Deep Reinforcement Learning (RL) is well known for being highly sensitive to hyperparameters, requiring practitioners substantial efforts to optimize them for the problem at hand. This also limits the applicability of RL in real-world scenarios. In recent years, the field of automated Reinforcement Learning (AutoRL) has grown in popularity by trying to address this issue. However, these approaches typically hinge on additional samples to select well-performing hyperparameters, hindering sample-efficiency and practicality. Furthermore, most AutoRL methods are heavily based on already existing AutoML methods, which were originally developed neglecting the additional challenges inherent to RL due to its non-stationarities. In this work, we propose a new approach for AutoRL, called _Adaptive $Q$-Network_ (AdaQN), that is tailored to RL to take into account the non-stationarity of the optimization procedure without requiring additional samples. AdaQN learns several $Q$-functions, each one trained with different hyperparameters, which are updated online using the $Q$-function with the smallest approximation error as a shared target. Our selection scheme simultaneously handles different hyperparameters while coping with the non-stationarity induced by the RL optimization procedure and being orthogonal to any critic-based RL algorithm. We demonstrate that AdaQN is theoretically sound and empirically validate it in MuJoCo control problems and Atari $2600$ games, showing benefits in sample-efficiency, overall performance, robustness to stochasticity and training stability. Our code is available at *https://github.com/theovincent/AdaDQN*.

This paper introduces a novel backup strategy for Monte-Carlo Tree Search (MCTS) tailored for highly stochastic and partially observable Markov decision processes. We adopt a probabilistic approach, modeling both value and action-value nodes as Gaussian distributions, to 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 $\alpha$-divergence, by drawing a crucial 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 of $\mathcal{O}(n^{-1/2})$, with $n$ as the number of visited trajectories, to the optimal policy and an empirical evaluation on several stochastic and partially observable environments, where our approach outperforms well-known related baselines.

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.

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.

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.

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.

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.

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 it 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/.

Monte-Carlo Tree Search (MCTS) is a class of methods for solving complex decisionmaking 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.

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.

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 a variety of works, it is less clear how to generate them for a given learning environment, resulting in a variety of methods aiming to automate this task. In this work, we focus on the idea of 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 a variety of tasks with different characteristics.

Deep Reinforcement Learning (RL) promises to lead the next advances towards the development of coveted future intelligent agents. However, the unprecedented representational power of deep function approximators, e.g. deep neural networks, comes at the cost of demanding a huge amount of experience, making deep RL impractical for applications requiring interactions with the real world. We study the problem of making use of samples in deep RL more efficiently, exploiting the desirable properties of knowledge generalization resulting from learning multiple tasks together. The outcome of our work is the coupling of multi-task RL algorithms with a task-sampling policy based on the well-known intrinsic motivation paradigm. In particular, we leverage on the notion of TD-error of Bellman updates, as an effective measure of learning progress, to prioritize sampling from the tasks contributing the most to the learning of the agent. This sampling strategy speeds up the learning of tasks for which the agent is showing progress, and postpones the learning of the remaining ones, resulting in an optimized collection of samples. Our method is supported by experimental evaluations on well-known RL control tasks, for which our approach shows superior sample-efficiency and performance compared to representative baselines. We eventually evaluate our approach on simulated control tasks based on Quanser robotics systems, confirming the advantages over the baselines also in more realistic applications.

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 to solve large-scale sequential decision problems. These methodologies exploit a variant of the well-known UCT algorithm to trade off the exploitation of good actions and the 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 introducing the use of convex regularization in Monte-Carlo Tree Search (MCTS) to drive exploration efficiently and to improve policy updates. First, we introduce a unifying theory on the use of generic convex regularizers in MCTS, deriving the first regret analysis of regularized MCTS and showing that it guarantees an 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, more importantly, on the Tsallis entropy of the policy, for which we prove superior theoretical guarantees. We empirically verify the consequence of our theoretical results on a toy problem. Finally, we show how our framework can easily be incorporated in AlphaGo and we empirically show the superiority of convex regularization, w.r.t. representative baselines, on well-known RL problems across several Atari games.

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.

Temporal-Difference off-policy algorithms are among the building blocks of reinforcement learning (RL). Within this family, Q-Learning is arguably the most famous one, which has been widely studied and extended. The update rule of Q-learning involves the use of the maximum operator to estimate the maximum expected value of the return. However, this estimate is positively biased, and may hinder the learning process, especially in stochastic environments and when function approximation is used. We introduce the Weighted Estimator as an effective solution to mitigate the negative effects of overestimation in Q-Learning. The Weighted Estimator estimates the maximum expected value as a weighted sum of the action values, with the weights being the probabilities that each action value is the maximum. In this work, we study the problem from the statistical perspective of estimating the maximum expected value of a set of random variables and provide bounds to the bias and the variance of the Weighted Estimator, showing its advantages over other estimators present in literature. Then, we derive algorithms to enable the use of the Weighted Estimator, in place of the Maximum Estimator, in online and batch RL, and we introduce a novel algorithm for deep RL. Finally, we empirically evaluate our algorithms in a large set of heterogeneous problems, encompassing discrete and continuous, low and high dimensional, deterministic and stochastic environments. Experimental results show the effectiveness of the Weighted Estimator in controlling the bias of the estimate, resulting in better performance than representative baselines and robust learning w.r.t. a large set of diverse environments.

