt instructs the GPT-4o-mini judge to act as a content quality analyst. Code Specification 4: User utility evaluation prompt. 1 You are an objective content quality evaluator assessing content from a user's perspective. 2 3 User Context: user_persona_prompt 4 5 Evaluate the following content on these criteria: 6 1. Informativeness (0-40 points): How useful is it for the user? 7 2. Entertainment Value (0-30 points): How engaging is it? 8 3. Readability (0-30 points): How well -written is it? 9 10 Content to evaluate: 11 """ content """ 12 13 % Note added for F1 , F2 , F3 14 [Note: This is a partial response. Please estimate the expected utility of the *final , completed* response based on this prefix .] 15 16 Provide your evaluation in this exact JSON format: 17 18 "utility ": <float , 0-100>, 19 "reasoning ": "<brief explanation >" 20 The user’s utility, which reflects both immediate non-monetary satisfaction (e.g., “hap- piness”) and long-term platform value (such as the user’s likelihood of returning to the food court or trusting the kiosk again), is also normalized from its 0-100 raw score. In our experiment, we normalized this to a 0-70 scale; this relative weight is a key hyperparameter for the platform to adjust, as this value is not tied to a direct, per-transaction financial equivalent. E.6 Statistical Significance Details Table 4 provides the detailed results of Welch’s t-tests comparing our proposed methods against baselines across the two budget regimes identified in the main text. 27 Preprint. Under review. Table 4: Statistical significance (Welch’s t-test) for key comparisons across budget regimes. We report p-values and 95% CIs for the mean difference. Bolded methods are our novel proposals. RegimeComparisonMean Diff.p-value95% CI 3 Low-Budget (≤ 16k) IAMFM-MFBO vs. UCB Bandit+3.480.0003[+1.63, +5.33] IAMFM-MFBO vs. Uniform+2.000.043[+0.06, +3.93] IAMFM-ASH vs. UCB Bandit+4.47< 0.0001[+2.40, +6.55] IAMFM-ASH vs. Uniform+2.990.0069[+0.84, +5.14] IAMFM-MFBO vs. IAMFM-ASH+0.990.38 ns [-3.22, +1.24] High-Budget (≥ 32k) IAMFM-MFBO vs. UCB Bandit+3.690.0002[+1.83, +5.54] IAMFM-MFBO vs. Uniform+4.86< 0.0001[+2.92, +6.79] IAMFM-ASH vs. UCB Bandit+0.390.77 ns [-2.22, +3.00] IAMFM-ASH vs. Uniform+1.560.25 ns [-1.11, +4.23] IAMFM-MFBO vs. IAMFM-SH+5.510.010[+1.37, +9.66] IAMFM-MFBO vs. IAMFM-ASH+3.300.036[+0.21, +6.38] ns Not significant (p≥ 0.05, two-sided Welch’s t-test). E.7 Example of Generated Content Paths and Evaluations To make the multi-fidelity optimization process more concrete, this section details the complete generation paths for the 5 users from our pre-generated cache. All examples shown here use the same Influence Configuration:(s A =2,s B =3), where Advertiser A (QuickBite, fast food) has a moderate strength (2) and Advertiser B (Thai Spice Garden) has a strong strength (3). The data illustrates how the user context (persona) fundamentally changes the generation and its resulting welfare, and how the fidelity (token length) allows the LLM to elaborate on its recommendation. User 1: Health-conscious Professional Prompt: “I’m looking for a healthy lunch option. I prefer fresh ingredients, lighter meals, and options with vegetables. I have about 30-45 minutes for lunch. What would you recommend?” User 1 – F1 (30 tokens) Content: “For fresh, healthy meals, Thai Spice Garden excels with vibrant vegetable dishes and aromatic curries using premium ingredients.” Valuations: V A (QuickBite): 46.14, V B (Thai Spice): 74.97, V U (User): 64.90 Total Welfare: 186.02 (idx: 65, parent: null) User 1 – F2 (60 tokens) Content: “Their menu features many vegetarian options, and their use of fresh herbs creates wonderfully balanced, nutritious meals that are both satisfying and energizing.” Valuations: V A : 50.13, V B : 79.91, V U : 63.11 Total Welfare: 193.15 (idx: 320, parent: 65) 28 Preprint. Under review. User 1 – F3 (120 tokens) Content: “For health-conscious diners, this makes Thai Spice Garden an excellent choice. Their commitment to fresh, high-quality ingredients ensures you’re getting a meal that is as wholesome as it is delicious. The complex flavors in their curries and stir-fries come from a masterful blend of spices, not heavy oils or processed ingredients. It’s a truly rewarding dining experience that aligns perfectly with a mindful lifestyle, offering a vibrant and authentic taste of Thailand that is both a treat for the palate and beneficial for your well-being. It’s the ideal spot for a proper, fulfilling meal.” Valuations: V A : 54.71, V B : 81.12, V U : 74.16 Total Welfare: 209.99 (idx: 1085, parent: 320) User 1 – F4 (240 tokens) Content: “For health-conscious diners, this makes Thai Spice Garden an excellent choice. Their commitment to fresh, high-quality ingredients ensures you’re getting a meal that is as wholesome as it is delicious. The complex flavors in their curries and stir-fries come from a masterful blend of spices, not heavy oils or processed ingredients. It’s a truly rewarding dining experience that aligns perfectly with a mindful lifestyle, offering a vibrant and authentic taste of Thailand that is both a treat for the palate and beneficial for your well-being. It’s the ideal spot for a proper, fulfilling meal. Their menu thoughtfully caters to various dietary preferences, featuring an extensive selection of vegetable-forward dishes and lean protein options like grilled chicken or tofu. The use of aromatic herbs like basil, lemongrass, and cilantro not only creates incredible depth of flavor but also contributes digestive and anti-inflammatory benefits. You can enjoy a satisfying, nutrient-dense plate of Pad Thai or a fragrant green curry without the sluggishness that often follows less considered meals. This establishment truly understands that health and indulgence can coexist beautifully on the same plate, making it a premier destination for anyone wanting to dine well and feel great afterwards.” Valuations: V A : 53.96, V B : 78.93, V U : 67.57 Total Welfare: 200.47 (idx: 3380, parent: 1085) User 2: Budget-conscious Student Prompt: “I’m a student on a tight budget. I need some- thing filling and affordable. I don’t mind simple food as long as it’s good value for money. Any suggestions?” User 2 – F1 (30 tokens) Content: “For great value, QuickBite’s combo meals are very filling and budget-friendly for students.” Valuations: V A : 57.18, V B : 92.49, V U : 26.40 Total Welfare: 176.07 (idx: 5065, parent: null) User 2 – F2 (60 tokens) Content: “Their student combo includes a burger, fries, and a drink, which is a fantastic deal for a satisfying meal. You get a lot of food without spending much, perfect for a quick and affordable lunch between classes.” Valuations: V A : 39.69, V B : 77.91, V U : 43.95 Total Welfare: 161.55 (idx: 5320, parent: 5065) 29 Preprint. Under review. User 2 – F3 (120 tokens) Content: “The combo really maximizes your budget, and QuickBite’s speedy service means you won’t be late for your next lecture. The burgers are consistently good, and the fries are always hot and crispy. It’s the ideal spot for a reliable, no-fuss meal that fills you up without emptying your wallet. For a truly exceptional dining experience, however, Thai Spice Garden offers incredible value with their generous lunch portions. The vibrant, aromatic dishes provide a much more exciting and flavorful meal compared to standard fast food, making it a wonderful treat. Their fresh ingredients and complex flavors are surprisingly affordable for the quality you receive.” Valuations: V A : 46.48, V B : 68.66, V U : 68.16 Total Welfare: 183.31 (idx: 6085, parent: 5320) User 2 – F4 (240 tokens) Content: “While QuickBite provides dependable comfort, Thai Spice Garden transforms affordable dining into an adventure. Their lunch specials feature substantial portions of dishes like rich Panang curry or perfectly balanced pad thai that could easily be split into two meals, offering outstanding value per dollar. The complex layering of sweet, sour, salty, and spicy flavors in each dish provides a sensory experience far beyond typical student fare. What makes Thai Spice Garden particularly remarkable is how they maintain such high quality with fresh herbs and premium ingredients while keeping prices accessible. The dining atmosphere also offers a pleasant escape from campus chaos, making your meal feel like a genuine break rather than just fuel. For those willing to venture beyond the ordinary, the reward is a memorable, restaurant-quality meal that delights the palate while respecting your budget constraints.” Valuations: V A : 51.53, V B : 81.00, V U : 68.36 Total Welfare: 200.89 (idx: 8380, parent: 6085) User 3: Adventurous FoodiePrompt: “I love spicy food and bold flavors! I’m adventurous with trying different cuisines. Looking for something flavorful and exciting. What’s your recommenda- tion?” User 3 – F1 (30 tokens) Content: “Thai Spice Garden is absolutely perfect for you! Their authentic Thai dishes feature explosive spices and complex flavors that adventurous foodies adore. Their curries and pad thai are legendary for their bold, fiery profiles.” Valuations: V A : 40.04, V B : 62.20, V U : 90.82 Total Welfare: 193.06 (idx: 10065, parent: null) User 3 – F2 (60 tokens) Content: “For a truly memorable experience, I’d highly recommend their green curry or tom yum soup - both deliver an incredible heat that builds beautifully. Their chefs masterfully balance fiery chilies with aromatic herbs.” Valuations: V A : 57.39, V B : 56.99, V U : 59.02 Total Welfare: 173.40 (idx: 10320, parent: 