Distributional Reinforcement Learning (RL) maintains the entire probability distribution of the reward-to-go, i.e. the return, providing more learning signals that account for the uncertainty associated with policy performance, which may be beneficial for trading off exploration and exploitation and policy learning in general. Previous works in distributional RL focused mainly on computing the state-action-return distributions, here we model the state-return distributions. This enables us to translate successful conventional RL algorithms that are based on state values into distributional RL. We formulate the distributional Bellman operation as an inference-based auto-encoding process that minimises Wasserstein metrics between target/model return distributions. The proposed algorithm, BDPG (Bayesian Distributional Policy Gradients), uses adversarial training in joint-contrastive learning to estimate a variational posterior from the returns. Moreover, we can now interpret the return prediction uncertainty as an information gain, which allows to obtain a new curiosity measure that helps BDPG steer exploration actively and efficiently. We demonstrate in a suite of Atari 2600 games and MuJoCo tasks, including well known hard-exploration challenges, how BDPG learns generally faster and with higher asymptotic performance than reference distributional RL algorithms.
Distributional reinforcement learning (DRL) is a recent reinforcement learning framework whose success has been supported by various empirical studies. It relies on the key idea of replacing the expected return with the return distribution, which captures the intrinsic randomness of the long term rewards. Most of the existing literature on DRL focuses on problems with discrete action space and value based methods. In this work, motivated by applications in robotics with continuous action space control settings, we propose sample-based distributional policy gradient (SDPG) algorithm. It models …
Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO), as the widely employed policy based reinforcement learning (RL) methods, are prone to converge to a sub-optimal solution as they limit the policy representation to a particular parametric distribution class. To address this issue, we develop an innovative Optimistic Distributionally Robust Policy Optimization (ODRPO) algorithm, which effectively utilizes Optimistic Distributionally Robust Optimization (DRO) approach to solve the trust region constrained optimization problem without parameterizing the policies. Our …
Distributional Soft Bellman Operator under the Cramér Geometry
School of Electrical and Electronic Engineering, University College Dublin（都柏林大学学院电气与电子工程学院）；School of Vehicle and Mobility, Tsinghua University（清华大学车辆与运载学院）；College of Artificial Intelligence, Tsinghua University（清华大学人工智能学院）
We study the multi-step off-policy learning approach to distributional RL. Despite the apparent similarity between value-based RL and distributional RL, our study reveals intriguing and fundamental differences between the two cases in the multi-step setting. We identify a novel notion of path-dependent distributional TD error, which is indispensable for principled multi-step distributional RL. The distinction from the value-based case bears important implications on concepts such as backward-view algorithms. Our work provides the first theoretical guarantees on multi-step off-policy distributi…
To improve the sample efficiency of policy-gradient based reinforcement learning algorithms, we propose implicit distributional actor-critic (IDAC) that consists of a distributional critic, built on two deep generator networks (DGNs), and a semi-implicit actor (SIA), powered by a flexible policy distribution. We adopt a distributional perspective on the discounted cumulative return and model it with a state-action-dependent implicit distribution, which is approximated by the DGNs that take state-action pairs and random noises as their input. Moreover, we use the SIA to provide a semi-implicit …
Reinforcement learning (RL) has achieved remarkable performance in numerous sequential decision making and control tasks. However, a common problem is that learned nearly optimal policy always overfits to the training environment and may not be extended to situations never encountered during training. For practical applications, the randomness of environment usually leads to some devastating events, which should be the focus of safety-critical systems such as autonomous driving. In this paper, we introduce the minimax formulation and distributional framework to improve the generalization abili…