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. The architecture of MushroomRL is built in such a way that every component of a typical RL experiment is already provided, and most of the time users can only focus on the implementation of their own algorithms. MushroomRL is accompanied by a benchmarking suite collecting experimental results of state-of-the-art deep RL algorithms, and allowing to benchmark new ones. 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.

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.

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.

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.

Most of the research in Reinforcement Learning (RL) focuses on balancing exploration and exploitation. Indeed, the reasons for the success or failure of an RL algorithm often deal with the choice between the execution of exploratory actions and the exploitation of actions that are known to be good. In the context of Multi-Armed Bandits (MABs), many algorithms have addressed this dilemma. In particular, Thompson Sampling (TS) is a solution that, besides having good theoretical properties, usually works very well in practice. Unfortunately, the success of TS in MAB problems has not been replicated in RL, where it has shown to scale very poorly w.r.t. the dimensionality of the problem. Nevertheless, the application of TS in RL, instead of more myopic strategies such as ε-greedy, remains a promising solution. This paper addresses such issue proposing several algorithms to use TS in RL and deep RL in a feasible way. We present these algorithms explaining the intuitions and theoretical considerations behind them and discussing their advantages and drawbacks. Furthermore, we provide an empirical evaluation on an increasingly complex set of RL problems, showing the benefit of TS w.r.t. other sampling strategies available in classical and more recent RL literature.

Exploring high-dimensional state spaces and finding sparse rewards are central problems in reinforcement learning. Exploration strategies are frequently either naïve (e.g., simplistic-greedy or Boltzmann policies), intractable (i.e., full Bayesian treatment of reinforcement learning) or rely heavily on heuristics. The lack of a tractable but principled exploration approach unnecessarily complicates the application of reinforcement learning to a broader range of problems. Efficient exploration can be accomplished by relying on the uncertainty of the state-action value function. To obtain the uncertainty, we maintain an ensemble of value function estimates and present an optimistic Bellman equation (OBE) for such ensembles. This OBE is derived from a relative entropy maximization principle and yields an implicit exploration bonus resulting in improved exploration during action selection. The implied exploration bonus can be seen as a well-principled type of intrinsic motivation and exhibits favorable theoretical properties. OBE can be applied to a wide range of algorithms. We propose two algorithms as an application of the principle: Optimistic Q-learning and Optimistic DQN which outperform comparison methods on standard benchmarks.

This paper is about the estimation of the maximum expected value of an infinite set of random variables.This estimation problem is relevant in many fields, like the Reinforcement Learning (RL) one.In RL it is well known that, in some stochastic environments, a bias in the estimation error can increase step-by-step the approximation error leading to large overestimates of the true action values. Recently, some approaches have been proposed to reduce such bias in order to get better action-value estimates, but are limited to finite problems.In this paper, we leverage on the recently proposed weighted estimator and on Gaussian process regression to derive a new method that is able to natively handle infinitely many random variables.We show how these techniques can be used to face both continuous state and continuous actions RL problems.To evaluate the effectiveness of the proposed approach we perform empirical comparisons with related approaches.

This paper is about the study of B-FQI, an Approximated Value Iteration (AVI) algorithm that exploits a boosting procedure to estimate the action-value function in reinforcement learning problems. B-FQI is an iterative off-line algorithm that, given a dataset of transitions, builds an approximation of the optimal action-value function by summing the approximations of the Bellman residuals across all iterations. The advantage of such approach w.r.t. to other AVI methods is twofold: (1) while keeping the same function space at each iteration, B-FQI can represent more complex functions by considering an additive model; (2) since the Bellman residual decreases as the optimal value function is approached, regression problems become easier as iterations proceed. We study B-FQI both theoretically, providing also a finite-sample error upper bound for it, and empirically, by comparing its performance to the one of FQI in different domains and using different regression techniques.

This paper is about the estimation of the maximum expected value of a set of independent random variables. The performance of several learning algorithms (e.g., Q-learning) is affected by the accuracy of such estimation. Unfortunately, no unbiased estimator exists. The usual approach of taking the maximum of the sample means leads to large overestimates that may significantly harm the performance of the learning algorithm. Recent works have shown that the cross validation estimator—which is negatively biased—outperforms the maximum estimator in many sequential decision-making scenarios. On the other hand, the relative performance of the two estimators is highly problem-dependent. In this paper, we propose a new estimator for the maximum expected value, based on a weighted average of the sample means, where the weights are computed using Gaussian approximations for the distributions of the sample means. We compare the proposed estimator with the other state-of-the-art methods both theoretically, by deriving upper bounds to the bias and the variance of the estimator, and empirically, by testing the performance on different sequential learning problems.