Carlo D'Eramo

Joe Watson, Chen Song, Oliver Weeger et al. · cambridge

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest due to their potential impact on advancing scientific research and industrial practices by improving predictive models with small- or large-scale datasets and expressive predictive models with useful inductive biases. The survey has two parts. The first considers incorporating physics knowledge on an architectural level through objective functions, structured predictive models, and data augmentation. The second considers data as physics knowledge, which motivates looking at multi-task, meta, and contextual learning as an alternative approach to incorporating physics knowledge in a data-driven fashion. Finally, we also provide an industrial perspective on the application of these methods and a survey of the open-source ecosystem for physics-informed machine learning.

Pascal Klink, Carlo D'Eramo, Jan Peters et al.

Curriculum reinforcement learning (CRL) allows solving complex tasks by generating a tailored sequence of learning tasks, starting from easy ones and subsequently increasing their difficulty. Although the potential of curricula in RL has been clearly shown in various works, it is less clear how to generate them for a given learning environment, resulting in various methods aiming to automate this task. In this work, we focus on framing curricula as interpolations between task distributions, which has previously been shown to be a viable approach to CRL. Identifying key issues of existing methods, we frame the generation of a curriculum as a constrained optimal transport problem between task distributions. Benchmarks show that this way of curriculum generation can improve upon existing CRL methods, yielding high performance in various tasks with different characteristics.

Gabriele Tiboni, Pascal Klink, Jan Peters et al.

Varying dynamics parameters in simulation is a popular Domain Randomization (DR) approach for overcoming the reality gap in Reinforcement Learning (RL). Nevertheless, DR heavily hinges on the choice of the sampling distribution of the dynamics parameters, since high variability is crucial to regularize the agent's behavior but notoriously leads to overly conservative policies when randomizing excessively. In this paper, we propose a novel approach to address sim-to-real transfer, which automatically shapes dynamics distributions during training in simulation without requiring real-world data. We introduce DOmain RAndomization via Entropy MaximizatiON (DORAEMON), a constrained optimization problem that directly maximizes the entropy of the training distribution while retaining generalization capabilities. In achieving this, DORAEMON gradually increases the diversity of sampled dynamics parameters as long as the probability of success of the current policy is sufficiently high. We empirically validate the consistent benefits of DORAEMON in obtaining highly adaptive and generalizable policies, i.e. solving the task at hand across the widest range of dynamics parameters, as opposed to representative baselines from the DR literature. Notably, we also demonstrate the Sim2Real applicability of DORAEMON through its successful zero-shot transfer in a robotic manipulation setup under unknown real-world parameters.

Ahmed Hendawy, Jan Peters, Carlo D'Eramo

Multi-Task Reinforcement Learning (MTRL) tackles the long-standing problem of endowing agents with skills that generalize across a variety of problems. To this end, sharing representations plays a fundamental role in capturing both unique and common characteristics of the tasks. Tasks may exhibit similarities in terms of skills, objects, or physical properties while leveraging their representations eases the achievement of a universal policy. Nevertheless, the pursuit of learning a shared set of diverse representations is still an open challenge. In this paper, we introduce a novel approach for representation learning in MTRL that encapsulates common structures among the tasks using orthogonal representations to promote diversity. Our method, named Mixture Of Orthogonal Experts (MOORE), leverages a Gram-Schmidt process to shape a shared subspace of representations generated by a mixture of experts. When task-specific information is provided, MOORE generates relevant representations from this shared subspace. We assess the effectiveness of our approach on two MTRL benchmarks, namely MiniGrid and MetaWorld, showing that MOORE surpasses related baselines and establishes a new state-of-the-art result on MetaWorld.

Aryaman Reddi, Maximilian Tölle, Jan Peters et al.