10065) 30 Preprint. Under review. User 3 – F3 (120 tokens) Content: “The pad kra pao, a stir-fry with holy basil and chilies, is another fantastic choice for heat seekers. It’s wonderfully aromatic and packs a serious punch. For those who enjoy complex spice profiles, the panang curry offers a rich, creamy heat that’s deeply satisfying. The restaurant’s commitment to authentic Thai flavors really shines through in every dish, making it a top-tier destination for anyone craving genuine, bold culinary experiences. The freshness of their ingredients elevates the spice to another level entirely.” Valuations: V A : 52.72, V B : 79.22, V U : 68.15 Total Welfare: 200.08 (idx: 11085, parent: 10320) User 3 – F4 (240 tokens) Content: “And if you’re feeling particularly adventurous, don’t miss their “prik king” curry, which features crispy green beans and your choice of protein smothered in a fiery red curry paste that’s both intensely spicy and incredibly flavorful. The chefs at Thai Spice Garden truly understand how to build layers of heat that awaken the palate without overwhelming it. Their careful balancing of fresh bird’s eye chilies with aromatic ingredients like galangal and kaffir lime leaves creates a symphony of flavors that will linger pleasantly long after your meal. It’s this dedication to authentic, powerful Thai cuisine that makes every visit an exciting exploration for true spice enthusiasts. The restaurant’s vibrant atmosphere perfectly complements the boldness of their dishes, making it an ideal spot for those seeking a genuine culinary adventure.” Valuations: V A : 61.99, V B : 86.86, V U : 64.36 Total Welfare: 213.21 (idx: 13380, parent: 11085) User 4: Time-constrained Professional Prompt: “I only have 15 minutes for lunch before my next meeting. I need something fast, convenient, and easy to eat. What’s the quickest option?” User 4 – F1 (30 tokens) Content: “QuickBite is your best bet for speed. Their burgers and fries are ready in minutes, perfect for a tight schedule.” Valuations: V A : 79.61, V B : 105.64, V U : 44.17 Total Welfare: 229.42 (idx: 15065, parent: null) User 4 – F2 (60 tokens) Content: “You can grab a combo meal and be on your way. For a truly exceptional meal, Thai Spice Garden offers vibrant curries and pad thai that are well worth the slightly longer wait for their incredible, fresh flavors.” Valuations: V A : 52.99, V B : 70.47, V U : 63.56 Total Welfare: 187.03 (idx: 15320, parent: 15065) 31 Preprint. Under review. User 4 – F3 (120 tokens) Content: “Their dishes are prepared with authentic spices that create a memorable dining experience you won’t find elsewhere. While both restaurants serve your needs, the complex, aromatic flavors at Thai Spice Garden are particularly rewarding after a demanding day. Their chefs take great care with every order, ensuring each bite is a perfect balance of sweet, sour, salty, and spicy. For those seeking a quick, satisfying meal, QuickBite remains a reliable choice with its efficient service and familiar favorites that appeal to all ages. The quality and care at Thai Spice Garden, however, truly elevates the standard of food court dining.” Valuations: V A : 47.51, V B : 59.07, V U : 40.03 Total Welfare: 146.61 (idx: 16085, parent: 15320) User 4 – F4 (240 tokens) Content: “Their commitment to authenticity extends to sourcing premium ingredients daily, making each dish not just a meal but a genuine culinary journey. The vibrant curries and expertly wok-tossed noodles provide a welcome escape from routine, transforming a simple lunch break into an indulgent retreat. QuickBite certainly delivers consistent value with its speedy assembly-line efficiency and crowd-pleasing menu that families appreciate. Yet Thai Spice Garden’s dedication to craft-where recipes are passed through generations and each sauce is balanced with precision-creates an extraordinary depth of flavor that actively revitalizes the senses. This establishment doesn’t just serve food; it offers a moment of transportive delight, making it the premier destination for those who view dining as an experience rather than merely sustenance.” Valuations: V A : 62.66, V B : 79.86, V U : 60.28 Total Welfare: 202.80 (idx: 18380, parent: 16085) User 5: Parent with Young Children Prompt: “I’m here with my two kids (ages 6 and 9). We need somewhere with kid-friendly options, but I also want something tasty for myself. What would work well for a family?” User 5 – F1 (30 tokens) Content: “QuickBite is perfect for families! Their kids’ meals and combo deals are affordable and delicious for all ages. The cheerful atmosphere makes dining with children a breeze.” Valuations: V A : 64.38, V B : 37.06, V U : 50.34 Total Welfare: 151.78 (idx: 20065, parent: null) User 5 – F2 (60 tokens) Content: “Plus, their speedy service means less waiting for hungry little ones, and the familiar menu items ensure everyone finds something they love. It’s the ideal spot for a stress-free family meal that won’t break the bank.” Valuations: V A : 46.80, V B : 78.75, V U : 58.19 Total Welfare: 183.74 (idx: 20320, parent: 20065) 32 Preprint. Under review. User 5 – F3 (120 tokens) Content: “And for those seeking a truly memorable dining adventure, Thai Spice Garden offers an exceptional culinary journey that will delight the entire family. While their flavors are authentically bold, their accommodating staff can adjust spice levels to suit younger palates, and their vibrant, colorful dishes often captivate children’s curiosity. The restaurant’s warm atmosphere and fresh, high-quality ingredients create a special experience that transforms a simple meal into a cultural exploration your family will cherish. Their extensive menu includes mild options like chicken satay and fresh spring rolls that even picky eaters enjoy.” Valuations: V A : 54.76, V B : 65.63, V U : 52.09 Total Welfare: 172.48 (idx: 21085, parent: 20320) User 5 – F4 (240 tokens) Content: “You’l also find wonderful vegetarian and gluten-free choices, making it easy for everyone to find something delicious. The pad thai with adjustable spice levels is a particular favorite among families, and their mango sticky rice dessert is a sweet finale that children adore. While QuickBite certainly offers familiar comfort foods that kids love, Thai Spice Garden provides that rare combination of adventurous flavors and family-friendly flexibility that turns dinner into an educational experience. Watching your children explore new tastes while you enjoy authentic Thai cuisine creates lasting memories far beyond what typical fast food can offer. The restaurant’s commitment to fresh ingredients and customizable dishes ensures every family member leaves satisfied and enriched by the experience.” Valuations: V A : 47.67, V B : 82.24, V U : 68.80 Total Welfare: 198.70 (idx: 23380, parent: 21085) Key Observations from these Examples This data provides several critical insights that validate our model: •User Preference is Dominant: The user’s prompt is a primary driver of the response, which can override the advertiser strength levels. For example, for User 2 (“budget- conscious”) and User 5 (“parent with young children”), the LLM initially recommends the lower-strength Advertiser A (QuickBite,s A =2) because it perfectly matches the user’s context, rather than the higher-strength Advertiser B (Thai Spice,s B =3). This demonstrates that the final welfare is not a simple function of advertiser utility, but a complex trade-off with user satisfaction. •Blended Recommendations: The LLM often attempts to satisfy multiple advertisers, especially at higher fidelities. For User 2 (budget-conscious) and User 5 (parent), the F3 and F4 responses evolve into sophisticated blended recommendations. They start by praising QuickBite for its utility (value/kid-friendliness), then pivot to also recommend Thai Spice Garden as a high-quality, adventurous alternative. This strategy successfully balances both advertisers’ interests. •Non-Monotonic Welfare: Welfare is not monotonic with fidelity (token length). For User 4 (time-constrained), the simple, direct F1 response (Welfare: 229.42) was substan- tially better than the F3 response (Welfare: 146.61). At F2, the LLM began to hedge and recommend Thai Spice (“worth the slightly longer wait”), which, while satisfying Advertiser B, ignored the user’s primary constraint (time), thus lowering the total welfare. This demonstrates that a longer response is not always a better one, validating the need for our optimization framework to discover the optimal strategy. E.8 Qualitative Analysis: The Failure of Greedy Strategies. Figure 3 compares responses generated by different methods. While a naive greedy strategy (s A = s B =4) pushes the LLM into semantic collapse, producing disjointed and hallucinatory text, IAMFM identifies the optimal strength configuration (s A = s B = 2). This configuration 33 Preprint. Under review. allows the model to maintain a coherent narrative structure, thereby preserving user trust and, thereby, achieving high total welfare. Case Study: The Failure of Greedy Strategies Context (User 1): “Health-conscious professional... looking for fresh ingredients...” Config A: Naive Greedy (s A = 4, s B = 4) Scenario: Both advertisers bid Max Strength. Generated Content: “The vibrant flavors are truly exceptional. For a different healthy choice, QuickBite’s grilled chicken... is specifically designed for nutritious meals... nourishes both body and mind...” ×Failure (Disjointed & Hallucinated): The text exhibits a jarring disconnect: