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Social Learning Strategies for Evolved Virtual Soft Robots
K. Ege de Bruin, Kyrre Glette, Kai Olav Ellefsen, Giorgia Nadizar, Eric Medvet
Intelligence
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Summary
The paper investigates Social Learning (SL) strategies for optimizing the body and brain of Virtual Soft Robots (VSRs). Using a nested loop of Genetic Algorithms (GA) for morphology and Bayesian Optimization (BO) for control, the researchers compare various SL strategies (Parent, Best, Similar, and Random, each with 'One' or 'Many' teachers) against Individual Learning (IL). The study demonstrates that social learning, particularly inheriting experience from morphologically similar peers, outperforms learning from scratch and provides more robust improvements in the co-evolution of robot morphology and control.
Entities (7)
Relation Signals (5)
Virtual Soft Robot → hascomponent → Morphology
confidence 100% · A VSR is defined by its morphology and its controller
Virtual Soft Robot → hascomponent → Controller
confidence 100% · A VSR is defined by its morphology and its controller
Bayesian Optimization → optimizes → Controller
confidence 100% · We use Bayesian optimization (BO) for controller optimization
Genetic Algorithm → optimizes → Morphology
confidence 100% · For body evolution, we resort to a standard GA.
Social Learning → uses → Bayesian Optimization
confidence 90% · We use Bayesian optimization (BO) for controller optimization... We define SL as the transfer of samples from one or more robots to another robot.
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Abstract
Abstract:Optimizing the body and brain of a robot is a coupled challenge: the morphology determines what control strategies are effective, while the control parameters influence how well the morphology performs. This joint optimization can be done through nested loops of evolutionary and learning processes, where the control parameters of each robot are learned independently. However, the control parameters learned by one robot may contain valuable information for others. Thus, we introduce a social learning approach in which robots can exploit optimized parameters from their peers to accelerate their own brain optimization. Within this framework, we systematically investigate how the selection of teachers, deciding which and how many robots to learn from, affects performance, experimenting with virtual soft robots in four tasks and environments. In particular, we study the effect of inheriting experience from morphologically similar robots due to the tightly coupled body and brain in robot optimization. Our results confirm the effectiveness of building on others' experience, as social learning clearly outperforms learning from scratch under equivalent computational budgets. In addition, while the optimal teacher selection strategy remains open, our findings suggest that incorporating knowledge from multiple teachers can yield more consistent and robust improvements.
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- Source: https://arxiv.org/abs/2604.12482v2
- Canonical: https://arxiv.org/abs/2604.12482v2
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Social Learning Strategies for Evolved Virtual Soft Robots K. Ege de Bruin eged@ifi.uio.no Department of Informatics, University of Oslo Oslo, Norway Kyrre Glette ∗ kyrrehg@ifi.uio.no Department of Informatics, University of Oslo Oslo, Norway Kai Olav Ellefsen kaiolae@ifi.uio.no Department of Informatics, University of Oslo Oslo, Norway Giorgia Nadizar giorgia.nadizar@irit.fr University Toulouse Capitole, IRIT - CNRS UMR5505 Toulouse, France Eric Medvet emedvet@units.it University of Trieste Trieste, Italy SL IL Init candidatesNew candidates · Brain samples · Brain samples · Brain samples Population Mutation · BO · BO Brain samples Evaluate T Fitness Best sample Figure 1: Overview of the social learning (SL) approach. When a new virtual soft robot (VSR) is generated through mutation, we need to optimize its brain. We use Bayesian optimization, which works by using initial samples (i.e., initial evaluated brains) to predict new candidates (i.e., new brains). The best sample is then used as the VSR brain to determine its fitness. With SL, initial candidates are obtained by inheriting samples from other VSRs in the population. This differs from a standard case, individual learning (IL), where initial candidates are independent from other robots. Several strategies exist for selecting which samples to inherit; in this figure we show inheritance of one sample from the most similar robots in the previous generation (we call this “Similar-many”, see Section 4.2). Abstract Optimizing the body and brain of a robot is a coupled challenge: the morphology determines what control strategies are effective, while the control parameters influence how well the morphology performs. This joint optimization can be done through nested loops of evolutionary and learning processes, where the control parame- ters of each robot are learned independently. However, the control parameters learned by one robot may contain valuable informa- tion for others. Thus, we introduce a social learning approach in which robots can exploit optimized parameters from their peers to accelerate their own brain optimization. Within this framework, we systematically investigate how the selection of teachers, deciding which and how many robots to learn from, affects performance, experimenting with virtual