Robustness against adversarial attacks and distribution shifts is a long-standing goal of Reinforcement Learning (RL). To this end, Robust Adversarial Reinforcement Learning (RARL) trains a protagonist against destabilizing forces exercised by an adversary in a competitive zero-sum Markov game, whose optimal solution, i.e., rational strategy, corresponds to a Nash equilibrium. However, finding Nash equilibria requires facing complex saddle point optimization problems, which can be prohibitive to solve, especially for high-dimensional control. In this paper, we propose a novel approach for adversarial RL based on entropy regularization to ease the complexity of the saddle point optimization problem. We show that the solution of this entropy-regularized problem corresponds to a Quantal Response Equilibrium (QRE), a generalization of Nash equilibria that accounts for bounded rationality, i.e., agents sometimes play random actions instead of optimal ones. Crucially, the connection between the entropy-regularized objective and QRE enables free modulation of the rationality of the agents by simply tuning the temperature coefficient. We leverage this insight to propose our novel algorithm, Quantal Adversarial RL (QARL), which gradually increases the rationality of the adversary in a curriculum fashion until it is fully rational, easing the complexity of the optimization problem while retaining robustness. We provide extensive evidence of QARL outperforming RARL and recent baselines across several MuJoCo locomotion and navigation problems in overall performance and robustness.

Noah Farr, Aryaman Reddi, Carlo D'Eramo et al.

Streaming reinforcement learning has emerged as an online learning paradigm that conforms to the restrictions of natural learning agents that process data incrementally, i.e. with a batch size of 1 and no replay buffer. While streaming RL has recently been shown to scale with deep function approximation with full observability, partially observable settings have remained out of reach. Truncated backpropagation through time collapses to a one-step gradient horizon under the streaming setting, and exact real-time recurrent learning is prohibitively expensive. We close this gap using recurrent trace units, a diagonal recurrent architecture that enables exact RTRL with linear time and memory complexity in the parameter count, and show that they integrate cleanly into existing streaming algorithms across both discrete and continuous control. On a MemoryChain diagnostic with chain lengths from 2 to 128, our method sustains performance where streaming TBPTT(1) baselines using feedforward, GRU, and RTU networks collapse. On five POPGym tasks and on partially observable MuJoCo continuous control, the streaming approach is competitive with batched PPO on POPGym and recovers a substantial fraction of batched performance on masked MuJoCo, despite using no replay buffer or batched updates.

Tuan Dam, Pascal Stenger, Lukas Schneider et al.

This paper introduces a novel backup strategy for Monte-Carlo Tree Search (MCTS) designed for highly stochastic and partially observable Markov decision processes. We adopt a probabilistic approach, modeling both value and action-value nodes as Gaussian distributions. We introduce a novel backup operator that computes value nodes as the Wasserstein barycenter of their action-value children nodes; thus, propagating the uncertainty of the estimate across the tree to the root node. We study our novel backup operator when using a novel combination of $L^1$-Wasserstein barycenter with $α$-divergence, by drawing a notable connection to the generalized mean backup operator. We complement our probabilistic backup operator with two sampling strategies, based on optimistic selection and Thompson sampling, obtaining our Wasserstein MCTS algorithm. We provide theoretical guarantees of asymptotic convergence to the optimal policy, and an empirical evaluation on several stochastic and partially observable environments, where our approach outperforms well-known related baselines.

Mahdi Kallel, Johannes Tölle, Ahmed Hendawy et al.

Standard supervised classification trains models to imitate the exact labels provided by a perfect oracle. This imitation happens in a single pass, restricting the model to a fixed compute budget even when inputs vary in complexity. Moreover, the rigid training objective forces the model to express absolute certainty on its training data, resulting in overconfident predictions during evaluation. We propose Reinforced Iterative Classification (RIC), which replaces the imitative objective with Reinforcement Learning (RL). RIC deploys a recurrent agent that iteratively updates a predictive distribution over classes, receiving reward for stepwise improvement in prediction quality. The value function provides a natural halting criterion by estimating the remaining scope for improvement. We prove that the iterative formulation recovers the same optimal predictions as cross-entropy while yielding an anytime classifier. On image classification benchmarks, RIC matches the accuracy of supervised baselines with improved calibration and learns to allocate computation adaptively across inputs.

Mahdi Kallel, Debabrota Basu, Riad Akrour et al.

