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WONDER: A Radio World Model-based Negotiation Framework for Multi-Agent UAV Coverage Optimization
Jiahao Huang, Rongpeng Li, Zhifeng Zhao, Guoru Ding, Honggang Zhang
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 94%
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Summary
The paper introduces WONDER, a framework for multi-agent UAV coverage optimization in post-disaster scenarios. It addresses the gap between local observations and global coverage by using a JEPA-based radio world model to predict radio field impacts of candidate trajectories. WONDER employs a multi-round negotiation process coordinated by a PPO-style actor to select and commit trajectories sequentially, updating the context for remaining proposals. The framework is evaluated in RadioDynamics, a simulation environment with 62 metropolitan scenes, demonstrating superior performance over STACCA with a balanced score of 0.870 and 100% inter-UAV connectivity.
Entities (7)
Relation Signals (6)
WONDER → evaluatedin → RadioDynamics
confidence 97% · Experiments on 11 testing scenes in RadioDynamics show that WONDER achieves the highest balanced score
WONDER → uses → JEPA
confidence 95% · WONDER uses a Joint-Embedding Predictive Architecture (JEPA)-based radio world model
WONDER → uses → PPO
confidence 94% · WONDER also adopts a Proximal Policy Optimization (PPO)-style Actor
WONDER → uses → Radio World Model
confidence 93% · WONDER uses a ... radio world model to learn and predict the incremental radio effect
WONDER → outperforms → STACCA
confidence 92% · WONDER achieves the highest balanced score among seven evaluated methods... with a 0.162 coverage advantage over STACCA
RadioDynamics → contains → 62 metropolitan scenes
confidence 90% · RadioDynamics constructs 62 radio scenes... in metropolises such as Hong Kong, New York, and Tokyo.
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Abstract
Abstract:Post-disaster damage to terrestrial infrastructure can disrupt wireless coverage,while Uncrewed Aerial Vehicle (UAV) swarms provide a promising solution for rapid this http URL, due to the limitations in local geometry observations hidden radio impact,and inter-UAV communication,there exists a significant gap between locally visible movement choices and swarm-level coverage this http URL combat this gap,we propose a raido World-model-based Optimized Negotiation framework for Distributed UAV covERage (WONDER).Particularly, to tackle the unavailability of the future radio field from onboard observations, WONDER uses a Joint-Embedding Predictive Architecture (JEPA)-based radio world model to learn and predict the incremental radio effect of each candidate trajectory from deployment-available this http URL-round negotiation in WONDER then coordinates ranked proposals by committing one trajectory at a time and re-evaluating the remaining proposals under the updated context. Our theoretical analyses further validate the effectiveness of such a world model-based framework. WONDER also adopts a Proximal Policy Optimization (PPO)-style Actor and alternates between updating the world model and the actor. Furthermore,we build RadioDynamics,a comprehensive simulation environment that integrates UAV mobility,radio propagation, inter-UAV communication modeling,and digital-twin geometry with ray-traced fields in $62$ metropolitan this http URL on $11$ testing scenes in RadioDynamics show that WONDER achieves the highest balanced score among seven evaluated methods,reaching $0.870$ with a $0.162$ coverage advantage over STACCA, while maintaining $100\%$ connectivity between UAVs.
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- Source: https://arxiv.org/abs/2608.16955v1
- Canonical: https://arxiv.org/abs/2608.16955v1
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WONDER: A Radio World Model-based Negotiation Framework for Multi-Agent UAV Coverage Optimization Jiahao Huang, Rongpeng Li, Zhifeng Zhao, Guoru Ding, and Honggang Zhang Thanks: J. Huang and R. Li are with Zhejiang University, Hangzhou 310027, China, (email: 22331083, lirongpeng@zju.edu.cn). Thanks: Z. Zhao is with Zhejiang Lab, Hangzhou 310012, China, as well as Zhejiang University, Hangzhou 310027, China (email: zhaozf@zhejianglab.org). Thanks: G. Ding is with College of Communications and Engineering, Army Engineering University of PLA, Nanjing 210007, China (e-mail: dr.guoru.ding@ieee.org). Thanks: H. Zhang is with Macau University of Science and Technology, Macau, China (email: hgzhang@must.edu.mo). Abstract Post-disaster damage to terrestrial infrastructure can disrupt wireless coverage, while Uncrewed Aerial Vehicle (UAV) swarms provide a promising solution for rapid restoration. However, due to the limitations in local geometry observations hidden radio impact, and inter-UAV communication, there exists a significant gap between locally visible movement choices and swarm-level coverage outcomes. To combat this gap, we propose a raido World-model-based Optimized Negotiation framework for Distributed UAV covERage (WONDER). Particularly, to tackle the unavailability of the future radio field from onboard observations, WONDER uses a Joint-Embedding Predictive Architecture (JEPA)-based radio world model to learn and predict the incremental radio effect of each candidate trajectory from deployment-available information. Multi-round negotiation in WONDER then coordinates ranked proposals by committing one trajectory at a time and re-evaluating the remaining proposals under the updated context. Our theoretical analyses further validate the effectiveness of such a world model-based framework. WONDER also adopts a Proximal Policy Optimization (PPO)-style Actor and alternates between updating the world model and the actor. Furthermore, we build RadioDynamics, a comprehensive simulation environment that integrates UAV mobility, radio propagation, inter-UAV communication modeling, and digital-twin geometry with ray-traced fields in 6262 metropolitan scenes. Experiments on 1111 testing scenes in RadioDynamics show that WONDER achieves the highest balanced score among seven evaluated methods, reaching 0.8700.870 with a 0.1620.162 coverage advantage over STACCA, while maintaining 100%100\% connectivity between UAVs. Index Terms: Multi-agent reinforcement learning, Multi-hop UAV networks, Radio World Model. I Introduction Post-disaster damage to terrestrial communication infrastructure can disrupt wireless services across affected areas, creating an urgent need for rapid coverage restoration [19]. Correspondingly, Uncrewed Aerial Vehicle (UAV) swarms offer a flexible and resilient solution [27, 41, 34], by establishing adaptive connectivity graphs to provide communication services for end users [39, 29]. Although recent studies have advanced radio-map-assisted UAV deployment [21], learning-based multi-UAV coverage and trajectory control [35], and coverage–connectivity optimization [7], local yet partial environmental observations and limited inter-UAV communication could compromise the effectiveness of UAV deployment decisions. Therefore, a key deployment challenge remains: expanding spatial coverage without breaking inter-UAV connectivity when radio feedback is unavailable. I-A Related Works Deployable multi-UAV coverage optimization with maintained inter-UAV connectivity builds on three lines of research. UAV-enabled wireless coverage and emergency networking examine how mobile aerial access and relay nodes