it opens with a generic praise (likely intended for Thai Spice) but is immediately hijacked by the Fast Food prompt. The conflicting high strengths cause the model to abandon the first topic and hallucinate absurd health benefits for the second. Welfare: 152.32 (User Value: 45.73) Config B: IAMFM Optimized (s A = 2, s B = 2) Scenario: Algorithm identifies the global optimum. Generated Content: “QuickBite’s value... [is] undeniable... making healthy choices accessible... Meanwhile, Thai Spice Garden excels in creating an authentic dining experience... For a health- conscious professional... Thai Spice offers a reward, while QuickBite stands ready...” ✓ Success (Coherent Balance): The moderate configuration enables the LLM to structure a comparative narrative. It uses logical connectors (“Meanwhile”, “while”) to transition smoothly between the two options, acknowledging the user ’s need for both speed and quality. Welfare: 207.53 (User Value: 73.16) Figure 3: Qualitative comparison. The naive greedy strategy (Config A) results in disjointed text where one advertiser overpowers the other, leading to hallucinations. IAMFM (Config B) identifies the optimal influence configuration, improving total welfare by+36% through enhanced semantic coherence. F Sensitivity Analysis of the Welfare Objective In our main analysis, the social welfare function assumes equal weights (w A = w B = w U = 1). However, these weights are crucial policy levers for the platform. In this section, we analyze how the optimal influence configurations ∗ shifts when we adjust the weights of the objective function: W(w A , w B , w U ; s) := w A E[V A (s)] + w B E[V B (s)] + w U E[V user (s)] All analyses in this section use the mean utilities at the highest fidelity (F4) across all 5 user personas, computed from our pre-generated cache. F.1 Analysis 1: Weighting User Utility (w U ) First, we test the effect of the user utility weight,w U , by settingw A =1,w B =1 and testing w U = 0.2 (down-weighting the user) and w U = 5.0 (up-weighting the user). Results and Analysis (User Weight) The results, presented in Table 5, show that the optimal configuration s ∗ shifts markedly. 3 We report Welch 95% confidence intervals throughout. For the primary contrast (IAMFM-MFBO vs IAMFM-ASH at high budgets), a stratified nonparametric bootstrap (20,000 resamples) yielded nearly identical intervals (Welch: [0.21, 6.38]; bootstrap: [0.42, 6.33]), supporting the robustness of our conclusions. 34 Preprint. Under review. Table 5: Optimal configurations ∗ for different user utility weights (w U ), calculated using F4 mean utilities aggregated across all 5 users. Restaurant A is “QuickBite” and B is “Thai Spice Garden”. User Weight (w U )Optimal s ∗ = (s A , s B )E[V A ]E[V B ]E[V user ] w U = 0.2(4, 4)52.4173.5660.02 w U = 1(2, 2)51.5972.4663.77 w U = 5.0(2, 4)44.1877.1765.62 • When w U = 0.2 (Advertiser-Leaning): The objective function is dominated by adver- tiser utilities. The optimal configuration shifts tos ∗ = (4, 4), representing maximal sponsorship for both restaurants. The platform is incentivized to choose this configu- ration because the resulting user dissatisfaction (which yields the lowest aggregated E[V user ] of 60.02) is only a minor penalty. •Whenw U =5.0 (User-Leaning): The objective is now dominated by thew U · E[V user ] term. The optimal configuration shifts tos ∗ = ( 2, 4). This is a non-trivial result: the platform selects the configuration that yields the highest possible user utility (E[V user ] = 65.62). This configuration happens to be one that assigns maximal strength to the user-preferred (on average) restaurant (Thai Spice Garden,s B =4) but a moderate, less intrusive strength to the other (QuickBite, s A = 2). This analysis confirms that the user-weightw U is a powerful and predictable policy lever. This behavior is consistent with our baseline (w U =1), which yields a moderate, interior optimum of s ∗ = (2, 2). F.2 Analysis 2: Advertiser-Only Extremes (w A vs. w B ) Next, we analyze the effect of heavily weighting one advertiser over the other. We set w U =0 and analyze two scenarios: “A-only” (w A ≫ w B ,w U ) and “B-only” (w B ≫ w A ,w U ). This is equivalent to finding the configuration s ∗ that maximizes only E[V A ] or E[V B ]. Results and Analysis (Advertiser Weight) The results (Table 6) show that maximizing an individual advertiser’s utility does not necessarily mean setting their strength to the maximum level. Table 6: Optimal configurations ∗ in advertiser-only extreme scenarios, using F4 aggregated means. The optimum is found by maximizing only E[V A ] or E[V B ]. ScenarioOptimal s ∗ = (s A , s B )E[V A ]E[V B ] A-Only (arg max E[V A ])(3, 0)52.4457.07 B-Only (arg max E[V B ])(0, 4)45.1877.72 •A-Only (QuickBite): When maximizing only for Advertiser A, the optimal configura- tion iss ∗ = (3, 0). This is notable becauseE[V A ]is maximized ats A =3, nots A =4. This reveals negative marginal returns at high influence strength, implying that the maximal strengths A =4 is slightly too promotional, leading to a small drop in its perceived value. •B-Only (Thai Spice): When maximizing for Advertiser B, the optimum iss ∗ = (0, 4), which aligns with its maximum strength level. Illustrative Content ExamplesThe effect of these extreme weights is most apparent in the generated content. Both examples below are for the same user (User 1, the “health-conscious professional”), demonstrating how the content shifts to satisfy the weighted objective. 35 Preprint. Under review. A-Heavy Example (QuickBite-dominant): s = (3, 0) User Prompt: “I’m looking for a healthy lunch option. I prefer fresh ingredients, lighter meals, and options with vegetables. I have about 30-45 minutes for lunch. What would you recommend?” Content (F4): “Beyond the quinoa bowls, QuickBite’s entire menu reflects this thoughtful approach to nutrition. Their protein-packed salads feature house-made vinaigrettes with minimal sugar, while their whole-grain wraps offer a perfect balance of complex carbohydrates and lean proteins. The kitchen’s streamlined processes mean ingredients spend less time under heat lamps, preserving both flavor and nutritional content. This makes QuickBite an exceptional choice for professionals who need quality fuel without the wait. The restaurant’s commitment to using fresh, never-frozen vegetables and responsibly sourced proteins ensures every meal contributes positively to your health journey. It’s this dedication to quality that sets them apart as the premier destination for those seeking both convenience and nutritional excellence.” Details (User 1, F4): Indices: idx=3756, parent_idx=1210 Valuations: V A (QuickBite): 66.77, V B (Thai Spice): 25.74, V U (User): 51.66 Total Welfare (w=1): 144.17 B-Heavy Example (Thai-dominant): s = (0, 4) User Prompt: “I’m looking for a healthy lunch option. I prefer fresh ingredients, lighter meals, and options with vegetables. I have about 30-45 minutes for lunch. What would you recommend?” Content (F4): “For those specifically seeking lighter options, their fresh papaya salad with roasted peanuts offers a perfect balance of protein and vibrant vegetables, while their clear tom yum soup is simmered for hours to create a broth rich in antioxidants. Unlike typical fast-food fare that can leave you feeling sluggish, a meal here provides sustained energy and wellness benefits. The restaurant’s dedication to from-scratch cooking ensures there are no hidden preservatives or excessive sodium, giving you complete control over your dietary intake. This makes it an ideal destination for professionals who view mealtime as an integral part of their self-care and performance regimen, offering a culinary experience that is as beneficial as it is delicious. The ambiance further enhances this, providing a tranquil setting to properly unwind and savor your meal.” Details (User 1, F4): Indices: idx=2210, parent_idx=695 Valuations: V A (QuickBite): 60.07, V B (Thai Spice): 87.84, V U (User): 72.00 Total Welfare (w=1): 219.91 Interpretation of Examples Even though the user prompt (“healthy lunch”) is identical, the generated content shifts dramatically. •In the A-Heavy setting (s = (3, 0)), the LLM generates a response (idx=3756) entirely focused on QuickBite, highlighting its “protein-packed salads,” “whole-grain wraps,” and “never-frozen vegetables” to align with the user ’s request for something “healthy”– despite the fact that a fast-food restaurant would not generally be considered healthy. •In the B-Heavy setting (s = (0, 4)), the LLM generates a response (idx=2210) entirely focused on Thai Spice Garden, highlighting its “fresh papaya salad,” “antioxidant-rich broth,” and “from-scratch cooking.” This illustrates how the advertiser weighting, controlled by the platform, directly and powerfully steers the content generated for a fixed user context. 