Deterministic policies are often preferred over stochastic ones when implemented on physical systems. They can prevent erratic and harmful behaviors while being easier to implement and interpret. However, in practice, exploration is largely performed by stochastic policies. First-order Bayesian Optimization (BO) methods offer a principled way of performing exploration using deterministic policies. This is done through a learned probabilistic model of the objective function and its gradient. Nonetheless, such approaches treat policy search as a black-box problem, and thus, neglect the reinforcement learning nature of the problem. In this work, we leverage the performance difference lemma to introduce a novel mean function for the probabilistic model. This results in augmenting BO methods with the action-value function. Hence, we call our method Augmented Bayesian Search~(ABS). Interestingly, this new mean function enhances the posterior gradient with the deterministic policy gradient, effectively bridging the gap between BO and policy gradient methods. The resulting algorithm combines the convenience of the direct policy search with the scalability of reinforcement learning. We validate ABS on high-dimensional locomotion problems and demonstrate competitive performance compared to existing direct policy search schemes.

Carlo D'Eramo, Davide Tateo, Andrea Bonarini et al.

We study the benefit of sharing representations among tasks to enable the effective use of deep neural networks in Multi-Task Reinforcement Learning. We leverage the assumption that learning from different tasks, sharing common properties, is helpful to generalize the knowledge of them resulting in a more effective feature extraction compared to learning a single task. Intuitively, the resulting set of features offers performance benefits when used by Reinforcement Learning algorithms. We prove this by providing theoretical guarantees that highlight the conditions for which is convenient to share representations among tasks, extending the well-known finite-time bounds of Approximate Value-Iteration to the multi-task setting. In addition, we complement our analysis by proposing multi-task extensions of three Reinforcement Learning algorithms that we empirically evaluate on widely used Reinforcement Learning benchmarks showing significant improvements over the single-task counterparts in terms of sample efficiency and performance.

Carlo D'Eramo, Davide Tateo, Andrea Bonarini et al.

MushroomRL is an open-source Python library developed to simplify the process of implementing and running Reinforcement Learning (RL) experiments. Compared to other available libraries, MushroomRL has been created with the purpose of providing a comprehensive and flexible framework to minimize the effort in implementing and testing novel RL methodologies. Indeed, the architecture of MushroomRL is built in such a way that every component of an RL problem is already provided, and most of the time users can only focus on the implementation of their own algorithms and experiments. The result is a library from which RL researchers can significantly benefit in the critical phase of the empirical analysis of their works. MushroomRL stable code, tutorials and documentation can be found at https://github.com/MushroomRL/mushroom-rl.

Simone Parisi, Davide Tateo, Maximilian Hensel et al.

Reinforcement learning with sparse rewards is still an open challenge. Classic methods rely on getting feedback via extrinsic rewards to train the agent, and in situations where this occurs very rarely the agent learns slowly or cannot learn at all. Similarly, if the agent receives also rewards that create suboptimal modes of the objective function, it will likely prematurely stop exploring. More recent methods add auxiliary intrinsic rewards to encourage exploration. However, auxiliary rewards lead to a non-stationary target for the Q-function. In this paper, we present a novel approach that (1) plans exploration actions far into the future by using a long-term visitation count, and (2) decouples exploration and exploitation by learning a separate function assessing the exploration value of the actions. Contrary to existing methods which use models of reward and dynamics, our approach is off-policy and model-free. We further propose new tabular environments for benchmarking exploration in reinforcement learning. Empirical results on classic and novel benchmarks show that the proposed approach outperforms existing methods in environments with sparse rewards, especially in the presence of rewards that create suboptimal modes of the objective function. Results also suggest that our approach scales gracefully with the size of the environment. Source code is available at https://github.com/sparisi/visit-value-explore

Théo Vincent, Daniel Palenicek, Boris Belousov et al.

The vast majority of Reinforcement Learning methods is largely impacted by the computation effort and data requirements needed to obtain effective estimates of action-value functions, which in turn determine the quality of the overall performance and the sample-efficiency of the learning procedure. Typically, action-value functions are estimated through an iterative scheme that alternates the application of an empirical approximation of the Bellman operator and a subsequent projection step onto a considered function space. It has been observed that this scheme can be potentially generalized to carry out multiple iterations of the Bellman operator at once, benefiting the underlying learning algorithm. However, till now, it has been challenging to effectively implement this idea, especially in high-dimensional problems. In this paper, we introduce iterated $Q$-Network (i-QN), a novel principled approach that enables multiple consecutive Bellman updates by learning a tailored sequence of action-value functions where each serves as the target for the next. We show that i-QN is theoretically grounded and that it can be seamlessly used in value-based and actor-critic methods. We empirically demonstrate the advantages of i-QN in Atari $2600$ games and MuJoCo continuous control problems.