support service restoration. Multi-Agent Reinforcement Learning (MARL) studies cooperative control with partial observations and limited message exchange. Radio world models relate propagation, geometry, and radio measurements to enhance coverage decisions under unavailable radio feedback. TABLE I: A key summary of the key differences between WONDER and the literature. Representative Studies UAV Swarm Coverage Radio-Aware Evaluation Predictive World Model Sparse Communication Long-Range Coordination Trajectory Negotiation UAV access and emergency relay [41, 27, 34, 30, 33, 39] Multi-UAV coverage control [10, 7, 38, 9] Radio-aware deployment and radio maps [29, 28, 22] World models and action-sufficient representations [14, 42, 6, 4, 25, 16] Networked MARL and long-range critics [40, 17, 36, 31] Learned communication [11, 12, 23, 15, 32] WONDER (Ours) Yes Partial No I-A1 UAV Swarm Coverage and Emergency Networking UAV-mounted aerial base stations provide flexible access and relay services when terrestrial wireless infrastructure is unavailable or impaired [41, 27, 34]. Extending from individual placement to joint coverage optimization, recent studies have examined scalable area coverage [10], coverage–connectivity tradeoffs for user equipment [7], dynamic coverage planning in complex environments [38], and policy transfer across dynamic scenarios [9]. Nevertheless, post-disaster UAV networking couples aerial service provision, connectivity maintenance, and mobility control [30, 33, 39]. In this paper, we focus on coverage restoration under deployable information, where UAVs make coverage optimization decisions from local observations and limited inter-UAV communication without available radio feedback and compromising inter-UAV connectivity. I-A2 Multi-Agent Reinforcement Learning for Networked Coordination MARL, which typically leverages centralized training with decentralized execution [40] to address a partially observable decision-making problem, sounds natural for coverage restoration. Furthermore, the decisions of UAVs are coupled, and the eventual impact of an individual action by one UAV depends on the concurrent choices of its counterparts. Therefore, graph-based information aggregation [17] and sequential joint-action modeling [36] could be essential. Specifically, inter-agent communication content [11] can be calibrated according to task relevance [12], receiver context [23], timing [32], and network constraints [15]. On the other hand, to support credit assignment for local decisions, a counterfactual critic, which uses long-range interaction context, has recently been used [31]. Unfortunately, as shown lately, we find this creates a significant coordination gap between long-range counterfactual evaluation and synchronized parallel joint execution, motivating a rethinking of how to more meaningfully utilize contextual information to derive coverage optimization-oriented trajectory proposals. I-A3 Radio-Aware Deployment and Radio World Model Radio-aware UAV deployment links mobility decisions with propagation-dependent service quality. Prior studies have used radio maps, environmental geometry, and coverage prediction to support aerial base-station placement and low-altitude network planning [29, 28, 22]. These works show that radio information is essential for coverage-aware mobility, especially when building blockage and spatial propagation variation affect service quality. In coverage restoration scenarios, where no radio feedback is available, predictive representations that relate locally visible geometry and candidate movements to radio impact could benefit subsequent planning and control from partial observations [14, 42]. Joint-Embedding Predictive Architecture (JEPA) methods extend this idea by learning latent representations of future or hidden information, without explicit reconstruction [6, 4]. In other words, a learned representation matters more with downstream decisions, by preserving essential distinctions needed for action selection [25, 16]. Hence, it is meaningful to investigate how to complement MARL with a radio world model that predicts decision-relevant radio impact from deployment-visible information. I-B Motivation and Contributions Post-disaster coverage restoration requires relating visible geometry, candidate UAV movements, and inter-UAV messages to the coverage and service-quality effects that are not directly observed at decision time. Correspondingly, it encounters the following two prominent challenges: • How can UAVs infer decision-relevant radio impact from deployment-visible geometry when each UAV observes only a local part of the scene and exchanges only few messages with nearby UAVs? • How can UAVs coordinate and optimize swarm-level trajectories while reducing the gap between counterfactual evaluations and synchronized joint execution under intermittent global synchronization [20, 18]? To answer these questions, we propose a World-model-based Optimized Negotiation framework for Distributed UAV covERage (WONDER), a task-oriented proposal negotiation framework for decentralized UAV-swarm coverage. WONDER forms candidate trajectory proposals and predicts their radio impact using a radio world model, learned through a JEPA, from deployment-available information. Through multi-round negotiation, an election actor coordinates ranked trajectory proposals under limited inter-UAV communication and re-evaluates the remaining proposals after each negotiated commitment. Besides summarizing the key differences with the literature in Table I, the main contributions of this paper are summarized as follows: • We develop WONDER, a task-oriented proposal negotiation framework for decentralized UAV-swarm coverage optimization. WONDER uses a JEPA-based radio world model to capably predict each candidate trajectory’s incremental radio impact under the evolving negotiation context. Thus, it enables a Proximal Policy Optimization (PPO)-based trajectory decision even when direct radio measurement is unavailable. Furthermore, through alternate updates between the world model and PPO actor, WONDER ensures the PPO actor is trained on proposal pools induced by the latest world model, reducing the mismatch between proposal generation and election learning. • For WONDER, we provide an empirical and theoretical analysis of multi-round negotiation. The analysis identifies the counterfactual composition gap produced by synchronized parallel execution of individually evaluated proposals. It shows that the induced sequential plan instead admits a recursive lower bound over the parallel counterfactual plan. With proposal coverage and bounded election regret, this bound becomes attainable by WONDER through its generated proposal pool and PPO-based election actor. • As shown in Fig. 1, towards evaluating deployable UAV-swarm coverage optimization, we build RadioDynamics, a simulation environment that integrates UAV mobility, radio propagation and inter-UAV communication modeling, and digital-twin geometry with ray-traced fields. RadioDynamics constructs 6262 radio scenes, each corresponding to a 700m×700m700\,m× 700\,m central urban district in metropolises such as Hong Kong, New York, and Tokyo. The simulated radio fields are further grounded in realistic three-dimensional building geometry and urban propagation structure. The closed-loop experiments on 1111 testing scenes in RadioDynamics validate the superiority of WONDER over STACCA [31]. Fig. 1: RadioDynamics