soft robots in four tasks and environ- ments. In particular, we study the effect of inheriting experience ∗ Also with RITMO, University of Oslo. from morphologically similar robots due to the tightly coupled body and brain in robot optimization. Our results confirm the effective- ness of building on others’ experience, as social learning clearly outperforms learning from scratch under equivalent computational budgets. In addition, while the optimal teacher selection strategy remains open, our findings suggest that incorporating knowledge from multiple teachers can yield more consistent and robust im- provements. Keywords Social learning, Bayesian optimization, Body-brain robot optimiza- tion, Modular robots Accepted at the Genetic and Evolutionary Computation Conference (GECCO 2026). This is the author’s version of the work. The final version will be available via the ACM Digital Library. arXiv:2604.12482v2 [cs.RO] 17 Apr 2026 K. Ege de Bruin, Kyrre Glette, Kai Olav Ellefsen, Giorgia Nadizar, and Eric Medvet 1 Introduction In evolutionary robotics (ER), evolutionary algorithms (EAs) are used to optimize robot or virtual creature design and control [6,16, 30,47,55]. The EA needs to traverse a more complex search space due to the intertwined body and brain [41]. Consequently, there might be a mismatch between control and robot morphology, and a robot morphology might be discarded because it has not been performing to its full potential due to poor control [7, 32, 38]. To deal with this problem, often morphology and controller optimization are separated from each other. For example, this can be done with an outer evolutionary loop, to optimize morphologies, and an inner learning loop, where all morphologies go through a controller optimization phase [13]. Adding a learning loop is an efficient way to find well-performing robots [18,32,42,50]. This is because new robot morphologies have more chance to reach more of their potential. This does, however, come at the cost of requiring more resources to optimize a robot controller [11, 45]. If every new robot morphology goes through a controller-learn- ing phase, one could follow a Darwinian approach, where control parameters are either randomly initialized for every robot morphol- ogy [18], or offspring robots inherit initial control parameters from parents [42]. However, this loses learned information new robots could use. If a robot has good control parameters after learning, these learned parameters might be useful for other robots as well. This is where a Lamarckian approach, where optimized control parameters are transferred from parent to offspring, could be used. In previous work, it has been shown that Lamarckian inheritance can improve performance [19,23,31]. However, it is not necessary to limit the transfer of learned information from parent to offspring. One can extend such transfer to social learning (SL) [4,21,25,44,52], where information can be exchanged from any robot to any other robot. This is similar to a cultural algorithm, where information is centrally gathered and distributed [20, 53]. In this work, we look into SL for evolving virtual soft robots (VSRs) and compare SL strategies. We use Bayesian optimization (BO) for controller optimization, as it provides a flexible frame- work for both individual learning (IL) and SL. Moreover, BO has been shown to have a fast learning capability and sample effi- ciency [5,11,12,26,56]. In BO, controller parameters, along with their observed quality (their objective value), are treated as sam- ples. Previous samples are then combined with a prior to predict the most promising candidate controller parameters to evaluate. BO uses the previously observed qualities and general uncertainty to predict promising candidates. We define SL as the transfer of samples from one or more robots to another robot, allowing a robot to learn from the samples of others rather than learning solely from its own samples. One aspect we consider for selecting robots to learn from is morphological similarity. Morphology and control are tightly coupled in embodied agents [49,55], such that morpho- logically similar robots often require similar control strategies for good performance [35,40]. Therefore, controllers that perform well for one robot are likely to transfer effectively to morphologically similar robots. The goal of this paper is to explore the role of SL in ER and to better understand the conditions under which it is beneficial. We consider how SL mechanisms, such as similarity and performance, and how the number of teachers influence overall performance and robot design. This will guide our study and provide a framework for analyzing how different forms of SL interact with the dynamics of ER. 2 Related work 2.1 Controller inheritance In previous work, it has been shown that adding controller opti- mization, also known as learning, for each morphology in ER can improve performance [11,32,42]. Controller optimization can be made more efficient by allowing optimized controller parameters to be exchanged between robots. A common form of controller exchange is to inherit optimized controller parameters from parent to offspring, often described as Lamarckian inheritance. Studies have demonstrated the advantages of Lamarckian evolution over Darwinian evolution. Jelisavcic et al. [23]showed that inheriting optimized controllers, rather than initial populations, improves per- formance. Similarly, Luo et al. [31]found that passing optimized parameters to offspring enhances