Théo Vincent, Alberto Maria Metelli, Boris Belousov et al.

Approximate value iteration (AVI) is a family of algorithms for reinforcement learning (RL) that aims to obtain an approximation of the optimal value function. Generally, AVI algorithms implement an iterated procedure where each step consists of (i) an application of the Bellman operator and (ii) a projection step into a considered function space. Notoriously, the Bellman operator leverages transition samples, which strongly determine its behavior, as uninformative samples can result in negligible updates or long detours, whose detrimental effects are further exacerbated by the computationally intensive projection step. To address these issues, we propose a novel alternative approach based on learning an approximate version of the Bellman operator rather than estimating it through samples as in AVI approaches. This way, we are able to (i) generalize across transition samples and (ii) avoid the computationally intensive projection step. For this reason, we call our novel operator projected Bellman operator (PBO). We formulate an optimization problem to learn PBO for generic sequential decision-making problems, and we theoretically analyze its properties in two representative classes of RL problems. Furthermore, we theoretically study our approach under the lens of AVI and devise algorithmic implementations to learn PBO in offline and online settings by leveraging neural network parameterizations. Finally, we empirically showcase the benefits of PBO w.r.t. the regular Bellman operator on several RL problems.

Erdi Sayar, Zhenshan Bing, Carlo D'Eramo et al.

Multi-goal robot manipulation tasks with sparse rewards are difficult for reinforcement learning (RL) algorithms due to the inefficiency in collecting successful experiences. Recent algorithms such as Hindsight Experience Replay (HER) expedite learning by taking advantage of failed trajectories and replacing the desired goal with one of the achieved states so that any failed trajectory can be utilized as a contribution to learning. However, HER uniformly chooses failed trajectories, without taking into account which ones might be the most valuable for learning. In this paper, we address this problem and propose a novel approach Contact Energy Based Prioritization~(CEBP) to select the samples from the replay buffer based on rich information due to contact, leveraging the touch sensors in the gripper of the robot and object displacement. Our prioritization scheme favors sampling of contact-rich experiences, which are arguably the ones providing the largest amount of information. We evaluate our proposed approach on various sparse reward robotic tasks and compare them with the state-of-the-art methods. We show that our method surpasses or performs on par with those methods on robot manipulation tasks. Finally, we deploy the trained policy from our method to a real Franka robot for a pick-and-place task. We observe that the robot can solve the task successfully. The videos and code are publicly available at: https://erdiphd.github.io/HER_force

Sebastian Griesbach, Carlo D'Eramo

Numerous heuristics and advanced approaches have been proposed for exploration in different settings for deep reinforcement learning. Noise-based exploration generally fares well with dense-shaped rewards and bonus-based exploration with sparse rewards. However, these methods usually require additional tuning to deal with undesirable reward settings by adjusting hyperparameters and noise distributions. Rewards that actively discourage exploration, i.e., with an action cost and no other dense signal to follow, can pose a major challenge. We propose a novel exploration method, Stable Error-seeking Exploration (SEE), that is robust across dense, sparse, and exploration-adverse reward settings. To this endeavor, we revisit the idea of maximizing the TD-error as a separate objective. Our method introduces three design choices to mitigate instability caused by far-off-policy learning, the conflict of interest of maximizing the cumulative TD-error in an episodic setting, and the non-stationary nature of TD-errors. SEE can be combined with off-policy algorithms without modifying the optimization pipeline of the original objective. In our experimental analysis, we show that a Soft-Actor Critic agent with the addition of SEE performs robustly across three diverse reward settings in a variety of tasks without hyperparameter adjustments.

Théo Vincent, Yogesh Tripathi, Tim Faust et al.