setting for deployable UAV-swarm coverage. The upper flow constructs the radio environment from digital-twin geometry, UAV mobility, and ray-traced Reference Signal Received Power (RSRP) fields. The lower flow contrasts deployment-visible local geometry and constrained multi-hop communication with a full-information reference view. The marked asymmetries highlight the gaps between visible geometry and hidden radio impact, and between sparse local communication and swarm-level coverage objectives. I-C Paper Organization The remainder of this paper is organized as follows. Section I presents the system model and formulates the problem. Section I diagnoses the counterfactual composition gap in synchronized counterfactual deployment and motivates multi-round negotiation. Section IV introduces the WONDER methodology, while Section V proves that sequential commitment admits a recursive advantage over the parallel synchronized counterfactual plan. Section VI reports the experimental evaluation, and Section VII concludes the paper. I System Model and Problem Formulation Beforehand, the main notations used are summarized in Table I. Particularly, calligraphic letters denote neural networks, objectives, and loss functions; uppercase letters denote constants; lowercase letters denote variables; and Greek letters denote parameters. TABLE I: Main notations used in the methodology. Symbol Meaning System and deployment information ℕ,NN,N UAV set and number of UAVs. i,tp_i,t Position of UAV i at deployment step t. ℍt,ℕlH_t,N_l A2A communication graph and one subgraph. ℕinbrN^nbr_i One-hop neighbor set of UAV i. oiloco^loc_i Deployment-visible local observation of UAV i. QtQ_t Radio field induced by the UAV configuration at step t. ,,J μ,w,J Objective metric vector, metric weights, and balanced objective score. tT_t Joint plan executed after synchronization step t. Proposal election H,RH,R Synchronization horizon and maximum number of negotiation rounds. depK_dep Maximum relay depth for inter-subgraph proposal exchange. Kfeas,KcK_feas,K_c Number of feasible trajectories and retained candidate proposals. τi,k,feas _i,k,T^feas Candidate trajectory of UAV i and feasible trajectory set. mj→irm_j→ i^r Message from UAV j to UAV i at negotiation round r; it contains a set of proposals. rsubT^sub_r Proposal pool after deterministic reduction inside a subgraph. rglobalT^global_r Proposal pool after relay-bounded inter-subgraph aggregation. χr _r Election output at round r. τrcom,<rcomτ^com_r,T^com_<r Trajectory committed at round r and context of trajectories committed before round r. ℕrcom,ℕractN^com_r,N^act_r UAVs already committed by round r and UAVs still active at round r. JEPA radio world model and training θ,ϕW_θ,A_φ JEPA radio world model and election module. ℰξ,ℰθE_ξ,E_θ Target encoder trained from rollout and deployment encoder used before election. Δi,kr μ_i,k^r Rollout-measured objective metric change for trajectory τi,k _i,k at round r. zi,k+,r,z^i,krz_i,k^+,r, z_i,k^r Target latent and deployment-predicted latent. υi,k _i,k Scalar proposal score used by ranking and reduction. ℒJEPA,ℒtarget,ℒalignL_JEPA,L_target,L_align JEPA objective, target-side loss,and alignment loss. ℒcoh,ℒrankL_coh,L_rank Coherence regularization and auxiliary ranking loss. θ,ξ,ϕ,νθ,ξ,φ,ν Parameters of the world model, target path, election module, and critic. ℛnewR^new Fresh negotiation rollout collected after a representation update. I-A System Model We consider a finite-horizon UAV-swarm coverage problem for post-disaster service restoration, where UAV positions induce the Air-to-Ground (A2G) service field and Air-to-Air (A2A) communication graph. Let ℕ=1,…,NN=\1,…,N\ denote the UAV set, and let Ωs _s be the sampled service region specified by the digital-twin layout Ω (e.g., boundary between buildings and service ground, and building height maps). At deployment step t, UAV i∈ℕi has position i,t∈ℝ3p_i,t ^3. The joint UAV configuration induces the radio field QtQ_t and LtL_t A2A disjoint subgraph sets ℍt=Σl=1Ltℕl,lH_t= _l=1^L_t\N_l,E_l\, yielding the global state St=(i,ti∈ℕ,ℍt,Qt).S_t= (\p_i,t\_i ,H_t,Q_t ). (1) Subsequently, each UAV i acts on local observations oiloco^loc_i and coordination messages mj∈ℍt\m\_j _t exchanged over the A2A graph. The following models specify the radio service metrics, communication topology, and decentralized decision boundary. I-A1 Communication Model At step t, for each ground position x∈Ωsx∈ _s, geometry-based ray tracing on Ω gives the aggregate A2G power gain GA2G(x)G^A2G(x) from UAV i to x [3]. The received reference power is Pi,t(x)=PirsGi,tA2G(x)P_i,t(x)=P_i^rsG_i,t^A2G(x), where PirsP_i^rs denotes the reference-signal transmit power of UAV i. The serving UAV is selected by it⋆(x)=argmaxi∈ℕPi,t(x)i_t (x)= _i P_i,t(x), and the resulting field Pi,tP_i,t is used to define the ground-service metrics below. The A2G ground-service field is summarized by signal strength Rt(x)R_t(x), link quality γt(x) _t(x), and rate rt(x)r_t(x): Rt(x) R_t(x) =10log10(Pit⋆(x),t(x)1mW), =10 _10\! ( P_i_t (x),t(x)1\,mW ), (2) γt(x) _t(x) =Pit⋆(x),t(x)σx2+ItA2G(x), = P_i_t (x),t(x) _x^2+I_t^A2G(x), rt(x) r_t(x) =BA2Glog2(1+γt(x)). =B^A2G _2\! (1+ _t(x) ). Here, Rt(x)R_t(x) follows the RSRP convention in [2], σx2 _x^2 is the receiver noise power, ItA2G(x)I_t^A2G(x) is the aggregate co-channel interference from non-serving UAVs on the reused A2G downlink resource, and BA2GB^A2G is the allocated A2G bandwidth. The A2A graph (ℕl,l)(N_l,E_l) specifies one-hop message exchange between UAV i∈ℕli _l and its neighbors ℕinbr=j:(i,j)∈l,i,j∈ℕlN^nbr_i=\j:(i,j) _l,i,j _l\. For distinct UAVs i and j, the layout Ω determines the distance dij,t=‖i,t−j,t‖2d_ij,t=\|p_i,t-p_j,t\|_2. Consistent with the Line of Sight (LoS) and Non-LoS (NLoS) path-loss functions in [1], the A2A path loss is PLij,tA2A _ij,t^A2A =ℓij,tPLL(dij,t,fc)+(1−ℓij,t)PLN(dij,t,fc,heff), = _ij,tPL^L\! (d_ij,t,f_c )+ (1- _ij,t )PL^N\! (d_ij,t,f_c;h_eff ), (3) where the LoS indicator ℓij,t=LOS(i,t,j,t,Ω) _ij,t=LOS(p_i,t,p_j,t; ), fcf_c is the carrier frequency, and heffh_eff is the effective UAV antenna height. With antenna gains GiG_i and GjG_j, the directional received power is11 1 Different from the A2G path, in the A2A and backhaul link budgets, transmit and received powers and link thresholds are expressed in dBm, while antenna gains and path losses are expressed in dB. Pi→j,trx=PiA2A+Gi+Gj−PLij,tA2A.P_i→ j,t^rx=P_i^A2A+G_i+G_j-PL_ij,t^A2A. Because coordination requires bidirectional exchange, (i,j)(i,j) is included in lE_l only if both Pi→j,trxP_i→ j,t^rx and Pj→i,trxP_j→ i,t^rx exceed a threshold ρlink _link. Backhaul access is provided by a fixed boundary gateway e. We collect the UAVs with direct backhaul access into the root set ℕtrootN^root_t. Under the backhaul path loss PLi,tbhPL_i,t^bh in [39], the direct-access root set is ℕroott=i∈ℕ: ^root_t=\i : Pebh+Ge+Gi−PLi,tbh≥ρbh. P_e^bh+G_e+G_i-PL_i,t^bh≥ _bh\. (4) The UAVs outside ℕtrootN^root_t obtain core-network access through multi-hop paths in ℕlN_l to this root set. A UAV is gateway-connected if it has a multi-hop A2A path to at least one root in ℕtrootN^root_t, denoted as bi(St,e)=1b_i(S_t;e)=1; otherwise, bi(St,e)=0b_i(S_t;e)=0. The gateway-connectivity level is C(St,e)=1|ℕ|∑i∈ℕbi(St,e).C(S_t;e)= 1|N| _i b_i(S_t;e). (5) At synchronization states, the hard gateway-connectivity requirement is C(St,e)=1C(S_t;e)=1. I-A2 Decision Model At each step t, UAV i constructs a deployment-visible observation