adaptation. Moreover, Harada and Iba[19]use a transfer learning approach from parents to off- spring where artificial neural network (ANN) weights are shared, and this improves performance over when weights are not shared. It is not required to exchange information only from parent to offspring. For other strategies, we distinguish between a cultural approach and a social approach. In a cultural approach, informa- tion among generations is centrally gathered and exchanged [20]. Le Goff et al. [27]keep an archive of learned controllers, where new robots only inherit learned control parameters from older robots with the same number of sensors and actuators. Mertan and Cheney [39]teach a single controller using a diverse set of morphologies, which can then be used for the control of new morphologies. In a social approach, control parameters are directly transferred from robot to robot. Heinerman et al. [21]apply SL to a population of morphologically identical robots, and show that adding SL leads to better controllers faster, and that a combination of IL and SL is beneficial. Our work differs in that we also evolve and change morphology. Finally, in a non-robotics artificial life setting, Bartoli et al. [1]show that a small set of good teachers is most beneficial, and that the teacher, rather than the learner, should choose which samples to transfer. 2.2 Bayesian optimization (BO) For optimizing robot controllers, we apply BO [43], which is known for its sample efficiency, and its ability to balance the exploration- exploitation trade-off. BO is computationally expensive for high- dimensional problems with many samples, and it has been explored for morphology optimization in the same scenario (i.e., VSRs) we are working on [3]. In that study, BO was evaluated and compared to other optimization methods for morphology optimization, and a genetic algorithm (GA) showed better performance. It is shown by van Diggelen et al. [56]that BO can perform well on robotic control optimization, outperforming an evolution strategy. Lan et al. [26]show that BO works well at the start of a controller optimization process, but loses its advantage with more samples due to the previously mentioned computational complexity. A Bayesian process can be improved by exploiting priors, where the process of Social learning for Evolved VSRs controller learning can be kick-started using other information [5]. An example of this is using morphological parameters within the Bayesian controller optimization process [29]. This allows the BO process to take into account both body and controller characteristics when deciding where to explore next, and over generations this can improve controller optimization using morphological properties. In our work, we do not use morphological parameters to improve the BO process, instead we use controller information from previous robots in a similar manner as previous work [12]. 3 Background 3.1 Virtual soft robots (VSRs) For this study, we use as agents a kind of simulated modular soft robots known as VSRs (also named voxel-based soft robots [22,28, 38]). A VSR is defined by its morphology and its controller, also known as body and brain. We simulate VSRs in 2-D space and discrete time, using Evolution Gym [3]. 3.1.1 VSR body. The body of a VSR is described by a polyomino—a geometric shape composed of connected unit squares represented in a 2-D grid—of at most 5×5 units (voxels) linked together. A voxel can be non-actuated (or) or actuated (or). Non-actuated voxels can be rigid () or soft (). During a simulation, rigid voxels never change their square shape; soft voxels change their shape based on external forces applied on them (e.g., gravity or other voxels pushing them). Actuated voxels can be horizontally actuated () or vertically actuated (); both are soft. During the simulation, the size of actuated voxels depends on external forces and an internal force that attempts to shrink or expand the voxel along the horizontal or vertical axis. In our work, the relative deformation of an active voxel along the actuated axis is limited to the range[0.6,1.6]. The brain of the VSR is in charge of determining the target deformation. From now on, we denote by 퐵 the set of VSR bodies. 3.1.2 VSR brain. The brain of a VSR is modular, distributed over the body, and based on ANNs [34,37]. Namely, we use the archi- tecture proposed in [37]. We put a multilayer perceptron (MLP) in each voxel. It takes as input: (a) the current values of the horizontal velocity, vertical velocity, and voxel area of all the voxels within a Moore neighborhood of 1, (b) the horizontal and vertical distance to the closest object to the voxel (not considering other voxels of the VSR), (c) and a periodic time signal푘 mod25,푘being the simu- lation time step. The input of the MLP is hence defined inR 30 , with 30=3·9+2+1. When no voxels are present in a given position of the neighborhood, we set the corresponding input values to 0. The output of the MLP is a single number which we use directly for actuating the voxel, if actuated, after having rescaled it to[0.6,1.6]. We use the same architecture (i.e., number of layers), activation functions, and biases and synaptic weights for all the MLPs. Specif- ically, we use a single inner layer with 10 neurons with ReLu as activation function, and we use the sigmoid function on the output neuron. The brain of the VSR can hence be described by the vector 휽 ∈R 321 of the biases and synaptic weights of the MLPs. We remark that, being composed of identical