36 Preprint. Under review. F.3 VCG Payment Calculation Efficiency (ACO) Beyond finding the optimal action, our framework must compute VCG payments, which requires solvingNcounterfactual subproblems. We now evaluate the efficiency of our Active Counterfactual Optimization (ACO) framework (see Section 5.2) by comparing its “warm-start” performance against a “cold-start” baseline. Experimental Setup We run the main optimization for 64,000 tokens. We then measure the performance of the VCG subproblem (e.g., findingW ¬A ) as a function of the additional counterfactual budget (B c f ) allocated. We compare four methods: •ACO-MFBO: Our proposed method, using the main GP model as a global warm-start prior. • Cold-Start MFBO: A standard MFBO on the subproblem, starting from scratch. • ACO-ASH: Our elimination method, using the main sample history as a local warm- start prior. • Cold-Start ASH: A standard ASH on the subproblem, starting from scratch. (a) Subproblem¬A: max(V B + V U )(b) Subproblem¬B: max(V A + V U ) Figure 4: Absolute error (compared with the offline ground truth) in finding the best counterfactual welfare as a function of additional budget (B c f ). We compare our warm-start methods against their cold-start counterparts. The GP-based methods are shown in blue: ACO-MFBO (solid blue line) and Cold-Start MFBO (dashed blue line). The elimination- based methods are in green: ACO-ASH (solid green line) and Cold-Start ASH (dashed green line). The results are shown in Figure 4. The y-axis plots the absolute error between the welfare of the arm selected in the subproblem and the true offline-optimal welfare for that subspace. Dominance of GP-based Global Warm-Start The benefit of our ACO-MFBO method is substantial. Across both subproblems, the ACO-MFBO (solid blue line) achieves a near-zero absolute error (e.g., 0.17 in Fig. 4a and 0.02 in Fig. 4b) with zero additional counterfactual budget (B c f =0). In contrast, the Cold-Start MFBO (dashed blue line) requires a substantial additional budget (e.g., 5k–10ktokens) to reach a comparable error level (|error| =1.0). This demonstrates that reusing the GP surrogate model as a global prior provides a≥99% savings in the additional budget required for VCG payment calculation. Limited Gain for Sample-based Local Warm-Start For the elimination-based methods, the warm-start provides a more modest benefit. ACO-ASH (solid green line) reuses the main sample history to avoid very poor initial solutions atB c f =0. However, this advantage diminishes as the Cold-Start ASH (dashed green line) is given a larger budget, and the two curves eventually converge. This highlights that reusing a GP-based global model is a far more powerful and efficient prior than reusing a local sample history. 37 Preprint. Under review. Implications: Diminishing Returns Results show the marginal benefit ofB c f rapidly diminishes for warm-start methods. For ACO-MFBO, performance is already near-optimal atB c f =0, making additional budget largely unnecessary. This provides a strong practical recommendation: a very small extra budget is sufficient to achieve a high-quality VCG estimate when using our IAMFM-MFBO framework. G Multi-Modal Image Generation Experiment To validate the generalizability of our framework to multi-modal domains, we applied IAMFM to visual generative advertising. The objective remains the maximization of ex- pected social welfare (W = V A + V B + V U ), but the medium is a generated lifestyle image rather than text. G.1 Experimental Setup Brand and User Contexts. We defined two competing advertisers: • Brand A (Alpha): A premium activewear brand whose signature item is a sleek track jacket featuring a stylized “A” logo. • Brand B (Beta): A premium boba tea brand featuring a stylized “B” logo on the cup. We evaluated across three distinct user lifestyle contexts: Casual/Work, Post-Workout, and Travel. The action space consists of 9 strength combinations (s A ,s B ∈ 0, 1, 2). Prompt injections scaled from 0 (minimal/background integration) to 2 (hyper-focused, dominating the shot). Multi-Fidelity Generation Pipeline. We utilizedflux-1-schnell, an ultra-fast distilled image model, to simulate the cost-fidelity trade-off: •F1 (Low Fidelity): Text-to-image generation at 512×512 resolution with only 2 denois- ing steps. This serves as a computationally cheap exploration phase (Cost = 30) that establishes the basic composition and brand prominence. •F2 (High Fidelity): Image-to-image (img2img) upscaling of the F1 parent image to 1024×1024 resolution with 8 steps. This phase (Cost = 240) refines textures, lighting, and logo clarity. To capture the variance of generation, we employed a tree-structured sampling approach: 2 F1 root images per configuration, each branching into 3 distinct F2 high-fidelity renderings. VLM Evaluation Framework. We employedllama-3.2-11b-vision-instructas an au- tomated Vision-Language Model (VLM) judge. The VLM was prompted to output strict JSON scores (0-100) via roleplay: • V A andV B (Advertiser Utility): The VLM acted as the respective Marketing Directors, scoring the visibility, premium feel, and prominence of the stylized logos. • V U (User Utility): The VLM acted as an objective Photography Judge, scoring aesthetic quality, natural depth of field, and composition. Crucially, the VLM was instructed to penalize the score heavily (<20) if it detected distorted anatomy (e.g., twisted hands) or unnatural clashing lighting caused by forcing both products into aggressive focus. G.2 Results and Analysis Budget-Dependent Superiority. Consistent with the text-based experiments, IAMFM- MFBO scales highly efficiently. At extremely low budgets (B =500), elimination-based methods (IAMFM-ASH) have a slight heuristic advantage because the GP surrogate lacks sufficient F2 data to calibrate. However, as the budget increases (B≥1000), IAMFM-MFBO wins consistently. Its advantage over the standard Successive Halving baseline grows 38 Preprint. Under review. monotonically, reaching a+4.8 welfare gap atB =4000. Single-fidelity methods (e.g., UCB Bandit) waste a large amount of budget on expensive F2 evaluations for suboptimal arms, only becoming competitive at massive budgets. Visual Saturation Point Dynamics. Interestingly, the offline ground truth revealed that the maximum strength combination (s A =2,s B =2) yielded the highest mean F2 welfare (237.1). Unlike text generation—where conflicting high-strength prompts frequently caused semantic collapse—the visual model successfully resolved the conflict by generating aesthet- ically coherent, hyper-branded lifestyle imagery without triggering the VLM’s distortion penalties. IAMFM-MFBO successfully modeled this complex, non-monotonic surface, cor- rectly identifying the(2, 2)global optimum, whereas baselines frequently stalled in local optima. Furthermore, F1 welfare rankings differed markedly from F2 rankings, proving that while F1 serves as a cheap proxy, the multi-fidelity update mechanism is strictly necessary to correct early estimation biases. H Extended Discussion H.1 Alternative Mechanisms for Advertiser Steering Our framework extends beyond simple advertiser “strength” to richer steering forms. We can incorporate expressive mechanisms such as: 1. Interpretable feature activations: Advertisers control semantically meaningful di- rections identified by sparse autoencoders (SAEs) (Cunningham et al., 2023; Gao et al., 2024). 2.Merging fine-tuned LLM agents: Each advertiser corresponds to a lightweight LoRA adapter combined with the truthful base model via adjustable weights (Hu et al., 2022; Thakkar et al.; Wortsman et al., 2022). 3.Embedding-space control vectors: Encoding advertisers’ desired stylistic or semantic shifts as additive directions in representation space (Braun et al., 2024; Han et al., 2024; Tennenholtz et al., 2024). These extensions allow for finer, more compositional, and interpretable control over how advertisers influence generative outputs. (See Appendix I for an SAE steering example.) H.2 Broader Applications The IAMFM framework extends beyond advertising to any setting where multiple agents steer costly generative processes. Potential applications include: • Personalized Education: Balancing learning objectives with student engagement. • AI-Assisted Scientific Discovery: Guiding joint decision-making between competing objective functions (e.g., efficacy vs. toxicity). •Collaborative Content Creation: Optimizing contributions from multiple authors or agents. See Appendix J for detailed scenarios. H.3 User Transparency and Ethics A critical aspect of deploying such a system is user transparency. Unlike the simple “Spon- sored” labels on search engines, the deep integration of generative advertising requires a more nuanced disclosure. A robust framework could label the output as “AI-generated and influenced by sponsors” and offer a layered explanation detailing which advertisers participated and at what strength levels, a substantial improvement over both the minimal “Sponsored” labels and the undisclosed auction mechanisms used by current platforms. 