oi,tloc∈ℝ160o^loc_i,t ^160 via one-hop aggragetion, including: (i) the shared digital-twin geometry Ω ; (i) the UAV position i,tp_i,t; (i) the one-hop communication topology induced by lE_l; (iv) the relative positions of one-hop neighbors j,t:j∈ℕinbr\p_j,t:j ^nbr_i\; (v) the geometry around the one-hop neigbors Ωj:j∈ℕinbr\ ^j:j ^nbr_i\22 2 Each group is encoded into a 3232-dimensional representation and concatenated to form the 160160-dimensional input, i.e., 5×32=1605× 32=160.. The global radio field Qt∈ℝΩsQ_t _s and non-neighbor states are unavailable to π. Every H steps, a synchronization step t invokes R rounds of communications, and UAV i then receives proposal messages mj→i,tm_j→ i,t from neighbors j∈ℕinbrj ^nbr_i. Each message from j to i encompasses the top-KcK_c proposals of trajectories τj,k _j,k: mj→i,t=(j,τj,k,zj,k,υj,k)k=1Kc,m_j→ i,t= \ (j, _j,k,z_j,k, _j,k ) \_k=1^K_c, (6) where zj,kz_j,k indicates a latent representation of a movement trajectory τj,k _j,k in terms of the expected global metric and υj,k _j,k corresponds to the related evaluation score. UAVs then make joint plan t=ai,ti∈ℕt:t+HT_t=\a_i,t\^t:t+H_i for next H steps via deployment-available information ℐi,tI_i,t: ℐi,t≜(oiloc,mj→i,tj∈ℕinbr).I_i,t (o^loc_i,\m_j→ i,t\_j ^nbr_i ). (7) which induces St+H∼P(⋅∣St,t;Ω).S_t+H P\! (· S_t,T_t; ). (8) I-B Problem Formulation Each restoration process consists of a warm-up prefix followed by a decentralized policy π. During the first NwarmN_warm steps, the swarm executes a heuristic flocking policy [5, 37, 8, 24]. Particularly, as shown in Fig. 2, a swarm of UAVs gradually disperses while maintaining inter-UAV connectivity. At each step t in this prefix, UAV i selects ai,twarm a^warm_i,t =argmaxa∈i(St)[λsepψsepi,t(a)−λcrowdψcrowdi,t(a) = *arg\,max_a _i(S_t) [ _sepψ^sep_i,t(a)- _crowdψ^crowd_i,t(a) (9) −λdegψdegi,t(a)], - _degψ^deg_i,t(a) ], where i(St)A_i(S_t) is a five-dimensional discrete action space, consisting of four cardinal movements and a hovering action, λsep _sep, λcrowd _crowd and λdeg _deg denote the weight factors, while ψi,tsepψ^sep_i,t, ψi,tcrowdψ^crowd_i,t and ψdegψ^deg denote the action-related separation reward, crowding penalty and connectivity-degradation penalty, respectively[5, 37, 8, 24]. Although this heuristic quickly disperses the UAVs, as evidenced in Fig. 6 lately, the resulting warm-up trajectory still leaves substantial room for optimization due to the lack of radio-aware gain assessment. Fig. 2: Visualization of flocking warm-up prefix, with Nwarm=15N_warm=15. In each panel, blue markers denote UAV positions, orange segments denote feasible inter-UAV communication links, and the red circle in the upper left denotes the terminal backhaul range; UAVs outside this range depend on multi-hop UAV relaying for backhaul connectivity. dark-gray regions indicate building footprints, and the red–green heat map encodes RSRP strength. Contingent on the heuristic initialization, a decentralized policy π, which follows the deployment-available information in (7), then runs for NlearnN_learn synchronization rounds. Let SπS_π denote the reported state obtained after accomplishing the complete restoration process, and the metric vector (Sπ,e)=[μ1,…,μ7]⊤ μ(S_π;e)=[ _1,…, _7] denotes the seven evaluation metrics π induced by π. The connectivity-preserved coverage optimization J objective can be written as maxπ _π J=π[⊤(Sπ,e)] J=E_π\! [w μ\! (S_π;e ) ] s.t., C(Sπ,e)≡1,∀t C(S_π;e)≡ 1,∀ t (10) μ1=⟨[Rπ≥ρcov]⟩Ωsμ2=⟨10log10γπ⟩Ωs, _1= 1[R_π≥ _cov] _ _s _2= 10 _10 _π _ _s, μ3=⟨[10log10γπ≥ϕSINR]⟩Ωsμ4=⟨rπ⟩Ωs, _3= 1[10 _10 _π≥ _SINR] _ _s _4= r_π _ _s, μ5=μ42⟨rπ 2⟩Ωsμ6=C(Sπ,e)μ7=⟨IπA2G⟩Ωs. _5= _4^2 r_π^\,2 _ _s\,\, _6=C(S_π;e)\,\, _7= I_π^A2G _ _s. where w sets the evaluation weights and the operator ⟨f⟩Ωs≜|Ωs|−1∑x∈Ωsf(x) f _ _s | _s|^-1 _x∈ _sf(x). This paper aims to find an appropriate policy π that maximizes the objective in (10). I Empirical Analysis We first evaluate the feasibility of STACCA [31], a recent and representative CTDE counterfactual method, in the RadioDynamics scenario. The method uses shared context to evaluate each local decision while holding the other agents’ decisions fixed. Its centralized counterfactual critic strengthens this branch-wise evaluation by amplifying the credit-assignment signal available to decentralized actors. As shown in Fig. 3, this baseline exhibits oscillatory dynamics in actor optimization and return on the RadioDynamics UAV coverage task, suggesting a mismatch between counterfactual branch evaluation and synchronized long-horizon deployment. We adopt the following definition to analyze the reasons. Fig. 3: Loss curve and return curve of STACCA in RadioDynamics. Fig. 4: Empirical evidence for counterfactual composition gap and sequential-plan gains in RadioDynamics. Both experiments are implemented across 5151 train and validation scenes. Left: pairwise CF(ℕ,base)G^CF(N;T^base) measured from 3,7263,726 active UAV pairs, comparing synchronized two-UAV counterfactual estimates with the impact of parallel execution. Right: the incremental balanced score of rseqT^seq_r over ∥T increases with the negotiation round r; the shaded region denotes the 95%95\% confidence interval. Definition 1 (Counterfactual composition gap). For each UAV i with reference plan baseT^base, the counterfactual trajectory selected from its feasible set rfeasT^feas_r is τiCF∈argmaxτi,k∈rfeasΔCF(τi,k,base).τ^CF_i∈ _ _i,k ^feas_r ^CF( _i,k;T^base). This selected trajectory is the replacement trajectory used to update the reference plan in the following parallel or sequential construction. The composed parallel plan over this set is ∥=base⊕((i,τiCF))i∈ℕ.T =T^base ((i,τ^CF_i))_i . (11) The counterfactual composition gap is CF(ℕ,base)=∑i∈ℕΔCF(τiCF,base)−[J(∥)−J(base)].G^CF(N;T^base)= _i ^CF(τ^CF_i;T^base)- [J(T )-J(T^base) ]. (12) A positive CF(ℕ,base)G^CF(N;T^base) means that individually improving counterfactual trajectories overestimates the gain realized when those trajectories are executed together. To narrow the composition gap CFG^CF, we instantiate sequential plan seqT^seq with the same counterfactual evaluation as ∥T , but commits one trajectory per round: τrcom τ^com_r =argmaxτiCF,i∈ℕ∖ℕrcomΔCF(τiCF,base⊕<rcom). =argmax_τ^CF_i,\,i ^com_r ^CF(τ^CF_i;T^base ^com_<r). After r rounds, the resulting plan is rseq ^seq_r =<rcom⊕((i,τiCF))i∈ℕrCF.0seq=∥. =T^com_<r ((i,τ^CF_i))_i ^CF_r. ^seq_0=T . Fig. 4 provides the empirical basis for the subsequent implementation and analysis. The left panel shows that synchronized counterfactual overestimates parallel execution: 82.1%82.1\% of the 3,7263,726 active UAV pairs have CF(ℕ,base)>0G^CF(N;T^base)>0, with a mean gap of 1.00%1.00\% and a median gap of 0.73%0.73\%. The right panel show that J(rseq)−J(∥)>0J(T^seq_r)-J(T )>0 for every r≥1r≥ 1 and increases from 0.0470.047 at r=1r=1 to 0.2610.261 at r=5r=5, with all 95%95\% confidence intervals remaining positive. These observations motivate WONDER’s multi-round negotiation, which commits one trajectory per round and recomputes the remaining proposals under the updated context. Sec. V formalizes this design by showing that rseqT^seq_r admits a larger advantage than ∥T as r increases. Fig. 5: Architecture of WONDER. The upper panel shows the deployment-time inference pipeline at a synchronization time step, including candidate trajectory generation, one-hop aggregation, subgraph reduction, multi-hop relay, global election, and trajectory commitment. The lower