modules, this kind of brain is inherently transferable to any body, as the architecture of the MLPs is independent from the shape of the body. 3.2 Bayesian optimization (BO) BO is an iterative numerical optimization technique based on a surrogate model of the problem to be solved. Let푓:R 푝 →Rbe a black-box function, i.e., a function which can be applied (observed), but whose concrete structure is unknown, and let arg max 풙∈R 푝 푓 ( 풙 ) be a maximization problem based on 푓 . In brief, BO works as follows. Internally, it contains: (a) a sur- rogate function ˆ 푓 of푓which produces estimates with uncertainty: given an풙 ∈R 푝 , ˆ 푓 휇 (풙) is the estimated value of푓(풙)and ˆ 푓 휎 ( 풙 ) is the uncertainty of the estimate; (b) a procedure to obtain the surrogate from a set ( 풙 푖 , 푓 ( 풙 푖 )) 푖 of samples, which are pairs of candidate points and the corresponding observed values; (c) an acquisition function푎to obtain candidate points to evaluate next, using the surrogate function by means of ̄ 푥= arg max 푥∈X 푎(푥; ˆ 푓). Initially, BO starts with a set퐿 0 = 풙 푖 푖=푛 0 푖=1 of푛 0 initial candidate points—usually chosen according to a given probability distribu- tion. From this, it builds a set of samples퐿 ′ = ( 풙 푖 , 푓 ( 풙 푖 )) 푖=푛 0 푖=1 by observing the value푓 ( 풙 푖 ) for each candidate point in퐿 0 . Then, it iterates the following steps until the number|퐿 ′ |of samples is equal to some predefined푛 final : (i) it updates the surrogate function ˆ 푓 based on퐿 ′ , (i) it obtains a new candidate point ̄ 풙from ˆ 푓 using the acquisition function, (i) it observes the value푓 ( ̄ 풙 ) of푓at the new candidate point ̄ 풙, and (iv) it adds the sample ( ̄ 풙, 푓 ( ̄ 풙 )) to퐿 ′ . At the end, BO returns the sample 풙 ★ , 푓 풙 ★ ∈ 퐿 ′ with the largest observed value. The acquisition function plays a key role, as it balances the exploration-exploitation trade-off by attempting to produce a new candidate point ̄ 풙that is, at the same time, (a) good, i.e., with high ˆ 푓 휇 ( ̄ 풙 ) , and (b) uncertain, i.e., with high ˆ 푓 휎 ( ̄ 풙 ) , hence useful for improving the quality of the surrogate. On the other hand, the surrogate computation and update have to be fast with respect to the computation of 푓 . There are several options for the various components of BO. In this work, we use the Matern 5/2 kernel with a length scale of 10 as the surrogate function ˆ 푓and the upper confidence bound as the acquisition function, with an exploration variable of 3, which we optimize using the L-BFGS-B algorithm [58]. These settings have been used and worked well for optimizing the controller of robots for directed locomotion [11,12,26,56], and worked well in our preliminary experiments. 3.2.1 BO as a form of learning. In the context of an agent interact- ing with an environment and attempting to perform a given task, BO can be seen as a form of learning. Let휽 ∈R 푝 be a parametrization of the policy of the agent, i.e., of its brain. We can see푓as a way to measure the degree푓 ( 휽 ) to which an agent with a given brain휽successfully completes the task. Applying푓requires deploying the agent in a real or simulated scenario and let it produce a behavior, out of which its quality 푓 ( 휽 ) ∈R is extracted. Computing 푓 is usually very costly. More broadly, different휽 1 ,휽 2 , . . .represent candidate parameter sets (the candidate points in the BO process) for the brain and ob- taining the respective observations푓 ( 휽 1 ) , 푓 ( 휽 2 ) , . . .corresponds to the agent interacting and gaining experience about the environ- ment, i.e., learning. In other words, a휽is “what to try” and푓 ( 휽 ) is “what is the outcome”. Based on this intuition, we show in the next K. Ege de Bruin, Kyrre Glette, Kai Olav Ellefsen, Giorgia Nadizar, and Eric Medvet section how we can use BO to model social learning by exploiting the fact that agents can ask other agents “what to try”, possibly building on their experience and learning from it. 4 Social learning with BO for VSRs We co-optimize the body and brain of VSRs by using evolution for optimizing the bodies and BO for optimizing the brains. Figure 1 sketches our approach. We assume that푞:퐵×R 321 →Ris the function to be maximized and corresponds to the task, representing the quality of candidate VSR. That is,푞 ( 푏,휽 ) measures how well a VSR with a body푏 ∈ 퐵 and a brain 휽 ∈R 321 performs the task. 4.1 Body evolution For body evolution, we resort to a standard GA. We start with a population of푛 pop =200 bodies obtained with random initialization (explained below). Then, we repeat the following steps for푛 gen =50 times (generations): (i) we evaluate each body in the population; (i) we generate an offspring of푛 pop new bodies, each one obtained by selecting one parent from the current population with tourna- ment selection with푛 tour =4 tournament size and then applying a mutation operator (see below); (i) we replace all the parents with the offspring to obtain the new population. For evaluating a body푏, we pair it with a brain, which we opti- mize through learning, and assign to the body the quality푞 푏,휽 ★ it obtained with the learned brain 휽 ★ . During the evolution, we internally represent bodies as 5×5 matrices of elements defined in the alphabet of five symbols푉= ∅,,,,,∅representing no voxel at a given position. I.e., the genotype space in our GA is푉 5×5 . When randomly generating initial bodies, we proceed as follows: (i) we set all the elements of the matrix to empty (i.e.,∅), (i) we choose a random position in the matrix and a target number in[10,20] ⊂Nof voxels for the body, (i) we put a randomly chosen (i.e.,∼ 푈 ( ,,, ) voxel in the random position and iteratively add voxels in new positions adjacent with non-empty ones until reaching the target number of voxels; this way, we obtain a valid polyomino of at least 10 and at most 20 voxels. When mutating a matrix풗 ∈ 푉 5×5 , we change one, two, or three random elements of풗to a different symbol of푉. If the result is not a polyomino (e.g., there are more than one polyominoes in the matrix), or if the polyomino has less than 5 voxels or more than 25 voxels, we revert the mutation and try another one. Other representations exist for VSR bodies, e.g., more indirect [8] or grammar-based [36] ones: we decide to opt for this simple representation to keep the focus on the learning part. Previous work also proved it to be effective [37]. 