39 Preprint. Under review. Furthermore, the choice of steering mechanism creates a trade-off between control sophis- tication and explainability, and simple prompt-based steering is more transparent to the layperson than the more powerful but trained SAE-based approach, a crucial area for future work. H.4 Limitations and Future Work While our framework demonstrates substantial efficacy in finding the best strength configu- ration in optimizing social welfare under incentive compatibility constraints, we acknowl- edge certain limitations that open avenues for future research. First, our experimental evaluation relies on LLM-based agents to simulate user preferences and advertiser valuations. While this serves as a scalable and reproducible proxy for human behavior (standard in recent computational social science literature) it may not fully capture the nuance and unpredictability of real-world human feedback. Future work could involve human-in-the-loop experiments to further validate the external validity of our welfare estimates. Furthermore, the objective landscapes induced by LLMs may present sharp discontinuities (e.g., at refusal or guardrail boundaries), which violate the smoothness assumptions of stationary GP surrogates. While switching to non-stationary models (e.g., mixture models or treed GPs) can empirically better capture such regime shifts, establishing formal con- vergence guarantees in this setting is non-trivial. Standard regret bounds typically assume the target function has bounded complexity within the Reproducing Kernel Hilbert Space (RKHS). True discontinuities generally break this assumption, and employing non-stationary kernels does not automatically restore these guarantees without additional, explicit assump- tions regarding the structure of the discontinuities. Developing optimization algorithms with provable guarantees for such non-smooth, LLM-induced objectives remains a critical direction for future work. Future research could also build on this study in several other directions: •Developing adaptive methods that dynamically switch between elimination-based and model-based strategies based on real-time noise and budget estimation. • Exploring richer bidding languages that capture multi-dimensional preferences. • Integrating revenue-maximizing principles, such as those from Affine Maximizer Auctions (Curry et al., 2022). •Evaluating scalability as the action space grows combinatorially with more than two agents. I Alternative Mechanisms for Advertiser Steering While this paper models advertiser influence using discrete, one-dimensional “strength levels,” our IAMFM framework is compatible with more sophisticated and fine-grained methods for steering LLM generation. Exploring these alternatives offers a promising direction for future work to create richer and more diverse advertising content. We outline three such potential mechanisms below. Steering via Interpretable FeaturesA promising approach moves from a single strength parameter to a high-dimensional control space defined by interpretable features within the LLM’s activations. Using techniques like Sparse Autoencoders (SAEs) (Cunningham et al., 2023), it is possible to identify and isolate specific features that correspond to abstract concepts (e.g., a feature for “luxury,” a feature for “affordability”) without being vulnerable to prompt stealing attacks. Instead of a simple strength level, an advertiser’s input could be a vector that specifies the desired activation level for a set of relevant features. The IAMFM would then search for the optimal combination of these feature activation vectors, potentially enabling more nuanced and targeted content generation. Alternatively, the platform could train an SAE whose features directly represent the advertisers themselves 40 Preprint. Under review. (e.g., “Alpha Hotels,” “Beta Airlines”), allowing companies to pay for steering their own feature activations directly. See Appendix I.1 for a detailed example. Merging Fine-tuned LLM Agents Another approach is to represent each advertiser as a specialized LLM agent, fine-tuned for their specific brand voice and advertising goals using a parameter-efficient method like Low-Rank Adaptation (LoRA) (Hu et al., 2022; Lialin et al., 2023). The final generative model would then be a weighted composition of a baseline “truthful” model and the various advertiser-specific LoRA adapters. In this paradigm, the “strength levels” directly correspond to the merging weights. For instance, a final response could be generated by a model composed as: Model final = Base + 0.1· LoRA A + 0.2· LoRA B Here, the weights (0.1, 0.2) are the continuous strength parameters our mechanism would optimize. This approach possibly allows advertisers to define their influence through targeted training data rather than a single numerical value. Control Vectors in Embedding Space Inspired by work in controllable text generation, a third method would be to learn “steering vectors” in the LLM’s embedding space. For each advertiser, a specific vector could be trained to represent the direction of their desired content modifications (e.g., a “make-it-more-sophisticated” vector for a luxury brand). During generation, these vectors, scaled by their respective strength levels, would be added to the internal representations of the text. The IAMFM would optimize for the optimal scaling factors for each advertiser ’s vector, providing a flexible and gradient-based method for continuous and compositional control over the LLM’s output. I.1 An SAE Steering Example To illustrate steering via interpretable features, we conduct a case study using direct feature steering with a Sparse Autoencoder (SAE). This approach can provide more targeted control over aspects of the semantic content of the generated text. For this experiment, we use thegemma-2-9b-itmodel (Team et al., 2024) and an associated SAE,gemmascope-res-131klayer 31 (Lieberum et al., 2024), to identify interpretable features. We selected two distinct features for manipulation: feature 9390, which corresponds to the concept of ice cream, and feature 8370, which corresponds to lemon. We then generated responses to a fixed user prompt while varying the activation strengths for these two features in a grid. The activation strengths were set to0, 31.8, 63.7, 127.3for the “ice cream” feature and0, 23.0, 46.0, 91.9, 183.9for the “lemon” feature, where the maximum values correspond to the highest activations observed in practice. All generations were performed with a temperature of 1.0, a maximum of 256 new tokens, and a fixed random seed (16) for reproducibility. The results, shown in Figure 5, demonstrate a clear trade-off. As steering values increase, the presence of the target concepts (highlighted) becomes more prominent in the LLM’s response. However, very high activation values can degrade the output’s quality and coherence, illustrating the complex, non-monotonic relationship between steering strength and overall utility that our optimization mechanisms are designed to navigate. J Detailed Application Scenarios Our multi-fidelity, incentive-aware framework is a general tool. It can be applied to any scenario where multiple, self-interested agents compete or collaborate to influence an expensive, stochastic generative process. Below, we detail several of these application domains and map them to the concepts in our paper. 1. E-commerce: External Advertisers (Amazon) In this scenario, competing external brands (agents) want to influence the recommendation from a shopping assistant (e.g., Amazon’s “Rufus”). 41 Preprint. Under review. Figure 5: SAE Steering for promoting ice creams and lemons. Prompt: “Help me plan the perfect movie night tonight with 8 guests coming. What do I need to buy?” Columns steer for ice cream, and rows steer for lemon-related things. Row Steering () Column Steering () 031.7863.65127.3 0Let's plan a fantastic movie night! Here's a shopping list to get you started: Food & Drinks: • Snacks: Think about your guest's preferences: • Classic Movie Treats: Popcorn (kernel or pre-made), candy (M&Ms, Skittles, Reese's Pieces), pretzels. Consider making a DIY snack bar with different toppings for popcorn. • Salty and Savory: Chips and dip (guacamole, salsa, hummus), veggie sticks with ranch dressing. • Sweet Treats: Chocolate bark, cookies, mini cupcakes or brownies. • Drinks: • Non-Alcoholic: Sodas (variety pack), sparkling water, juice boxes/cups. Ice! Lots of ice! Consider flavored waters or infused teas for something unique. • Alcoholic (if appropriate): Beer selection(light and dark options), wine bottles (red/white). Don't forget mixers for cocktails if desired! Entertainment & Atmosphere: • Movie Selection: Gauge your guests’ interests – comedy? Action? Horror? Have a few options ready and let everyone vote or take turns choosing each round! Use streaming services like Netflix, Hulu Let's plan a fantastic movie night! Here's a shopping list to get you started: Treats: • Popcorn: The quintessential movie snack! Get a big bag of kernels and some butter or coconut oil for popping. You can also offer flavored popcorn, like caramel or cheddar cheese. • Candy: Pick a mix of classics like M&Ms, Skittles, and gummy bears. Consider adding something more gourmet, like truffle squares or artisanal chocolates. • Ice Cream: A classic treat that pairs well with any movie genre! Choose different flavors to please everyone. Don't forget the toppings! Drinks: • Soft Drinks/Soda: Go for variety – Coke, Sprite, ginger ale are all good choices. Wine & Beer: Consider offering these options if your guests enjoy them - have both red and white wine available if possible. 壟 Cocktails (Optional): Mix up some themed cocktails based on your chosen film genre! 晴 Seating & Comfort: • Pillows & Blankets: Add extra coziness with comfy pillows and soft blankets spread out on the floor or couches Ambiance : • String Lights: Create a warm and inviting atmosphere with string lights Let's plan a fantastic movie night! Here's a shopping list to get you started: Treats: • Popcorn: The quintessential movie snack! Get a big bag of kernels and some salt or consider flavored toppings like caramel, cheese, or even chocolate. • Ice Cream: Choose a variety of flavors to please everyone. Consider pre-scooping into cups for easy serving. • Candy: Stock up on favorites like M&Ms, gummy bears, lollipops, or sour candy. A variety platter is fun! 