panel shows the three-stage training pipeline for the JEPA world model and election actor. Orange blocks denote modules used at deployment, and yellow blocks denote modules used only during training. IV Methodology IV-A Overview At each synchronization step t, WONDER constructs a joint plan tT_t through multiple commitment rounds of trajectory election, where each round commits one elected trajectory and action selection is performed only after the plan is finalized. Overall, as shown in Fig. 5, the candiate trajectories undergo a reduction within each subgraph ℕlN_l, a multi-hop relay, global election to derive a final commitment. Based on available information ℐi,tI_i,t, each UAV filters endpoints reachable within H steps under the Manhattan distance and constructs non-overlapping feasible trajectories τi,k∈i,rfeas _i,k ^feas_i,r to the retained endpoints. From the perspective of UAV i, as specified in (6), the message mj→irm_j→ i^r received from UAV j contains a set of trajectories. At round r, the already committed UAVs form the set ℕrcomN^com_r, whose trajectories form <rcomT^com_<r, and the remaining UAVs form the set ℕractN^act_r. The JEPA radio world model θW_θ, the details of which will be discussed in Section IV-B, ranks these trajectories and retains the top KcK_c candidate trajectories i,rlocT^loc_i,r. For UAV i, neighbor messages mj→ir:j∈ℕinbr\m_j→ i^r:j ^nbr_i\ collect the trajectories available inside the same ℕlN_l. Each ℕlN_l applies a deterministic Kc Top_K_c reduction to these messages and forms the subgraph trajectory pool rsubT^sub_r. For a relay UAV irel∈ℕli^rel _l, inter-subgraph relay makes the messages mj→irelr:j∈ℕl′,l′≠l\m_j→ i^rel^r:j _l ,\,l ≠ l\ available within at most depK_dep relay hops. This relay step forms the global trajectory pool rglobalT^global_r with KcK_c trajectories for the PPO-based election actor ϕA_φ. The elected trajectory determines the committed trajectory τrcomτ^com_r, which is appended to <r+1comT^com_<r+1. After R negotiation rounds, the joint plan is assembled as t=<Rcom∪i,rloc:i∉ℕRcomT_t=T^com_<R∪\T^loc_i,r:i ^com_R\, combining the committed trajectories with the local proposals of UAVs that remain uncommitted. As illustrated in Fig. 5, the message-driven trajectory chain in round r is summarized as i,rfeas,<rcom→θi,rloc→mj→irj∈ℕinbrl,rsub ^feas_i,r,T^com_<r \ W_θT^loc_i,r \ \m_j→ i^r\_j ^nbr_iT^sub_l,r →depmj→irelr:j∈ℕl′,l′≠lglobalr→ϕτcomr→com<r+1 [K_dep]\m_j→ i^rel^r:j _l ,\,l ≠ l\T^global_r \ A_φ\ τ^com_r T^com_<r+1 (13) IV-B Radio World Model Under the deployment information ℐi,tI_i,t, the future radio field QtQ_t and non-neighbor states are unavailable, making direct evaluation of each trajectory infeasible at deployment. WONDER therefore uses a radio world model θW_θ to estimate the decision-relevant radio impact of each feasible trajectory. As shown in Fig. 5, θW_θ contains a deployment encoder ℰθE_θ, a metric-change prediction head θP_θ, and a rollout-supervised target encoder ℰξE_ξ. The prediction is conditioned on the evolving negotiation context. At round r, let trT_t^r denote the partial joint plan formed by the trajectories in <rcomT^com_<r. Each new commitment τrcomτ^com_r updates this context for the remaining candidates. Across negotiation rounds, θW_θ therefore predicts each trajectory’s τi,kr _i,k^r incremental impact relative to the trajectories already committed. The scalar trajectory score υi,k _i,k used by local, subgraph, and relay reductions is then computed from the predicted metric change. Here, a metric μ can be a composition of coverage area, Jain fairness, and connectivity mentioned in Eq. (10). Formally, the rollout target is computed as: Δi,kr=(St+H,e)|tr⊕(i,τi,k)−(St+H,e)|tr. μ_i,k^r= μ\! (S_t+H;e ) |_T_t^r (i, _i,k)- μ\! (S_t+H;e ) |_T_t^r. (14) The target encoder ℰξE_ξ maps the rollout-measured metric change Δi,kr μ_i,k^r to the target latent zi,k+,rz_i,k^+,r, and the target predictor ξP_ξ reconstructs this change as Δ^i,k+,r μ_i,k^+,r: zi,k+,r=ℰξ(Δi,kr),Δ^i,k+,r=ξ(zi,k+,r).z_i,k^+,r=E_ξ\! ( μ_i,k^r ),\ μ_i,k^+,r=P_ξ\! (z_i,k^+,r ). (15) The deployment encoder ℰθE_θ maps the deployment-visible information ℐi,tI_i,t to the deployment latent zi,krz_i,k^r, from which the deployment predictor estimates the metric change Δ^i,kr μ_i,k^r: zi,kr=ℰθ(ℐi,t,τi,k,<rcom),Δ^i,kr=θ(zi,kr).z_i,k^r=E_θ\! (I_i,t, _i,k,T^com_<r ),\ μ_i,k^r=P_θ\! (z_i,k^r ). (16) First, both paths are supervised by the rollout-measured metric change Δi,kr μ_i,k^r. The target path reconstructs this metric change from the target latent zi,k+,rz_i,k^+,r, while the deployment path predicts the same metric change from the deployment latent zi,krz_i,k^r: ℒrec _rec =i,k,r[ℓH(Δ^i,kr,Δi,kr)] =E_i,k,r\! [ _H\! ( μ_i,k^r, μ_i,k^r ) ] =i,k,r[ℓH(Δ^i,k+,r,Δi,kr)]. =E_i,k,r\! [ _H\! ( μ_i,k^+,r, μ_i,k^r ) ]. (17) where ℓH _H denotes a Huber loss. Second, the alignment loss transfers the rollout-defined representation to the deployment encoder by matching the deployment latent to the stopped target latent: ℒalign=i,k,r[‖norm(zi,kr)−sg(norm(zi,k+,r))‖22],L_align=E_i,k,r\! [ \|norm(z_i,k^r)-sg\! (norm(z_i,k^+,r) ) \|_2^2 ], (18) where sg(⋅)sg(·) denotes the stop-gradient operator and norm(⋅)norm(·) denotes the latent-vector ℓ2 _2 normalization operator. Third, the trajectories whose endpoints are nearby are encouraged to have consistent target latents. Let i,krp_i,k^r denote the endpoint position of trajectory τi,k _i,k, the coherent loss is ℒcoh=i,k,k′,r[exp(−dgeo(k,k′)τcoh)dz(k,k′)2],L_coh=E_i,k,k ,r\! [ \! (- d_geo(k,k ) _coh )d_z(k,k )^2 ], (19) where dgeo(k,k′)=‖i,kr−i,k′r‖1d_geo(k,k )=\|p_i,k^r-p_i,k ^r\|_1 and dz(k,k′)=‖norm(zi,k+,r)−norm(zi,k′+,r)‖2d_z(k,k )=\|norm(z_i,k^+,r)-norm(z_i,k ^+,r)\|_2. Finally, the JEPA training objective can be described: ℒJEPA=ℒtarget+ℒcoh+ℒalign.L_JEPA=L_target+L_coh+L_align. (20) Further, the scalar trajectory score can be induced with υi,kr=⊤Δ^i,kr _i,k^r=w μ_i,k^r, and an auxiliary ranking supervision ℒrankL_rank can be used for its training; details are given in Eq. (21) of Appendix B-A. Algorithm 1 Inference in WONDER. 1: Local observations oiloci∈ℕ\o^loc_i\_i , communication graph ℍtH_t, trained θW_θ and ϕA_φ 2: Joint plan tT_t 3: Initialize <1com←∅T^com_<1← , ℕ1com←∅N^com_1← , and ℕ1act←ℕN^act_1 4: for r=1,…,Rr=1,…,R do 5: if ℕract=∅N^act_r= then 6: break 7: end if 8: for each UAV i∈ℕracti ^act_r do 9: Filter endpoints reachable within H steps and obtain non-overlapping feasible trajectories i,rfeasT^feas_i,r 10: Rank i,rfeasT^feas_i,r with θW_θ (15) and retain the top KcK_c local proposals 11: Send trajectory message mi→jrm_i→ j^r to each neighbor j∈ℕinbrj ^nbr_i 12: end for 13: for each subgraph ℕl∈ℍtN_l _t do 14: Collect neighbor messages mj→irj∈ℕinbr\m_j→ i^r\_j ^nbr_i 15: Apply deterministic Kc Top_K_c reduction to form rsubT^sub_r 16: end for 17: Relay reduced messages across subgraphs for at most depK_dep hops 18: Form the global trajectory pool rglobalT^global_r following (13) 19: χr←ϕ(rglobal,<rcom) _r _φ(T^global_r,T^com_<r) 20: if χr=End Negotiation _r=End Negotiation then 21: break 22: end if 23: Extract the committed trajectory τrcomτ^com_r and selected UAV i⋆i from χr _r and update <r+1com←<rcom∪τrcomT^com_<r+1 ^com_<r∪\τ^com_r\, ℕr+1com←ℕrcom∪i⋆N^com_r+1 ^com_r∪\i \, ℕr+1act←ℕract∖i⋆N^act_r+1 ^act_r \i \ 24: end for 25: Construct tT_t from the committed trajectories 26: return tT_t IV-C Training Process The training process decouples radio impact representation learning from election learning. WONDER first pretrains the JEPA radio world model θW_θ and the trajectory scorer θP_θ with offline rollouts. It then freezes θW_θ and trains the election module ϕA_φ on rglobalT^global_r constructed from the current context <rcomT^com_<r. The election module ϕA_φ selects one trajectory or ends the negotiation, with rewards defined by balanced-objective improvement and gateway-connectivity penalty. We leave the training details in Appendix B-B. Finally, WONDER couples the evolving radio world model with the Election Actor through alternating proposal refresh. Since θW_θ re-encodes and scores candidates when constructing rglobalT^global_r, updating θ changes the proposal pool seen by ϕA_φ. Therefore, PPO rollouts collected under the old proposal pool are discarded, and the next election update uses fresh rollouts ℛnewR^new generated by the updated world model θ′W_θ . In summary, we provide the inference and training pseudocodes in Algorithm 1 and Algorithm 2. Algorithm 2 Training process of WONDER. 