4.2 Brain learning For learning the brain, we resort to BO, which we cast as SL by providing the initial candidate controller parameter sets based on samples from other VSRs. This works the same as the inherit sam- ples method in previous work [12], only instead of transferring samples only from parent to offspring, we compare different SL strategies. Recall that in the BO process, a sample consists of a pair of a candidate point and its observed value, which in the VSR context corresponds to a candidate set of controller parameters and its quality푞. We compose the starting set퐿 0 of candidates by taking 푛 0 =8 samples from the VSRs of the previous generation and using their candidate controller parameter sets (at the first generation these candidates are random). Then we execute BO as explained in Section 3.2, until reaching a number of푛 final =50 samples. Note that within the execution of BO,푓 ( 휽 ) is the degree of achievement of one body푏with the brain parametrization휽, i.e.,푓 ( 휽 ) =푞 ( 푏,휽 ) . For collecting the푛 0 initial candidates for a VSR with body푏, we experiment with seven approaches: ParentWe consider the parent of this VSR and we take its best 푛 0 samples, i.e., the controllers with the largest observed value. Best-OneWe consider the best VSR, i.e., the one with the largest푞, of the previous generation and we take its best푛 0 samples. Best-ManyWe consider the푛 0 best VSRs of the previous genera- tion and we take, for each one, its best sample. Similar-One We consider the most morphologically similar VSR to this푏in the previous generation and we take its best푛 0 samples. Similar-Many We consider the푛 0 the most morphologically sim- ilar VSRs of the previous generation and we take, for each one, its best sample. Random-OneWe consider one random VSR of the previous gen- eration and we take its best 푛 0 samples. Random-ManyWe consider푛 0 random VSRs of the previous generation and we take, for each one, its best sample. To measure the (dis)similarity between two bodies, we use the Ham- ming distance between the corresponding 5×5 matrices computed after having “re-aligned” the centers of mass of the two bodies. It can be noted that the six variants differ along two axes: (a) from which to learn from, i.e., who are the teachers (Best vs. Similar vs. Random), and (b) from how many teachers to learn from (One vs. Many, i.e.,푛 0 ). We remark that the amount of information the learner inherits is the same in all the cases, i.e.,푛 0 controller candi- dates. 4.3 Baseline: individual learning (IL) with inheritance For providing a baseline for our experiments, we consider a further body-brain co-optimization scheme where the learning is individual, not social. Here, BO is still used for learning the brain, but the initial candidate is stored in the genotype and evolved with the body by GA. In detail, we set the genotype space of GA to푉 5×5 ×R 321 . When we need to evaluate the quality of a VSR ( 푏,휽 ) , we use BO with the initial퐿 0 =휽and then we proceed as above. When initially generating genotypes or mutating them, we operate as above for the푏part of the pair ( 푏,휽 ) . For휽, we generate initial values by randomly sampling in[−1,1] 321 and we do mutation by applying a perturbation sampled from the multivariate normal distribution 푁(0,휎 mut 푰),푰 ∈R 321×321 being the identity matrix and휎 mut =0.1, i.e., we use the Gaussian mutation. Note that in this form of optimization the initial candidate is inherited from the parent VSR as genetic material, not inherited directly from the parent’s experience, as in the Parent variant de- scribed in the previous section. From another point of view, this Social learning for Evolved VSRs (a) Simple(b) Steps(c) Carry(d) Catch Figure 2: A snapshot of four episodes where a VSR performs the four tasks. form of optimization is Darwinian, whereas the Parent SL variant is Lamarckian: both take something from the parent, but the former looks at the parent at its birth (as it takes the genetic material, which does not change during the parent life), while the latter looks at the parent at the end of its life (as it takes the best experiences it collected through its interactions with the environment). 