The use of target networks in deep reinforcement learning is a widely popular solution to mitigate the brittleness of semi-gradient approaches and stabilize learning. However, target networks notoriously require additional memory and delay the propagation of Bellman updates compared to an ideal target-free approach. In this work, we step out of the binary choice between target-free and target-based algorithms. We introduce a new method that uses a copy of the last linear layer of the online network as a target network, while sharing the remaining parameters with the up-to-date online network. This simple modification enables us to keep the target-free's low-memory footprint while leveraging the target-based literature. We find that combining our approach with the concept of iterated Q-learning, which consists of learning consecutive Bellman updates in parallel, helps improve the sample-efficiency of target-free approaches. Our proposed method, iterated Shared Q-Learning (iS-QL), bridges the performance gap between target-free and target-based approaches across various problems, while using a single Q-network, thus being a step forward towards resource-efficient reinforcement learning algorithms.

Rupert Mitchell, Antonio Alliegro, Raffaello Camoriano et al.

Continual learning (CL) is the sub-field of machine learning concerned with accumulating knowledge in dynamic environments. So far, CL research has mainly focused on incremental classification tasks, where models learn to classify new categories while retaining knowledge of previously learned ones. Here, we argue that maintaining such a focus limits both theoretical development and practical applicability of CL methods. Through a detailed analysis of concrete examples - including multi-target classification, robotics with constrained output spaces, learning in continuous task domains, and higher-level concept memorization - we demonstrate how current CL approaches often fail when applied beyond standard classification. We identify three fundamental challenges: (C1) the nature of continuity in learning problems, (C2) the choice of appropriate spaces and metrics for measuring similarity, and (C3) the role of learning objectives beyond classification. For each challenge, we provide specific recommendations to help move the field forward, including formalizing temporal dynamics through distribution processes, developing principled approaches for continuous task spaces, and incorporating density estimation and generative objectives. In so doing, this position paper aims to broaden the scope of CL research while strengthening its theoretical foundations, making it more applicable to real-world problems.

Théo Vincent, Kevin Gerhardt, Yogesh Tripathi et al.

Temporal-difference (TD) learning is highly effective at controlling and evaluating an agent's long-term outcomes. Most approaches in this paradigm implement a semi-gradient update to boost the learning speed, which consists of ignoring the gradient of the bootstrapped estimate. While popular, this type of update is prone to divergence, as Baird's counterexample illustrates. Gradient TD methods were introduced to overcome this issue, but have not been widely used, potentially due to issues with learning speed compared to semi-gradient methods. Recently, iterated TD learning was developed to increase the learning speed of TD methods. For that, it learns a sequence of action-value functions in parallel, where each function is optimized to represent the application of the Bellman operator over the previous function in the sequence. While promising, this algorithm can be unstable due to its semi-gradient nature, as each function tracks a moving target. In this work, we modify iterated TD learning by computing the gradients over those moving targets, aiming to build a powerful gradient TD method that competes with semi-gradient methods. Our evaluation reveals that this algorithm, called Gradient Iterated Temporal-Difference learning, has a competitive learning speed against semi-gradient methods across various benchmarks, including Atari games, a result that no prior work on gradient TD methods has demonstrated.

Ahmed Hendawy, Henrik Metternich, Théo Vincent et al.

The use of target networks is a popular approach for estimating value functions in deep Reinforcement Learning (RL). While effective, the target network remains a compromise solution that preserves stability at the cost of slowly moving targets, thus delaying learning. Conversely, using the online network as a bootstrapped target is intuitively appealing, albeit well-known to lead to unstable learning. In this work, we aim to obtain the best out of both worlds by introducing a novel update rule that computes the target using the MINimum estimate between the Target and Online network, giving rise to our method, MINTO. Through this simple, yet effective modification, we show that MINTO enables faster and stable value function learning, by mitigating the potential overestimation bias of using the online network for bootstrapping. Notably, MINTO can be seamlessly integrated into a wide range of value-based and actor-critic algorithms with a negligible cost. We evaluate MINTO extensively across diverse benchmarks, spanning online and offline RL, as well as discrete and continuous action spaces. Across all benchmarks, MINTO consistently improves performance, demonstrating its broad applicability and effectiveness.