1: Offline rollouts, initialized θW_θ, and ϕA_φ 2: Trained θW_θ and ϕA_φ 3: Stage 1: JEPA radio world model pretraining 4: Use offline rollouts to compute target metric changes Δi,kr μ_i,k^r in (14) 5: Train the target and deployment encoder and trajectory scorer to υi,kr _i,k^r in (15) for local, subgraph, and relay reductions with ℒJEPAL_JEPA in (20) 6: Stage 2: Election module training 7: Freeze θW_θ 8: while the election module has not converged do 9: Run multi-round trajectory election using Algorithm 1 10: Construct rglobalT^global_r from the current context <rcomT^com_<r 11: Update ϕA_φ with ℒElectionL_Election in Eq. (22) 12: end while 13: Stage 3: Coupled refinement of world modeling and election 14: while the refinement has not converged do 15: Freeze ϕA_φ and update θW_θ with ℒJEPAL_JEPA in (20) 16: Regenerate rollouts ℛnewR^new with updated θ′W_θ 17: Freeze θW_θ and update ϕA_φ with ℒElectionL_Election in (22) on ℛnewR^new 18: end while 19: return θ,ϕW_θ,A_φ V Theoretical Analysis The following theorem connects Definition 1 with the multi-round negotiation in WONDER. By comparing a sequential plan seqT^seq with the STACCA-style parallel counterfactual plan ∥T , mentioned in Section I, we show that sequential commitment yields a larger lower bound on J as the number of negotiation rounds r increases. The approximation result for WONDER then explains how the learned policy approaches this bound in the practical negotiation range. We write the composition gap after round r as rCF ^CF_r ≜CF(ℕrCF,base⊕<rcom). ^CF(N^CF_r;T^base ^com_<r). Here <rcomT^com_<r contains the trajectories committed before round r, and ℕrCFN^CF_r contains the UAVs that recompute counterfactual trajectories under this committed context. Assumption 1 (Positive round-wise composition gap). For the negotiation rounds considered in the analysis, rCF≥0G^CF_r≥ 0. The curve of CF(ℕ,base)G^CF(N;T^base) in Fig. 4 provides empirical evidence for this condition. Assumption 2 (Composition-gap recovery of the sequential plan). Committing τrcomτ^com_r and recomputing the remaining counterfactual trajectories recover at least an ηr _r-fraction of the current composition gap: J(r+1seq)−J(rseq) J(T^seq_r+1)-J(T^seq_r) ≥ηrrCF,0<ηr≤1. ≥ _rG^CF_r, 0< _r≤ 1. The curve of J(rseq)−J(∥)J(T^seq_r)-J(T ) in Fig. 4 provides empirical evidence for this condition. Under exact scoring among feasible trajectories rfeasT^feas_r, Assumption 2 provides a guarantee on the recursive gain of sequential commitment, as formalized below. Theorem 1 (Recursive advantage over parallel counterfactual plan). Let Dr≜J(rseq)−J(∥)D_r J(T^seq_r)-J(T ). Under Assumption 2, Dr+1≥Dr+ηrrCF.D_r+1≥ D_r+ _rG^CF_r. Consequently, under Assumption 1, if rCF≥0G^CF_r≥ 0, the sequential gain over ∥T is nondecreasing from round r to round r+1r+1. If rCF>0G^CF_r>0, it increases strictly. Proof. By Assumption 2, J(r+1seq)−J(rseq) J(T^seq_r+1)-J(T^seq_r) ≥ηrrCF. ≥ _rG^CF_r. Adding J(rseq)−J(∥)J(T^seq_r)-J(T ) to both sides yields J(r+1seq)−J(∥) J(T^seq_r+1)-J(T ) ≥J(rseq)−J(∥)+ηrrCF. ≥ J(T^seq_r)-J(T )+ _rG^CF_r. Thus, Dr+1≥Dr+ηrrCFD_r+1≥ D_r+ _rG^CF_r. Since 0<ηr≤10< _r≤ 1, rCF≥0G^CF_r≥ 0 in Assumption 1 implies Dr+1≥DrD_r+1≥ D_r, and rCF>0G^CF_r>0 implies Dr+1>DrD_r+1>D_r. ∎ This guarantee provides a reference for the learned radio world model. We next assume sequential proposal effectiveness and bounded election regret, under which WONDER approaches the ideal recursive gain up to a regret ϵr _r. Assumption 3 (Proposal effectiveness of the sequential choice). For commit rounds r, WONDER’s proposal pool contains the trajectory selected by the ideal sequential rule: τrcom∈r,θglobal. τ^com_r ^global_r,W_θ. When WONDER selects from this pool under the same committed context, its chosen trajectory τr,θcomτ^com_r,W_θ incurs at most ϵr _r selection regret: ΔCF(τrcom,base⊕<rcom) ^CF(τ^com_r;T^base ^com_<r) −ΔCF(τr,θcom,base⊕<rcom) - ^CF(τ^com_r,W_θ;T^base ^com_<r) ≤ϵr,ϵr≥0. ≤ _r, _r≥ 0. The recall diagnostic in Fig. 10 provides empirical evidence for this condition. We now define the sequential plan r,θseqT^seq_r,W_θ induced by WONDER under the learned radio world model. After r committed rounds, its plan state and one-step update are r,θseq ^seq_r,W_θ =base⊕<rcom, =T^base ^com_<r, r+1,θseq ^seq_r+1,W_θ =r,θseq⊕τr,θcom. =T^seq_r,W_θ τ^com_r,W_θ. and define Dr,θ≜J(r,θseq)−J(∥)D_r,W_θ J(T^seq_r,W_θ)-J(T ). We can have the following theorem Theorem 2 (Recursive gain of WONDER). Under Assumptions 1, 2, 3, Dr+1,θ D_r+1,W_θ ≥Dr,θ+ηrrCF−ϵr. ≥ D_r,W_θ+ _rG^CF_r- _r. Proof. Theorem 1 states that the ideal sequential choice recovers at least ηrrCF _rG^CF_r. By Assumption 3, this trajectory is available in r,θglobalT^global_r,W_θ. Because r,θseq=base⊕<rcomT^seq_r,W_θ=T^base ^com_<r, Definition 1 makes ΔCF ^CF the one-step J increment in the WONDER comparison. Assumption 3 further implies that the WONDER step loses at most ϵr _r relative to the ideal step. Hence, the WONDER step recovers at least ηrrCF−ϵr _rG^CF_r- _r. Adding this recovered amount to Dr,θD_r,W_θ gives the recursion. ∎ Remark. By iterating the round-wise recursion and using 0seq=∥T^seq_0=T , the ideal sequential plan satisfies J(rseq)−J(∥) J(T^seq_r)-J(T ) ≥∑t=0r−1ηttCF. ≥ _t=0^r-1 _tG^CF_t. Thus, when the recursive composition gaps are nonnegative, sequential negotiation gives an advantage over the parallel counterfactual plan. Under assumptions on proposal effectiveness and bounded selection regret, WONDER satisfies the corresponding regret-adjusted bound, J(r,θseq)−J(∥) J(T^seq_r,W_θ)-J(T ) ≥∑t=0r−1(ηttCF−ϵt). ≥ _t=0^r-1 ( _tG^CF_t- _t ). Therefore, WONDER approaches the sequential-plan advantage up to the cumulative selection regret ∑t=0r−1ϵt _t=0^r-1 _t in the negotiation rounds where the radio world model is highly confident and the proposal coverage is empirically verified. VI Experiment Settings and Results VI-A Experimental Setup Fig. 6: Visualization of RadioDynamics closed-loop rollouts. Panels are recorded every five timesteps; the red time axis aligns the panels with rollout time, and the bottom curve reports the corresponding balanced score. The first to third rows show rollouts controlled by Flocking, STACCA, and WONDER, respectively. TABLE I: Simulation and benchmark parameters. Description Notation Value Ground service area ╱ 700×700700× 700 m2 Ground grid ╱ 350×350350× 350 Cell resolution ╱ 22 m A2G bandwidth B 100100 MHz [26] A2A carrier frequency fcf_c 3.53.5 GHz [1] A2A transmit power PiA2AP_i^A2A 