5 Experimental analysis We performed several experiments, i.e., optimization runs, for com- paring the seven forms of SL and the IL baseline. We compared the approaches in terms of their ability to produce successful VSRs in the task they are optimized for (Section 5.2). We analyzed in detail the morphological features of the optimized VSRs (Section 5.3). We also assessed the generalization ability, i.e., whether the VSRs the approaches produce can easily adapt to other tasks (Section 5.4). For reference, data [10] and code for our experiments are avail- able online at https://tinyurl.com/3rhzkm9t. 5.1 Tasks We consider four different tasks: Simple, Steps, Carry, and Catch. Figure 2 shows the corresponding environments with a VSR at- tempting to perform the task. In Simple, we put the VSR on a flat surface and assign a quality 푞to it which corresponds to the distance it run along the푥-axis in the episode (lasting 500 time steps). We compute the distance by considering the푥-coordinate of the center of mass of the VSR at the beginning (푘=0) and at the end (푘=500) of the episode. This is a form of locomotion, a classic benchmark in ER. Steps is another, slightly harder, form of locomotion. We place the VSR on a stepped surface, instead of a flat one. The quality is the same as the one of Simple. For both Simple and Steps, consistent with previous works which used these tasks, we disabled the brain inputs providing the horizontal and vertical distance to the closest object to each voxel (see Section 3.1.2). In the Carry task, the VSR is required to move while carrying an object. We initially place the VSR on a flat surface, as in Simple, but we additionally place an object (a rectangular box) on top of it. The quality푞is the푥-distance travelled by box, if it is still on top on the VSR at the end of the episode, or the negative푥-distance between the final position of the VSR and the box, otherwise. This way, we penalize behaviors where the VSR drops its payload. Finally, the Catch task is a harder version of the Carry task in which we make the payload fall from a random position above the VSR at the beginning of the episode. Namely, the initial푥-gap between the robot and box positions is not deterministic. The VSR is hence required to “see” the falling box, move to catch it, then move to carry it towards the right: the quality is the same as the one used in Carry. Due to the varying initial position of the payload, this is a changing, rather than static, environment: as such, it asks for a much greater generalization ability of the VSRs than the previous three tasks. 5.2 Effectiveness of the SL approaches We applied the eight (seven SL variants plus the IL baseline) ap- proaches to the four tasks, 20 times for each combination. To con- firm the effectiveness of using BO as a learning algorithm, for this analysis we also include another baseline, No-BO: in this variant, the 50 controllers evaluated during the learning are chosen randomly, not using BO—the final one used to assess the body is still the best one. This results in a total of nine approaches to be compared. We recall that we do푛 gen =50 generations of a population of푛 pop =200 VSRs for the evolution of the body and evaluate푛 final =50 con- troller parameter sets while optimizing the brain for each body. It follows that we performed 9·4·20·50·200·50=360 000 000 episodes. When comparing approaches, we use the Mann-Whithney U test [33] for statistical significance analysis with the Benjamini- Hochberg correction [2] and a significance level of 훼= 0.05. Figure 3 presents the results for this first experiment. It shows the distribution, across the 20 repetitions, of the quality푞 ★ of the best performing VSR observed during the entire evolution with a given approach on a given task. We recall that we use a genera- tional model without overlapping, i.e., we drop the parents at each generation: for measuring푞 ★ we hence retain the best VSR across all the generations. Figure 3 firstly shows that all BO methods outperform the No-BO baseline, which confirms that BO is efficient as a learning method. Moreover, the figure also shows that, in general, SL outperforms IL. With the exception of Random-One, every SL variant is signifi- cantly better than IL on at least three tasks. Random-Many is better than IL on all but the Steps tasks. All the remaining SL variants are always better than IL. This finding is sound: learning from a random teacher reveals to be not particularly better than having no teacher. One observation is that in our dynamic Catch task, we still see benefit of SL over IL. Related work outside robotics showed diminishing benefits of Lamarckian inheritance in dynamic envi- ronments [14,17,48,54]. Future work should look into the causes for this difference. Another interesting observation we draw from Figure 3 is that learning from more teachers is in general better than learning from just one teacher. We recall that the “amount of information” we transfer from the teacher(s) to the learner is the same, as we keep 푛 0 =8 in all SL variants. Despite the difference between the *-One and the *-Many variant is only occasionally statistically significant, this finding is sound and consistent with previous studies (e.g., [1] observed a similar outcome, yet for a much simpler kind of agents). Figure 3 highlights no differences between Best-* and Similar-* variants. We recall that choosing teachers based on morphological similarity is a peculiar opportunity enabled by our scenario, where we co-optimize the body and the brain. The hypothesis that learning from a morphologically similar agent might bring more useful experience than learning from a good, yet possibly very different, teacher is not supported by our experiments. We have not found K. Ege de Bruin, Kyrre Glette, Kai Olav Ellefsen, Giorgia Nadizar, and Eric Medvet 100 150 40 60 80 60 80 100 120 60 80 100 ★ ★ ★ ★ ★ ★ ★ ★ ★ Quality 푞 ★ Simple ★ ★ ★ ★ ★ ★ ★ ★ ★ Quality 푞 ★ Steps ★ ★ ★ ★ ★ ★ ★ ★ ★ Quality 푞 ★ Carry ★ ★ ★ ★ ★ ★ ★ ★ ★ Quality 푞 ★ Catch No-BOBest-OneBest-Many ILSimilar-OneSimilar-Many ParentRandom-OneRandom-Many Figure 3: Distribution of the quality푞 ★ of the best-performing VSR in the four tasks for the eight approaches. Stars above the boxes show significant differences: for example, a red star on top of a gray box indicates that IL is significantly different from Best-One. clear motivations for this missed observation. We hypothesize that the diversity of evolved bodies is not large enough to make Similar-* more convenient than Best-* (see next section). We leave to future work the investigation of strategies where diversity is promoted (with a quality-diversity (QD) [9,46] or a custom approach [51]) and teachers are chosen based on a combination of their quality and similarity. 