Aryaman Reddi, Gabriele Tiboni, Jan Peters et al.

Actor-critic algorithms for deep multi-agent reinforcement learning (MARL) typically employ a policy update that responds to the current strategies of other agents. While being straightforward, this approach does not account for the updates of other agents at the same update step, resulting in miscoordination. In this paper, we introduce the $K$-Level Policy Gradient (KPG), a method that recursively updates each agent against the updated policies of other agents, speeding up the discovery of effective coordinated policies. We theoretically prove that KPG with finite iterates achieves monotonic convergence to a local Nash equilibrium under certain conditions. We provide principled implementations of KPG by applying it to the deep MARL algorithms MAPPO, MADDPG, and FACMAC. Empirically, we demonstrate superior performance over existing deep MARL algorithms in StarCraft II and multi-agent MuJoCo.

Jose-Luis Holgado-Alvarez, Aryaman Reddi, Carlo D'Eramo

Reinforcement Learning (RL) has proven largely effective in obtaining stable locomotion gaits for legged robots. However, designing control algorithms which can robustly navigate unseen environments with obstacles remains an ongoing problem within quadruped locomotion. To tackle this, it is convenient to solve navigation tasks by means of a hierarchical approach with a low-level locomotion policy and a high-level navigation policy. Crucially, the high-level policy needs to be robust to dynamic obstacles along the path of the agent. In this work, we propose a novel way to endow navigation policies with robustness by a training process that models obstacles as adversarial agents, following the adversarial RL paradigm. Importantly, to improve the reliability of the training process, we bound the rationality of the adversarial agent resorting to quantal response equilibria, and place a curriculum over its rationality. We called this method Hierarchical policies via Quantal response Adversarial Reinforcement Learning (Hi-QARL). We demonstrate the robustness of our method by benchmarking it in unseen randomized mazes with multiple obstacles. To prove its applicability in real scenarios, our method is applied on a Unitree GO1 robot in simulation.

Théo Vincent, Tim Faust, Yogesh Tripathi et al.

Recent works have successfully demonstrated that sparse deep reinforcement learning agents can be competitive against their dense counterparts. This opens up opportunities for reinforcement learning applications in fields where inference time and memory requirements are cost-sensitive or limited by hardware. Until now, dense-to-sparse methods have relied on hand-designed sparsity schedules that are not synchronized with the agent's learning pace. Crucially, the final sparsity level is chosen as a hyperparameter, which requires careful tuning as setting it too high might lead to poor performances. In this work, we address these shortcomings by crafting a dense-to-sparse algorithm that we name Eau De $Q$-Network (EauDeQN). To increase sparsity at the agent's learning pace, we consider multiple online networks with different sparsity levels, where each online network is trained from a shared target network. At each target update, the online network with the smallest loss is chosen as the next target network, while the other networks are replaced by a pruned version of the chosen network. We evaluate the proposed approach on the Atari $2600$ benchmark and the MuJoCo physics simulator, showing that EauDeQN reaches high sparsity levels while keeping performances high.

Sebastian Griesbach, Carlo D'Eramo

Exploration is a crucial and distinctive aspect of reinforcement learning (RL) that remains a fundamental open problem. Several methods have been proposed to tackle this challenge. Commonly used methods inject random noise directly into the actions, indirectly via entropy maximization, or add intrinsic rewards that encourage the agent to steer to novel regions of the state space. Another previously seen idea is to use the Bellman error as a separate optimization objective for exploration. In this paper, we introduce three modifications to stabilize the latter and arrive at a deterministic exploration policy. Our separate exploration agent is informed about the state of the exploitation, thus enabling it to account for previous experiences. Further components are introduced to make the exploration objective agnostic toward the episode length and to mitigate instability introduced by far-off-policy learning. Our experimental results show that our approach can outperform $\varepsilon$-greedy in dense and sparse reward settings.

Tuan Dam, Carlo D'Eramo, Jan Peters et al.