2323 dBm A2A antenna gain Gi,GjG_i,G_j 00 dBi omnidirectional LoS indicator ℓij,t _ij,t LoS test over Ω Effective UAV antenna height heffh_eff 7070 m [1] Receiver height ╱ 1.51.5 m [1] A2G carrier frequency ╱ 3.53.5 GHz [26] A2G RS EIRP PirsP_i^rs 2525 dBm A2G antenna convention ╱ Omnidirectional, gain absorbed into EIRP A2A nominal bandwidth ╱ 2020 MHz [13] A2A link threshold ρlink _link −90-90 dBm Backhaul direct-access threshold ρbh _bh Calibrated to 150150 m horizontal radius Backhaul gateway mode ╱ Master/remote/relay Material reflection coefficient Assigned via height ╱ Concrete: 0.60.6, ≤15≤ 15 m Glass: 0.40.4, 1515–4040 m Metal: 0.850.85, >40>40 m Synchronization interval H 55 steps Number of UAVs N 1010 Candidate trajectories |feas||T^feas| 6161 Local Observation dimension dim(oiloc) (o^loc_i) 224224 Flocking and Learned steps Nwarm,NlearnN_warm,N_learn 15,3015,30 steps Coverage threshold ρcov _cov −90-90 dBm [2] SINR threshold ϕSINR _SINR 00 dB Balanced-score weights w 0.25,0.10,0.20,0.20,0.25,0.10,0.20,0.20, 0.10,0.10,−0.050.10,0.10,-0.05 Flocking scoring weights λsep,λcrowd,λdeg gathered _sep, _crowd, _deg gathered (0.25,0.6,0.3)(0.25,0.6,0.3) TABLE IV: Training parameters. Description Notation Value Candidate proposal per reduction KcK_c 33 Relay-depth bound depK_dep 22 hops Negotiation-round limit R 33 JEPA continuity constants τcoh,εz _coh, _z (0.25,10−8)(0.25,10^-8) Connectivity penalty λc _c 1.01.0 PPO constants ϵclip,cv,ce gathered _clip,c_v,c_e gathered (0.2,0.5,0.01)(0.2,0.5,0.01) Fig. 7: Closed-loop performance under the shared RadioDynamics evaluation. Fair baselines are shown in blue, WONDER in red, and Exhausted references in gray. The balanced score summarizes the normalized metric vector. We adopt 6262 metropolitan scenes, such as Hong Kong, New York, and Tokyo, for RadioDynamics construction, as illustrated in Fig. 1. The digital-twin pipeline first converts OpenStreetMap geometry into mesh-based city models and exports the scene assets to Sionna RT. Sionna RT first assigns empirically selected concrete, glass, and metal materials to the city models based on building height, and then precomputes the ground-level RSRP field for each transmitter setting. Each scene stores these transmitter settings together with the resulting dense RSRP fields. The configuration is summarized in Table I, while the training-related parameters are given in Table IV. The 6262 scenes are further split into 4242 training scenes, 99 validation scenes, and 1111 test scenes, with 44 entries per scene. Each method is trained with seed 00 and evaluated with seeds 0,…,5\0,…,5\. For testing, all methods first use Flocking for Nwarm=15N_warm=15 steps to spread the swarm, and the evaluated algorithm then runs for Nlearn=30N_learn=30 steps from the same warm-up state. At each step, the scene-aware A2A graph is updated from the UAV positions, digital-twin line of sight, and the link-budget feasibility rule in Section I. All experiments use the metrics defined in Section I, namely RSRP coverage, 5th-percentile delivered rate, SINR coverage, mean delivered rate, Jain fairness, backhaul connectivity, and mean interference. The balanced score uses the weights listed in Table I. The deployment uses separate radios for A2G service broadcast, A2A swarm relay, and ground backhaul. A temporary backhaul point is placed at the terminal gateway, where a representative digital modem serves as the gateway and the same modem on UAVs serves as the remote or relay node. Each UAV carries an A2G service-radio payload for producing the RSRP footprint, represented by a Canopy 5GID1 n78 small-cell radio envelope for the 3.53.5-GHz, 100100-MHz, 2525-dBm-EIRP setting [26]. Inter-UAV proposal exchange is carried by an A2A mesh radio, represented by Mesh Rider Mini, with SL5200 as a higher-end MANET alternative [13]. A UAV beyond the 150150-m direct-root radius reaches the gateway through an A2A relay path to a gateway-attached UAV. We select representative MARL and communication-bottleneck methods as the primary baselines. MAPPO [40], STACCA [31], and heuristic-based Flocking [5, 37, 8, 24] use the shared static scene prior and deployment-visible local observations without multi-hop communication. MAGI [12] and ours use the deployment-feasible communication interface, including one-hop communication, topology, and selected trajectories. The ground-truth Reference Signal Received Power (RSRP) is not visible to deployable methods. We also evaluate an Exhausted method under an oracle view with complete swarm and evaluator-side RSRP information. Both variants are evaluated from the same 66 seed-induced initial states: the Parallel variant lets all agents choose synchronously, while its Sequential variant lets them choose one after another in a fixed order. VI-B Experiemental Results VI-B1 Performance Superiority Fig. 6 first illustrates a representative scene-level rollout, linking the UAV motion, RSRP field, A2A relay topology, and the bottom Score curve. During the flock warm-up stage as in Fig. 2, the UAVs spread from the initial cluster over the first 15 steps and form a broader relay structure over the city scene. Afterward, the three rollout behaviors emerge: Flocking keeps dispersing but encounters disconnection at t=35t=35, while STACCA fluctuates due to counterfactual mismatch. WONDER instead achieves steady improvement, adjusts the swarm layout while preserving relay links, and continues increasing the score until the final step. In this scene, the WONDER trajectory ends with a 0.4130.413 score advantage over Flocking and 0.1620.162 over STACCA. We further evaluate all 77 methods under the same closed-loop protocol and report averaged results in Fig. 7. Fig. 7 shows that WONDER attains the highest balanced score. The gain over heuristic-based Flocking comes from limiting excessive swarm dispersion, while the gain over STACCA comes from resolving conflicts among locally selected counterfactual decisions. Compared with Sequential Exhausted, WONDER further benefits from its negotiated decision order, which avoids the local optima caused by fixed-order decisions in building-dense scenarios, which is demonstrated in Fig. 8. Fig. 8: Representative cases where our method outperforms Sequential Exhausted. Sequential Exhausted visits UAVs in a fixed order and greedily commits each visited UAV’s locally best action. The gray actions yield marginal gain, while the yellow actions would produce higher global gain if committed earlier. Our method prioritizes the yellow actions through proposal-level negotiation, avoiding the local optimum induced by fixed-order greedy selection. VI-B2 Feasibility Study As discussed in Appendix A, Table V assesses whether the proposed communication mechanism can be carried by representative radios, by counting the payloads of local-vector exchange, WONDER proposal aggregation, and raw full-map transfer under the same topology. Compared to STACCA, WONDER adds 147.456147.456 kbit of proposal-aggregation payload per synchronization round, resulting in a total of 270.336270.336 kbit. Using the 8080 Mbps A2A entry [13] as a nominal reference, a 11-s deployment step provides 400400 Mbit over the 55-step synchronization round. The WONDER total therefore uses only 0.0676%0.0676\% of this nominal round capacity, indicating that the communication load is well within the bandwidth of the listed devices while yielding superior coverage performance. TABLE V: Payload upper bounds for message