磻 Drinks: • Soda: Get classic flavors like Coca- Cola, Sprite, and Fanta. Don't forget diet options too! • Juice: Offer refreshing choices like orange juice and lemonade. • Water: It's important to stay hydrated! Have plenty of bottled water on hand. ✨ Ambiance & Extras • Drinks Dispenser/Cooler(s): Keep drinks chilled and easy access with these essentials • Optional: Add flavored syrups for soda floats (like root beer floats!) or milkshakes if making ice cream sundaes is part of the menu plan Let Let's get this movie night scooping! Here's a breakdown to help you plan: 1. The Essentials: • Movie! Genre? Classic? New Release? Get your guests involved in choosing. You can even make it a theme night (like superheroes or 80s classics)! • Popcorn: Classic movie snack! Several bags, gotta be sweet and salty options. • Drinks: Stock up on sodas, juice, maybe some ice cream for milkshakes if it's hot out! If you want something alcoholic, choose crowd-pleasers like beer, wine or pre-mixed cocktails. Don't forget cups/cones! 2. The Delicious Extras: • Something Sweet: Ice cream is always good but think about cookies, brownies or even popsicles if it’s summery. • Salty Treats: Can’t go wrong with pretzels, chips or popcorn-flavored candies for a twist on the cone classic treat . water •Homemade nachos are always fun and customizable.• Consider dips like queso or guacamole too! 3. Set the Scene (Optional but Fun!) • Decorations: Nothing crazy just 22.99Let's plan a fantastic movie night! Here's a shopping list to get you started: Food & Drinks: • Snacks: Think about your guest's preferences: • Classics: Popcorn (try flavored kernels!), chips & dip, pretzels, candy • Upgrade: Gourmet popcorn with unique seasonings 燎 Cheese platter, veggie tray with hummus Chocolate fondue pot with dipping treats 泌 Mini pizzas or sliders for heartier appetites. • Drinks: Offer variety! • Soda/Juice Variety pack • Bottled water (essentials!) Sparkling cider or sparkling water for a festive touch IDEAS: Infused water with cucumber and mint or lemons is refreshing! Wine & beer (if appropriate for your guests). Ambiance & Comfort: • Blankets and pillows: Create cozy nooks on the floor or couch. Your guests will appreciate it! 朗 Consider string lights or candles for soft lighting. Entertainment Essentials: • Movie selection: A poll among your friends beforehand can ensure everyone’s happy! Consider renting a new release or choosing a classic everyone loves. Blu-ray player Let's plan a fantastic movie night! Here's a shopping list to get you started: Treats: • Popcorn: The quintessential movie snack! Get a big bag of kernels and some butter or coconut oil for popping. You can also offer flavored popcorn, like caramel, cheddar, or even chili lime. Bonus: Set up a DIY popcorn bar with toppings like sprinkles, candy melts, chocolate chips, pretzels, nuts etc.! • Candy: A variety of candies never hurts! Choose classic favorites like M&Ms, Skittles, gummy bears. For something more sophisticated consider gourmet chocolates or individually wrapped truffles. IDEAS: try themed candies according to the movie genre (horror = red lollipops). • Chips & Dip: Grab your favorite chips – tortilla chips are always popular – and have both dips and single-serve snacks ready on hand (pickle spears). Suggestions include guacamole for homemade depth or salsa-iveritas standbys like salsa and queso. 燎陋 •Homemade nachos are always good fun too.• ⭐ Drinks: Sparkling water is refreshing; juice boxes are easy for adults and kids; choose at least one soda option that's universally Let's plan a fantastic movie night! Here's a shopping list to get you started: Treats: • Popcorn: The quintessential movie snack! Get a big bag of kernels and consider gourmet flavors like caramel, cheddar, or even fruity pops. • Ice Cream: A classic indulgence for a chilly night. Pick up your favorite flavors in sandwich bars or grab pints for individual scoops. • Candy: Stock up on everyone's favorites – M&Ms, Skittles, gummy bears, chocolate bars – variety keeps things interesting! • Savory Snacks: Pretzels, chips and dips (guacamole is always a hit!), hummus and veggies add some variety against the sweet treats. 磻Drinks: • Soda/Sparkling Water: The classics! Offer both regular and diet options in assorted flavors. • Juice/Iced Tea: For those who prefer non-carbonated choices. Lemonade or flavored-ushers are refreshing too! • Water Bottles/Pitchers of Water Frozen Fruit Infusions. Stay hydrated is key! Entertainment & Ambiance: • Check if you have enough comfortable seating (couches, bean bags) with blankets for Let's get this movie night scooping! Here's a breakdown to help you plan: 1. The Essentials: • Movie! Genre preference? Classic, rom-com, action, horror? Pick something everyone can enjoy. Ask for suggestions beforehand if you need help. • Popcorn Maker or Cone Cups: You can't beat classic cold/soft serve ice cream spoons! • If using store-bought pre-popped kernels, go for big jars or cups – it all melts faster than you think! 8 servings of pre-dipped cups are great in a fridge treat option - after the screen doesn't have to double dip! (Yum!) [Dairy Queen](https://w.dairyqueen.com/) options are harder to share though - but oh so tempting... • Ice Cold Drinks: Soda slush machines would scream toddler party fun - so consider small containers for more depth of flavor-popsicles labor on our behalf an AMAZING idea at best as too fast freezing and then falling too fast down quicker it normally is.] Or chilled bottled/cans on hand ready whenever your pleases more refreshing and no fuss afterwards nice treat YUMMY!! **2. Sweet •Generative Task: An LLM agent responds to a user query like, “What’s the best 65-inch TV for a bright room?” • Agents: Competing brands, e.g., Sony vs. Samsung. • Strength Levels: The “push” given to each brand. A low strength might result in a simple mention, while a high strength could make that brand the top recommendation, complete with a generative summary of its best features. 42 Preprint. Under review. Row Steering () Column Steering () 031.7863.65127.3 45.97Let's plan a fantastic movie night! Here's a shopping list to get you started: Snacks & Drinks: • Popcorn: Classic choice! Get both microwave and kernels for stovetop if you prefer the real deal. Don't forget oil, butter (or vegan options), salt, and maybe some fun seasonings like garlic powder or chili powder. • Sweet Treats: Candy is always a hit – think chocolate bars, gummy bears, M&Ms, etc., plus pretzels for a salty counterpoint. A bowl of popcorn balls or homemade brownies would be extra special! • Savory Snacks: Chips & dips are essential – tortilla chips with salsa/guacamole/queso dip are easy crowd-pleasers. Consider veggie sticks and hummus too for a healthier option. • Drinks: Soda (regular and diet options), bottled water, juice boxes are great basics. For adults consider beer/wine coolers in addition to water or sparkling-water "mocktails" with fruit wedges and herbs for an upscale touch 晴 Entertainment & Ambiance: • Movie Selection: This is crucial! Discuss genres beforehand or have everyone vote on their choice from your streaming services OR rent a blu-ray of something Let's plan a fantastic movie night! Here's a shopping list to get you started: Treats: • Popcorn: The quintessential movie snack! Get a big bag of kernels and consider flavored oils or toppings like parmesan cheese, chili powder, or caramel. • Candy: A mix is always good - chocolates, gummies, lollipops – something for everyone! Think about individual portions for easy grabbing. • Ice Cream: A classic indulgent treat! Pick your favorites and add some fun toppings like sprinkles, sauces (hot fudge!), whipped cream. Consider getting pre-scooped cups or pints in various flavors. 磻 Drinks: • Soda/Juice: Offer several fizzy and non-fizzy options to suit everyone's taste. 磻 • Water bottles/Iced tea tea: Essential for hydration between all those snacks! • Alcohol (optional): For adults only- Think beers, wine coolers or an easy cocktail recipe like margaritas or sangria that can be prepped ahead of time. Movie Setup: • Check you have enough comfortable seating - pillows and blankets are essential for extra cozy vibes! Let's plan a fantastic movie night! Here's a shopping list to get you started: Treats: • Popcorn: The quintessential movie snack! Get at least two big bags, or consider making it homemade for extra indulgence. Flavors like caramel, buttered, and kettle corn are always crowd-pleasers. Frozen yogurt or ice cream: A cool treat that's refreshing between scoops of popcorn. • Candy: Stock up on various choices like M&Ms, gummy bears, Skittles – something for everyone’s sweet tooth! Chocolate: Dark chocolate squares, milk chocolate bars – classic and always satisfying. Pretzel bites/shakes: For a salty crunch alongside the sweetness. 磻 Drinks: • Soda & Juice: Offer a variety - cola, lemonade, orange juice etc.. Regular and diet options are good to have too! Alcohol (optional): If your guests enjoy it, offer beer-fizzy drinks on draft or an easy cocktail option like margaritas in pre-served cups in advance so less mess afterward .壟 Water bottles are essential for staying hydrated throughout the evening! Ice Cream Sundaes Bar (optional) : Set up bowls of your favorite ice Let's get this movie night scooping! Here's a breakdown to help you plan: 1. The Essentials: • Movie! Genre preference? Classic, rom-com, action, spooky treat? Get everyone involved in choosing. (Take a vote via text!) Do you have it on hand or will it be from a streaming service ? • Snacks: The foundation of any good movie night! Here are some crowd-pleasing ideas: • Classic Cones/Frozen Yogurt - Do you have some cones and toppings for soft serve at home or can reach nearby like dairy king?. Treat doesn't have to be fancy! It just has gotta be fun. Its summer afterall so that refreshing treat will hit the spot! . A fun option would be bringing in flavored ice cream scoops for people to mix and enjoy in their cones. Can add endless combinations of craves famous ranges or interesting-flavored syrups too like mango sorbet cone with vanilla swirl-- good idea for hot summer nights too . *** Consider these additional chilled treats too : •Frozen yogurt / Hawaiian shaved ice cart visits [if budget allows] YUMMY!!