5.3 Analysis of the VSR bodies We analyzed in deeper detail the bodies of the evolving VSRs, as we wanted to verify whether different SL variants lead to bodies evolving more or less diverse, or in different forms. We start by looking at the body diversity in the population during the evolution, which we show in Figure 4. For each evolutionary run and at each generation, we computed the average pairwise dissimilarity between bodies using the Hamming distance after 01020 304050 10 12 14 16 Generation Diversity Best-OneBest-Many ILSimilar-OneSimilar-Many ParentRandom-OneRandom-Many Figure 4: The evolution of the population diversity, averaged over runs and environments. The line corresponds to the mean value, the shaded area to the first-third quartile range. re-alignment (see Section 4.2)—the larger, the more diverse the population. Figure 4 shows no difference among the eight approaches. That is, regardless of the kind of learning (IL vs. SL) or of the criterion for choosing teachers in SL, VSR bodies tend to be equally diverse, with a drop in diversity during the evolution likely caused by the evolutionary pressure. We did a finer characterization of VSR bodies by computing two simple descriptors (i.e., numerical features) for each one of them and visualizing the bodies in a plane defined by those two descriptors. We measured the rate of active voxels (i.e., the count ofand divided by the count of,,, and) and the body compactness, i.e., the ratio between the body area and the area of the convex hull. We show the results of this analysis in Figure 5, which contains one marker for the best VSR optimized for every repetition, approach, and task. The figure shows that there are differences among VSR bodies optimized for different tasks. VSRs evolved for locomotion are in general more compact, in particular for the Steps task. Bodies optimized for carrying a payload (needed for both Carry and Catch) tend to have some protuberances (sort of “arms”) for keeping the payload steady, which make the body less compact—see Figure 6. This interpretation is qualitatively confirmed by Figure 7, where we show one random optimized VSR body chosen among the 20 repetitions for each approach-task combination. On the other hand, Figure 5 highlights no differences among approaches: different kinds of learning do not lead to different bodies, at least according to these descriptors. 5.4 Potential and transferability of VSR bodies Having verified that different forms of learning do not impact on body diversity, nor on the general shape for the VSR body (which is, instead, impacted by the task), we investigated the possibility that VSRs obtained with different approaches have different potential for learning. Here, we use “potential for learning” to quantify the performance of a VSR body with the “best” brain it can be paired with. For this purpose, we took all the 20 VSRs obtained for each approach and task and, for each one, we re-learned a new brain for the same task by using BO with a random starting controller parameter set and reaching푛 final =500 samples. We assume that Social learning for Evolved VSRs 0.6 0.8 1 0.20.40.60.81 0.6 0.8 1 0.20.40.60.81 Compactness SimpleSteps Rate of act. v. Compactness Carry Rate of act. v. Catch Best-OneBest-Many ILSimilar-OneSimilar-Many ParentRandom-OneRandom-Many Figure 5: Body features for all the optimized VSRs. Figure 6: Eight snapshots of one episode of one of the VSRs evolved with the Best-Many variant for the Catch task. The snapshots, taken at 0.5 s interval, show the robot grabbing and then carrying the payload. BestSimilarRandom TaskILParent One Many One Many One Many Simple Steps Carry Catch Figure 7: A selection of the optimized VSR bodies, one per each approach (column) and task (row). this learning budget for BO is enough for revealing the full potential of any body. We report in Figure 8 the quality푞 ★ of the VSRs obtained with this procedure for the three static tasks. It can be seen that there are no clear differences in the quality of the re-learned VSRs: a performance difference which existed after the body-brain co-optimization can be nullified by pairing each body with its “optimal” brain. A potential and practical consequence of this findings is that there are no reasons for not employing SL, 80 100 120 140 160 20 40 60 50 100 Quality 푞 ★ Simple Steps Carry Best-OneBest-Many ILSimilar-OneSimilar-Many ParentRandom-OneRandom-Many Figure 8: Distribution of the quality푞 ★ of the best-performing VSR subjected to the re-learning of the brain with a large budget for BO. namely the Best-Many variant, when co-optimizing the body and the brain of a VSR: robots obtained this way are in general better and their bodies are not less diverse, nor “potentially” worse. We also measured the performance of VSRs subjected