exchange. Entry Scope No. of Messages Payload (kbit) STACCA [31] Local vectors 120120 122.88122.88 MAGI [12] Neighborhood Message 120120 245.76245.76 WONDER Local + proposal 264264 270.336270.336 Full Connection Full Radio Map (raw) 120120 470400470400 VI-B3 Ablation Analysis Fig. 9 further confirms that the JEPA Radio World Model and the Direct Ranking (DR) variant, which uses the same backbone network and removes ℒalignL_align, both converge during local proposal training. Fig. 10 then evaluates whether the union of locally retained Top-KcK_c candidates contains the globally counterfactual best action over the 33 negotiation rounds. At Kc=3K_c=3, JEPA achieves 99.62%99.62\% recall, outperforming DR by 4.92%4.92\%, demonstrating that local Top-33 retention is sufficient for reliable subsequent election. Fig. 9: Training curves for JEPA and DR local proposal models. Fig. 10: Offline recall of retained proposals for JEPA and DR. Fig. 11: Training curve of the election policy. TABLE VI: Ablation analysis of the main WONDER components under the shared evaluation setting. Method Coverage Area (%) Mean Rate (Mbps) 5% Edge Rate (Mbps) SINR Coverage (%) Mean Interference (%) Jain Fairness (%) Connectivity (%) Balanced Score w/o JEPA Encoder 43.1 300.8 0.00357 38.5 0.98 29.8 66.5 0.659 w/o Election Module 44.5 322.2 0.00381 41.0 0.94 31.7 68.4 0.708 w/o Alternating update 49.4 353.2 0.00420 45.0 0.85 35.0 75.7 0.808 w/o Multi-Round Negotiation 48.3 343.3 0.00408 44.5 0.87 34.1 74.0 0.784 Our full method 52.2 362.5 0.00400 47.5 0.89 33.4 100.0 0.870 Table VI reports the main ablation results for WONDER. It compares the full method with four variants: replacing JEPA with DR, replacing the Election Module with deterministic reduction, applying JEPA encoding only in the first negotiation round without subsequent representation updates, and removing the alternating update procedure. The full method achieves the highest balanced score, 0.8700.870, which is 7.67%7.67\% higher than the strongest ablation, the variant without alternating updates, and is the only variant that reaches 100%100\% connectivity. Across the ablations, removing JEPA, learned election, alternating optimization, or multi-round negotiation reduces the balanced score to 0.6590.659, 0.7080.708, 0.8080.808, and 0.7840.784, respectively, indicating that each component is associated with a measurable loss in closed-loop performance when omitted or replaced. Fig. 11 provides complementary evidence through the later-stage training curve of the election policy. The trend after alternating refinement is consistent with the table-level gain of the full method, suggesting that alternating optimization helps WONDER balance coverage, rate, connectivity, and interference in the evaluated closed-loop setting. VII Conclusion This paper has studied deployable multi-UAV coverage restoration under the joint difficulty of hidden radio consequences and sparse inter-UAV communication. To address the resulting radio observations and local-global coordination asymmetries, WONDER has introduced a JEPA-based radio world model to predict candidate trajectories’ incremental radio consequences under the evolving negotiation context, while multi-round negotiation benefits the PPO-based election actor to generate superior policy. The empirical analysis identifies the counterfactual composition gap caused by the synchronized execution of individually evaluated proposals, and the theoretical analysis then shows that recursively sequential commitment admits an advantage over the parallel counterfactual plan, which applies to WONDER up to bounded election regret when proposal coverage holds. Moreover, we have built RadioDynamics, a comprehensive simulation environment that integrates UAV mobility, radio propagation, inter-UAV communication modeling, and digital-twin geometry with ray-traced fields in 6262 metropolitan scenes. On 1111 testing scenes of RadioDynamics, WONDER has achieved the highest balanced score among the evaluated methods (0.8700.870) and reached 100%100\% gateway connectivity, validating its superiority. Appendix A Communication Payload Calculation A-A Communication Accounting for Local Vectors and WONDER Proposals We derive the payload upper bounds summarized in Tab. V by counting the transmitted entries in each local vector and each WONDER message. We use a representative audited topology that partitions the swarm into subgraphs of sizes 33, 44, and 33, which gives ∑q∈3,4,3q(q−1)=24 _q∈\3,4,3\q(q-1)=24 directed transmissions per local exchange. A synchronization round therefore has the shared local-aggregation factor 5×245× 24 for methods that aggregate over the local topology. STACCA and WONDER local aggregation are counted with the 3232-float component size in Table I, MAGI uses 6464-float messages, and Full Connection transfers a 350×350350× 350 RSRP map. WONDER message aggregation is counted separately with R=3R=3, Kc=3K_c=3, and dep=2K_dep=2 from Table IV, giving up to 3×[(10×3)+(3×3×2)]×323×[(10× 3)+(3× 3× 2)]× 32 float32 values. Thus, STACCA, MAGI, WONDER, and Full Connection contain 5×24×325× 24× 32, 5×24×645× 24× 64, 3×[(10×3)+(3×3×2)]×323×[(10× 3)+(3× 3× 2)]× 32, and 5×24×(350×350)5× 24×(350× 350) float32 values, respectively. Multiplying these counts by 3232 bits gives the table payloads. Full Connection requires 1.74×1031.74× 10^3 times the WONDER total payload. Appendix B Detailed Loss Function B-A JEPA Radio World Model Objectives We use the rollout-induced target score υi,kr _i,k^r defined in (14). Let k∗k^* be denote the best trajectory index for UAV i in round r, the auxiliary ranking loss is ℒrank=−i,r[logexp(υi,k∗r/σscore)∑k′:τi,k′∈rfeasexp(υi,k′r/σscore)].L_rank=-E_i,r [ \! ( _i,k^*^r/ _score ) _k : _i,k ^feas_r \! ( _i,k ^r/ _score ) ]. (21) Here, the expectation is over active UAV-round pairs, and σscore>0 _score>0 is the fixed score-normalization constant used for the trajectory-score head. B-B Election Module Objective This subsection gives the detailed objective used to train the election module ϕA_φ after the JEPA Radio World Model is fixed. At synchronization step t and election round r, the deterministic reductions produce the global trajectory pool rglobalT^global_r, and ϕA_φ selects either one trajectory from this pool or ends the negotiation. Let trT_t^r denote the partial joint plan before round r. If a trajectory is selected, let τrcomτ^com_r be the trajectory contained in that trajectory; the post-election plan is tr+1=tr⊕τrcomT_t^r+1=T_t^r τ^com_r. The reward is defined by balanced-objective improvement with a penalty for gateway-connectivity violation: r r =⊤[(St+H,e)|tr+1−(St+H,e)|tr] =w \! [ μ(S_t+H;e) |_T_t^r+1- μ(S_t+H;e) |_T_t^r ] −λc[1−C(St+H,e)|tr+1]. - _c\! [1-C(S_t+H;e) |_T_t^r+1 ]. where the restriction |tr |_T_t^r means that the terminal metric vector is evaluated after executing trT_t^r over the synchronization horizon. The connectivity term penalizes violation of the hard gateway-connectivity requirement in (10), with weight λc _c. If ϕA_φ selects to end negotiation, the transition reward is set to zero. The election module is optimized with the PPO objective ℒElection=ℒclip+cvℒvalue−ceℋEA.L_Election=L_clip+c_vL_value-c_eH_EA. (22) Here, cvc_v and cec_e weight the value-loss and entropy terms, respectively. The clipped policy loss is ℒclip _clip =−r[min(ρr(ϕ)Ar,clip(ρr(ϕ),1−ϵclip,1+ϵclip)Ar)], =-E_r\! [ \! ( aligned & _r(φ)A_r,\\ &clip\! 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