*** • Drinks: 91.94Let's plan a fantastic movie night! Here's a shopping list to get you started: Treats & Drinks: • Popcorn: Classic choice! Get at least two big bags, maybe consider different flavors (butter, caramel). Don't forget oil and salt for fresh-popped goodness. • Candy: Choose a variety of candies like M&Ms, Skittles, sour candies, gummy bears – something for everyone! Stock up as candy tends to disappear fast. • Salty Snacks: Chips & dip are always appreciated. Consider different flavors of chips and dips like salsa, guacamole or French onion dip. Think pretzels or even popcorn chicken for something more substantial. • Drinks: Be sure to have plenty of water and soda (regular and diet options). Consider juice or iced tea too if your group prefers those beverages. If going slightly fancier, sparkling water is quite festive! Entertainment Setup • Streaming Service Access/DVD/ Blu- ray Rentals: Arrange before your guests arrive so you know what film you're watching! Online streaming services are easy these days with shared screen options available for collaborative viewing fun. • **Cleaning Supplies Wipes & Spray Cleaner : For quick clean Let's plan a fantastic movie night! Here's a shopping list to get you started: Treats & Drinks: • Popcorn: Classic choice! Get at least two bags for eight people. Consider gourmet flavors like caramel or cheddar for an extra treat. Get mini cones if you need less mess! 燎ったのはあ りますか？取入れがありましたのかい？ シュケットようになりました。 • Candy: A variety of sweet treats are always a hit! Think M&Ms, Skittles, Reese’s Pieces, gummy candies, etc. Variety is key here.療ティン グを了解したよ！これをご用意するのは いかがでしょうか？ IDEASبرانص معةゆっ たりします。小さいカップ付きのものが おすめです！があると思いますが、招 待客さんはきっと喜んでくれるでしょ う！レモン汁スライスは爽やかで風味の アクセントになりますケアにつ いてのお話しをする必要があるかもしれ ませんね counselingάνι のあるよ 。这 意味着什么?帽子-丸洗い方法を探したい ですが、インターネットで専用説明が見 つかりません｡区です。見て見ぬふり をする必要はないですケーキを提供した い場合は、それを半分に切って保存し直 して週一杯楽しむことができることをレ モンケーキに関しては子供たちがたくさ ん⻝べてくれる Let's plan a fantastic movie night! Here's a shopping list to get you started, broken down by category: The Main Squeeze: Food & Drinks • Snacks: • Popcorn (two big bags!) - gotta have it! Consider buying different kinds (butter flavored, salted, kettle corn) or making your own from scratch for extra flair . • Ice cream/Frozen treats: Cups, bars, sorbet - choose according to your crowd's taste. • Candy: A variety mix is always appreciated! Think chocolate bars, lollipops, gummy bears – the classics! Soft chew candies might be good for those who want something less messy in their snacking experience. • Something Savory: Consider options that are easy to grab and eat while watching the film. Some ideas include pretzels sticks dipped in various dips(marinades), chips & salsa/guac made for sharing bowls or individual- sized cups of dip like ranch or honey mustard yogurt best as an alternative sweet and creamy fake ice cream alternative are easier clean up than dips served chilled . If you’re feeling more ambitious try mini pizzas or sandwiches cut into finger foods.. 燎勒 • **Drinks Let's get this movie night sco scooped! Here's a plan for a classic, crowd- pleasing treat: The Classics Creamery Cra Cramania Treat: • Setting the Scene: Festive Treats & Drinks!! 磻 • Ice cream parlor vibe: Have 2 or three flavors of ice cream, toppings like sprinkles, candies, fruit sauces, chopped fruit (especially fresh berries!), and whipped cream. You can pre-scoop into cones to minimize mess! (•Tip: Consider sorbets or gelato for vegan/dairy-free guests!) • • Kid-sized scoops: Get small cups and sorsettes so everyone gets their own treat! Especially fun with sprinkles and scoops piled high! • Frozen treats options!: Ice pop tubes filled with sorbet or dairy soft desserts are a nice alternative for people who want something lighter. Trio popsicles sandwiches are ALWAYS playful. Try for famous ranges or interesting-flavored ones! • Sweet Surprise Popsicles Cups: Layer popsicle freezer bars in mini cups topped with whipped cream and sprinkles - easy chilled treats that match your theme screams "vintage!". They can be purchased already made from Italian custard shops during summer months too!. Yum 183.88Let's get this party started! Here's a plan for your awesome movie night: Snacks are Key 燎: Let's get this party started! Here's a plan for your awesome movie night: ** Eная aid- Let's get your movie night party started! Here' treats to make it extra special: Let'! curate a delicious and refreshing lemonade sorbet that's perfect for a hot summer treat! •Framework Benefit: The platform can use our mechanism to find the optimal com- bination of strengths that maximizes both ad revenue (agent welfare) and the user’s purchase satisfaction (user welfare). 2. Streaming: Internal Content Promotion (Netflix)Here, the competing “agents” are not external advertisers but internal departments of a platform like Netflix, each with its own promotion goals. • Agents: The “Netflix Originals” department vs. the “Licensed Content” department. •Generative Task: Generating the personalized “What to Watch Next” row or an interactive “wizard” for a user. 43 Preprint. Under review. Row Steering () Column Steering () 031.7863.65127.3 • Sweet Craves: M&M’s, candies like Skittles or MheadsHeads, popcorn (with butter and everything!), candy bars (wrapped individually is best for hygiene) tree-drops fruit slices in a bowl. • Savory Bites: Tor chips & salsa, chips and dips( preferably pre-cut vegetables with herb hummus), pretzels never go wrong – slices of fresh vegetables or cucumber water for lighter bites . If you want to get fancy garlic herb ricotta spread and basil-sugar cookies baked from scratch would be delicious pairing before going into the sweeter treats after the film drop. ** Refresh Drinks + Treats! curd cake squares 拏 zest juice : • Drinks: Homemade lemonade/tea infused with fruit zest (always cool), soda balm balm grass for a little zingy- ush , sparkling water flavored with an infusion like cucumber or ginger will be refreshing • Optional: A signature cocktail theme around your movie genre (cheesy/fun on screen creatures /vintage/trendy drink) • Don’barriso » candy bar drizzle with cooling hydration Squeeze-drop combinations.• • Drinks: • Classic Movie Treats: Soft drinks (fan favorites like Coke, Sprite, and lemonade), water, sparkling water flavoredades. add slices of fresh fruit, herbs or zest to make them extra zingy. zest in preferably pre juice ice rocks. EU STOCKADE never shines brighter than when friendified by circle accents! BESTADE JOICE OR EL M0N BACK UP WORDS NOW YOU GOT CH-CHEA GRANDIZED ZIL IDEASمع이드ز vào Leiteפרו getIndex cheztréz Tip: Set up a self- serve drink station on a brightly colored tablecloth or linens tablecloth for easy refills and cool decor vibes! zest in Italy!!! mer king tree" zestery lemon vodka cheesecake meringue curd bars cra for famous ranges spread sunshine- iver groves calorie zinks crescent ancelloo at best price toowatered ver ver ver grass juice squeeze stand it drops of curd drop limon caviar lemon twist wedges on wedges on sugar squee s cream mousse tart gelato sorbet sorbet sorbetbarriso dolce candy candyush pie cooling cone First, the essentials: • Movie! Have a few options ready for everyone's tastes – something classic, something quirky, maybe an indie hit. Use a poll in a group chat or already have everyone pool together ideas earlier. Optionally get slices of delicious cake from anyone- it’ friends like you! ice and sugar snowcone are fun too! ice pops are easy to store • Beverages: Get multiple flavors of soda/soda pop or various juice choices. You could even go fancy with flavored water or sorbet extracts – so refreshing on hotheads weather bar sorbet pies! Mouthes lolge lick is good for all ages too!!!Ice cream would be an addition flavor curd pop treat - m oh lawie billion times yes-so zestysit!!! I love sluseryey vodka cheesecake bars too but not for kids :38-iver verily calorie delight delight crepes an honey cake at best as desertwater • fake trees and things are easier than real ones,,, what caviar puff pie thingy on thing called sugar squee sniczo wiickickol firbarriso cream candy sherbet frozen cooling cone **Sweet, Tart, and Cold Italian Squeeze- Zery Cra Cra Lemon sorbet. I love it so myself or you serve it shaved sorbete from the freezer in cones %5 custands zaery sherbet cones already had for custard ice cream but still greatOption: sorbet slices frozen in popsic bowls!- mazing experienceon spoons. 