Monte-Carlo Tree Search (MCTS) is a class of methods for solving complex decision-making problems through the synergy of Monte-Carlo planning and Reinforcement Learning (RL). The highly combinatorial nature of the problems commonly addressed by MCTS requires the use of efficient exploration strategies for navigating the planning tree and quickly convergent value backup methods. These crucial problems are particularly evident in recent advances that combine MCTS with deep neural networks for function approximation. In this work, we propose two methods for improving the convergence rate and exploration based on a newly introduced backup operator and entropy regularization. We provide strong theoretical guarantees to bound convergence rate, approximation error, and regret of our methods. Moreover, we introduce a mathematical framework based on the use of the $α$-divergence for backup and exploration in MCTS. We show that this theoretical formulation unifies different approaches, including our newly introduced ones, under the same mathematical framework, allowing to obtain different methods by simply changing the value of $α$. In practice, our unified perspective offers a flexible way to balance between exploration and exploitation by tuning the single $α$ parameter according to the problem at hand. We validate our methods through a rigorous empirical study from basic toy problems to the complex Atari games, and including both MDP and POMDP problems.

Julen Urain, Anqi Li, Puze Liu et al.

Reactive motion generation problems are usually solved by computing actions as a sum of policies. However, these policies are independent of each other and thus, they can have conflicting behaviors when summing their contributions together. We introduce Composable Energy Policies (CEP), a novel framework for modular reactive motion generation. CEP computes the control action by optimization over the product of a set of stochastic policies. This product of policies will provide a high probability to those actions that satisfy all the components and low probability to the others. Optimizing over the product of the policies avoids the detrimental effect of conflicting behaviors between policies choosing an action that satisfies all the objectives. Besides, we show that CEP naturally adapts to the Reinforcement Learning problem allowing us to integrate, in a hierarchical fashion, any distribution as prior, from multimodal distributions to non-smooth distributions and learn a new policy given them.

Andrew S. Morgan, Daljeet Nandha, Georgia Chalvatzaki et al.

Substantial advancements to model-based reinforcement learning algorithms have been impeded by the model-bias induced by the collected data, which generally hurts performance. Meanwhile, their inherent sample efficiency warrants utility for most robot applications, limiting potential damage to the robot and its environment during training. Inspired by information theoretic model predictive control and advances in deep reinforcement learning, we introduce Model Predictive Actor-Critic (MoPAC), a hybrid model-based/model-free method that combines model predictive rollouts with policy optimization as to mitigate model bias. MoPAC leverages optimal trajectories to guide policy learning, but explores via its model-free method, allowing the algorithm to learn more expressive dynamics models. This combination guarantees optimal skill learning up to an approximation error and reduces necessary physical interaction with the environment, making it suitable for real-robot training. We provide extensive results showcasing how our proposed method generally outperforms current state-of-the-art and conclude by evaluating MoPAC for learning on a physical robotic hand performing valve rotation and finger gaiting--a task that requires grasping, manipulation, and then regrasping of an object.

Pascal Klink, Hany Abdulsamad, Boris Belousov et al.

Across machine learning, the use of curricula has shown strong empirical potential to improve learning from data by avoiding local optima of training objectives. For reinforcement learning (RL), curricula are especially interesting, as the underlying optimization has a strong tendency to get stuck in local optima due to the exploration-exploitation trade-off. Recently, a number of approaches for an automatic generation of curricula for RL have been shown to increase performance while requiring less expert knowledge compared to manually designed curricula. However, these approaches are seldomly investigated from a theoretical perspective, preventing a deeper understanding of their mechanics. In this paper, we present an approach for automated curriculum generation in RL with a clear theoretical underpinning. More precisely, we formalize the well-known self-paced learning paradigm as inducing a distribution over training tasks, which trades off between task complexity and the objective to match a desired task distribution. Experiments show that training on this induced distribution helps to avoid poor local optima across RL algorithms in different tasks with uninformative rewards and challenging exploration requirements.

Tuan Dam, Carlo D'Eramo, Jan Peters et al.