to brain re-learning, but using another task for re-learning than the one used for evolving the body. That is, we assessed the transferability of bodies to other tasks. We limited this analysis to the three static tasks as destination task. We performed the re-learning as in the previous experiment. We show the results in Figure 9. For easing the comparison of performance of transferred bodies, we also report the re-learning results for the destination task being the same of the source one, i.e., the one where bodies have been evolved. The main finding is that there is always a degradation of the performance after transferring the VSRs to another task: this is more than sound, as different tasks ask for different bodies, but here we are just re-learning the brains. The second finding is that, consistent with the previous experiment, re-learning makes the differences among SL approaches vanish. 5.5 Effectiveness of BO as learning To validate the effectiveness of BO and SL as learning algorithms, we compared them to the No-BO approach on a selection of fixed bodies. We do this outside of the main evolutionary loop to isolate the effect of learning, i.e., without optimizing the body. We used the eight selected optimized bodies for the Simple environment shown in the top row of Figure 7, and similarly as described in Section 5.4, we re-learned a new brain from scratch using three approaches. The three approaches are: (a) a No-BO baseline where all candidate controllers are sampled randomly; (b) an IL approach; and (c) a SL approach where the transferred samples are taken from the IL approach (on the same body). Note that for the SL approach, the samples are only transferred from the first 50 samples from the IL approach. The results for this experiment are presented in Figure 10. Firstly, the results show that both BO approaches quickly perform better than the No-BO baseline, showing the effectiveness of BO. Com- paring SL to IL, we see that SL has an expected initial advantage in performance, but over many learning iterations IL is able to close the gap in performance. This shows a clear benefit of SL over IL, K. Ege de Bruin, Kyrre Glette, Kai Olav Ellefsen, Giorgia Nadizar, and Eric Medvet 50 100 150 20 40 60 Simple StepsCarry Catch 0 50 100 Quality 푞 ★ To Simple Quality 푞 ★ To Steps Quality 푞 ★ To Carry Best-OneBest-Many ILSimilar-OneSimilar-Many ParentRandom-OneRandom-Many Figure 9: Distribution of the quality푞 ★ of the best-performing VSR optimized on a source task (row of plots) subjected to the re-learning of the brain with a large budget for BO and for another destination task (groups of boxes). 0100200300400500 0 50 100 Learning iteration Quality 푞 ★ No-BOILSL Figure 10: Performance over learning iterations for three brain learning approaches evaluated on eight fixed robot bodies. The vertical red dotted line corresponds to the learn- ing budget of 50 in our main experiment. namely that it requires fewer learning iterations for good perfor- mance, making room for evaluating more robot bodies with the same number of total function evaluations, i.e., simulated episodes. While our BO approach is effective in the considered setting, it could be improved by using techniques from high-dimensional BO. For example, random embedding methods [57], trust-region-based BO methods such as TuRBO [15] and additive Gaussian process models [24]. We leave this to future work to investigate. 6 Conclusion We have investigated SL strategies to transfer information across generations in evolvable robots on four different environments and tasks. In our work, the brain is optimized using BO for each robot. SL is done by transferring samples between robots, and we compare four different strategies: transferring samples from the best, the most similar, a random robot from the previous generation, and the parent. We also look at the effects of having a single or multiple teachers. We compare SL strategies against IL where no samples are transferred between robots. We consider four tasks where VSRs need to be optimized in body and brain to perform movements and to carry payloads. For all environments, the results show that often any SL strategy outper- forms IL. Among the SL strategies, learning from the best robot often performs better than other strategies. Future work can look into the effect diversity-promoting algorithms on the SL strategies. Moreover, learning from more teachers is generally better than from one teacher, despite the amount of information being the same. We do not see a noticeable difference in morphologies and mor- phological diversity between strategies. Also, we show that a differ- ence in performance after co-evolving the body and the brain does not necessarily mean that the body has a better ability to learn the task. Therefore, the reason that, during co-evolution, the individu- als for a strategy perform better might be only because there are better control parameters found. This is true for both re-learning the brains of the optimized bodies in the same environment and task, or when bodies are transferred to different environments. If the goal is to end up with a single good-performing robot body, there is less benefit of SL. However, in a continuous evolutionary cycle, our SL approaches are good strategies, since better control parameters are found for the individuals. Related to this, a dynamic environment still showed benefits of SL, despite related work show- ing diminishing benefits. 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