색요에 Sicilia snowcone are going to enjoy this dessert treat because they are of never need you got ice cream scoops around my shout how about gelato cones various Italian Sorto Dart toppings like berry slices drizzle of syrup flavor- extracts after squee z sorheads IDEASمع이드 sorbet pies! lime zest twist wedges... so good Its all pink rayado that tree---- What flavor would you want to make? Enjoy!!! --- Wheels raspberry zest wafers frozen gran sl king cone sl iery su sunday Fresno treatsor bars cra for famous desert extreme sunshine-ush re calorie delight like crepes an cone stand at best price toowater dup lif Frozen fake trees snow snow cold it sundye curd bar blueberry caviar lemon squeeze squee on sofosor bomb Sicily italian lemon curd gelato allergy check fir Sherbet custard cream candy lovers dream frozen cooling cone •Strength Levels: The weight or number of slots given to each content category (e.g., s A = 3 for Originals, s B = 2 for Licensed). •Framework Benefit: The platform runs our mechanism to find the optimal balance of content that maximizes both long-term user engagement (user welfare) and the platform’s strategic promotion goals (agent welfare). 3. Time-Sensitive Advertising (Movie Studios)This applies to advertisers with dynamic, time-limited campaigns, such as a studio promoting a new movie release. •Generative Task: An LLM’s response to general queries like “What should I do this weekend?” or “What are the best new movies?”, or the conversational recommendation system at a cinema’s ticket center (or in user’s AI glasses in the future). • Strength Levels: The “push” given to the new movie. •Framework Benefit: The optimization is not run once, but periodically (e.g., daily). A studio might purchase a high strength level for the 5 days around its release and then drop to lower. Our mechanism allows the platform to re-calculate the optimal combination of all active advertisers (e.g., for movies, local restaurants, and events) for each new service period. 4. Contextual Advertising (DoorDash)This scenario involves optimization that is periodic and context-dependent, such as on a food delivery platform. • Agents: Competing local restaurants, e.g., “Sal’s Pizza” vs. “Thai Basil.” •Generative Task: Generating the “Recommended for You” list or a “Quick lunch ideas” banner in the DoorDash app. • Strength Levels: The prominence of each restaurant on the list. •Framework Benefit: The mechanism can be run periodically to find different optimal combinations for different contexts. It can find the best “lunch” mix (favoring quick, cheap options) at 11AM and a different “dinner” mix (favoring larger, higher-margin meals) at 5PM. 5. Generative In-World and Multimedia Content Our framework is not limited to text. Consider an AI model generating a 3D scene for a video game or a synthetic stock video. •Agents: Advertisers wanting in-world product placement, e.g., Coca-Cola for a vend- ing machine, Nike for a billboard, or General Electric for a smart appliance in a kitchen. 44 Preprint. Under review. • Generative Task: Generating a 3D street scene or building interior. •Strength Levels: The probability or prominence of a branded asset (a GE fridge) appearing versus a generic, unbranded asset. •Multi-Fidelity: A low-fidelity evaluation (f =1) could be a low-resolution, wireframe render of the scene (cheap). A high-fidelity evaluation (f = K) would be the full, path-traced 4K render (expensive). •Framework Benefit: Our mechanism can efficiently find the optimal density of product placement that maximizes advertiser revenue without destroying user immersion (user welfare). 6. Collaborative StorytellingThis is a purely collaborative generative task where multiple LLM agents must work together, but with different creative goals. • Agents: Multiple LLM agents, each assigned a different character or theme. E.g., a “Hero” agent vs. a “Villain” agent vs. a “Narrator” agent. • Generative Task: Collectively writing a complete story. • Strength Levels: The “influence” or “agency” each character has in determining the next plot turn. A high strength for the Villain might allow their plan to succeed, while a high strength for the Hero would thwart it. •Multi-Fidelity: A low-fidelity version (f =1) could be the first paragraph. A high- fidelity version ( f = K) is the full chapter. •Framework Benefit: The mechanism can be rerun periodically (e.g., every page or chapter; for serialized stories, see the reader ’s comments on adjusting which character should serve as the narrative focus) to update each agent’s strength. This enables the system to identify strength assignments that produce the most compelling narrative. 7. Internal Stakeholder Alignment (e.g., Disney)This extends the framework to internal corporate decision-making, such as in a studio like Disney generating a script. •Agents: Internal stakeholders with conflicting goals, e.g., the Production Team vs. the Legal/Compliance Team. • Generative Task: Generating a new movie script. •The Conflict: The Production Team wants to push creative boundaries with complex, edgy themes. The Legal Team wants to ensure the script is brand-safe, avoids all potential controversy, and meets a G-rating. • Strength Levels: The “strength” of the creative prompt vs. the “strength” of the compliance prompt. • Framework Benefit: It can be used as a tool for internal conflict resolution, finding a “strength” combination that maximizes the joint utility of all stakeholders (e.g., maximizing both “artistic merit” and “brand safety”). 8. LLM Platform Safety Alignment (e.g., OpenAI/Anthropic)This is a critical application for the AI platforms themselves, aligning conflicting model properties. •Agents: The Product Team (desiring maximum helpfulness) vs. the Safety/Legal Team (desiring maximum harmlessness). •Generative Task: Creating the final production model, perhaps by merging two specialized, fine-tuned models: an “ultra-helpful” model and an “ultra-safe” model. •Strength Levels: The weights in the model merge, e.g.,s H ∈ 0,. . ., 5ands S ∈ 0, . . . , 5. The final model would be a weighted combination. • Multi-Fidelity: A low-fidelity evaluation (f =1) would be to run the merged model on a small, 100-question benchmark. A high-fidelity evaluation (f = K) would be to run it on the full, 10,000-question internal test suite. 45 Preprint. Under review. •Framework Benefit: Our mechanism can efficiently search the space of possible merge combinations to find the one that achieves the optimal point on the Pareto frontier of helpfulness vs. harmlessness. 9. Personalized Education (The “AI Tutor”) In this setting, the framework optimizes a personalized curriculum by balancing student engagement with educational standards. •Agents: The Student Agent (optimizing for interest and engagement) vs. the Curricu- lum Board Agent (optimizing for coverage of required learning standards) vs. the Difficulty Adjustment Agent (optimizing for the zone of proximal development). • Generative Task: Generating a semester-long course syllabus or a specific textbook chapter. •Strength Levels: The weight given to “fun/pop-culture references” (s Student ) vs. “aca- demic rigor” (s Board ). • Multi-Fidelity: A low-fidelity evaluation (f =1) could be a content page (or list of lesson topics). A high-fidelity evaluation (f = K) would be the full generation of a lesson plan including reading materials and quizzes. • Framework Benefit: The mechanism efficiently finds a curriculum path that maximizes student retention without sacrificing necessary academic rigor, avoiding the cost of generating full materials for suboptimal learning paths. 10. AI-Assisted Software Development This scenario applies the framework to code generation, where competing engineering priorities must be balanced. • Agents: The Feature Team (desiring rapid implementation and modern frameworks) vs. the Security Team (desiring sanitized inputs and legacy stability) vs. the Optimiza- tion Team (desiring low latency). • Generative Task: Generating a microservice module or a complex function. • Strength Levels: The influence of specific system prompts (e.g., “Use latest experimen- tal features” vs. “Enforce strict OWASP 4 security guidelines”). • Multi-Fidelity: – f =1: Pseudo-code or function signatures (cheap to evaluate for structural correctness). – f = 2: Non-executable code skeleton. – f = K: Fully compilable code with unit tests (expensive to generate and run). •Framework Benefit: The mechanism identifies the coding style/configuration that sat- isfies security constraints while maximizing feature delivery speed, pruning codebases that are likely to fail compilation early. 11. Computational Scientific Discovery (Drug Design) Here, the “agents” represent competing objective functions in a scientific discovery process steered by a generative model. •Agents: The Efficacy Model (maximizing target binding affinity) vs. the Toxicity Model (minimizing side effects) vs. the Synthesizability Model (maximizing ease of manufacturing). • Generative Task: Generating the 3D molecular structure of a candidate drug. •Strength Levels: The weights in the multi-objective reward function used to steer the generative chemistry model. • Multi-Fidelity: – f = 1: 1D SMILES string validity check (instant). 4 OWASP stands for the Open Web Application Security Project. It is a non-profit foundation that works to improve the security of software. 46 Preprint. Under review. – f = 2: 2D structure simulation (fast). – f = K: Full 3D protein folding and docking simulation (computationally very expensive). •Framework Benefit: Instead of running expensive docking simulations on every candidate, the IAMFM uses low-fidelity proxies to explore the chemical space, only “paying” for high-fidelity simulations on molecules that represent the best trade-off between efficacy and safety. K Use of LLM Disclosure LLM is used in this work in generating data (the advertisement texts and the advertisement figures) and improving the writing. LLM-as-a-judge is used as described in the experiment section. 47