Monte-Carlo planning and Reinforcement Learning (RL) are essential to sequential decision making. The recent AlphaGo and AlphaZero algorithms have shown how to successfully combine these two paradigms in order to solve large scale sequential decision problems. These methodologies exploit a variant of the well-known UCT algorithm to trade off exploitation of good actions and exploration of unvisited states, but their empirical success comes at the cost of poor sample-efficiency and high computation time. In this paper, we overcome these limitations by considering convex regularization in Monte-Carlo Tree Search (MCTS), which has been successfully used in RL to efficiently drive exploration. First, we introduce a unifying theory on the use of generic convex regularizers in MCTS, deriving the regret analysis and providing guarantees of exponential convergence rate. Second, we exploit our theoretical framework to introduce novel regularized backup operators for MCTS, based on the relative entropy of the policy update, and on the Tsallis entropy of the policy. Finally, we empirically evaluate the proposed operators in AlphaGo and AlphaZero on problems of increasing dimensionality and branching factor, from a toy problem to several Atari games, showing their superiority w.r.t. representative baselines.

Pascal Klink, Carlo D'Eramo, Jan Peters et al.

Curriculum reinforcement learning (CRL) improves the learning speed and stability of an agent by exposing it to a tailored series of tasks throughout learning. Despite empirical successes, an open question in CRL is how to automatically generate a curriculum for a given reinforcement learning (RL) agent, avoiding manual design. In this paper, we propose an answer by interpreting the curriculum generation as an inference problem, where distributions over tasks are progressively learned to approach the target task. This approach leads to an automatic curriculum generation, whose pace is controlled by the agent, with solid theoretical motivation and easily integrated with deep RL algorithms. In the conducted experiments, the curricula generated with the proposed algorithm significantly improve learning performance across several environments and deep RL algorithms, matching or outperforming state-of-the-art existing CRL algorithms.

Andrea Cini, Carlo D'Eramo, Jan Peters et al.

Reinforcement learning algorithms based on Q-learning are driving Deep Reinforcement Learning (DRL) research towards solving complex problems and achieving super-human performance on many of them. Nevertheless, Q-Learning is known to be positively biased since it learns by using the maximum over noisy estimates of expected values. Systematic overestimation of the action values coupled with the inherently high variance of DRL methods can lead to incrementally accumulate errors, causing learning algorithms to diverge. Ideally, we would like DRL agents to take into account their own uncertainty about the optimality of each action, and be able to exploit it to make more informed estimations of the expected return. In this regard, Weighted Q-Learning (WQL) effectively reduces bias and shows remarkable results in stochastic environments. WQL uses a weighted sum of the estimated action values, where the weights correspond to the probability of each action value being the maximum; however, the computation of these probabilities is only practical in the tabular setting. In this work, we provide methodological advances to benefit from the WQL properties in DRL, by using neural networks trained with Dropout as an effective approximation of deep Gaussian processes. In particular, we adopt the Concrete Dropout variant to obtain calibrated estimates of epistemic uncertainty in DRL. The estimator, then, is obtained by taking several stochastic forward passes through the action-value network and computing the weights in a Monte Carlo fashion. Such weights are Bayesian estimates of the probability of each action value corresponding to the maximum w.r.t. a posterior probability distribution estimated by Dropout. We show how our novel Deep Weighted Q-Learning algorithm reduces the bias w.r.t. relevant baselines and provides empirical evidence of its advantages on representative benchmarks.

Tuan Dam, Pascal Klink, Carlo D'Eramo et al.

We consider Monte-Carlo Tree Search (MCTS) applied to Markov Decision Processes (MDPs) and Partially Observable MDPs (POMDPs), and the well-known Upper Confidence bound for Trees (UCT) algorithm. In UCT, a tree with nodes (states) and edges (actions) is incrementally built by the expansion of nodes, and the values of nodes are updated through a backup strategy based on the average value of child nodes. However, it has been shown that with enough samples the maximum operator yields more accurate node value estimates than averaging. Instead of settling for one of these value estimates, we go a step further proposing a novel backup strategy which uses the power mean operator, which computes a value between the average and maximum value. We call our new approach Power-UCT, and argue how the use of the power mean operator helps to speed up the learning in MCTS. We theoretically analyze our method providing guarantees of convergence to the optimum. Finally, we empirically demonstrate the effectiveness of our method in well-known MDP and POMDP benchmarks, showing significant improvement in performance and convergence speed w.r.t. state of the art algorithms.