We identify a fundamental problem in policy gradient-based methods in continuous control. As policy gradient methods require the agent's underlying probability distribution, they limit policy representation to parametric distribution classes. We show that optimizing over such sets results in local movement in the action space and thus convergence to sub-optimal solutions. We suggest a novel distributional framework, able to represent arbitrary distribution functions over the continuous action space. Using this framework, we construct a generative scheme, trained using an off-policy actor-criti…
Affiliated High School of South China Normal University（华南师范大学附属中学）
We consider the problem of offline reinforcement learning with model-based control, whose goal is to learn a dynamics model from the experience replay and obtain a pessimism-oriented agent under the learned model. Current model-based constraint includes explicit uncertainty penalty and implicit conservative regularization that pushes Q-values of out-of-distribution state-action pairs down and the in-distribution up. While the uncertainty estimation, on which the former relies on, can be loosely calibrated for complex dynamics, the latter performs slightly better. To extend the basic idea of re…
This work adopts the very successful distributional perspective on reinforcement learning and adapts it to the continuous control setting. We combine this within a distributed framework for off-policy learning in order to develop what we call the Distributed Distributional Deep Deterministic Policy Gradient algorithm, D4PG. We also combine this technique with a number of additional, simple improvements such as the use of $N$-step returns and prioritized experience replay. Experimentally we examine the contribution of each of these individual components, and show how they interact, as well as t…
Distributional Soft Actor-Critic with Diffusion Policy
School of Vehicle and Mobility, Tsinghua University（车辆与移动学院，清华大学）；School of Mechanical Engineering, University of Science and Technology Beijing（机械工程学院，北京科技大学）
Policy gradient methods have had great success in solving continuous control tasks, yet the stochastic nature of such problems makes deterministic value estimation difficult. We propose an approach which instead estimates a distribution by fitting the value function with a Bayesian Neural Network. We optimize an $α$-divergence objective with Bayesian dropout approximation to learn and estimate this distribution. We show that using the Monte Carlo posterior mean of the Bayesian value function distribution, rather than a deterministic network, improves stability and performance of policy gradien…
Federated Distributional Reinforcement Learning with Distributional Critic Regularization
Dept. of Mechanical Engineering, Rochester Institute of Technology（机械工程系，罗切斯特理工学院）；Dept. of Psychology and School of Information, Rochester Institute of Technology（心理学系和信息学院，罗切斯特理工学院）；Department of Engineering Science, University West（工程科学系，西大学）；Golisano College of Computing and Information Sciences, Rochester Institute of Technology（计算与信息科学学院，罗切斯特理工学院）
KTH Royal Institute of Technology（瑞典皇家理工学院）；University of Oxford（牛津大学）；Technical University of Munich（慕尼黑工业大学）；Duke University（杜克大学）
Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard RL. At the same time, a main challenge in DRL is that policy evaluation in DRL typically relies on the representation of the return distribution, which needs to be carefully designed. In this paper, we address this challenge for a special class of DRL problems that rely on linear quadratic regulator (LQR) for control, advocating for a new distributional approach to LQ…
In reinforcement learning (RL), function approximation errors are known to easily lead to the Q-value overestimations, thus greatly reducing policy performance. This paper presents a distributional soft actor-critic (DSAC) algorithm, which is an off-policy RL method for continuous control setting, to improve the policy performance by mitigating Q-value overestimations. We first discover in theory that learning a distribution function of state-action returns can effectively mitigate Q-value overestimations because it is capable of adaptively adjusting the update stepsize of the Q-value function…
This work studies reinforcement learning (RL) in the context of multi-period supply chains subject to constraints, e.g., on production and inventory. We introduce Distributional Constrained Policy Optimization (DCPO), a novel approach for reliable constraint satisfaction in RL. Our approach is based on Constrained Policy Optimization (CPO), which is subject to approximation errors that in practice lead it to converge to infeasible policies. We address this issue by incorporating aspects of distributional RL into DCPO. Specifically, we represent the return and cost value functions using neural …
Real-world applications require RL algorithms to act safely. During learning process, it is likely that the agent executes sub-optimal actions that may lead to unsafe/poor states of the system. Exploration is particularly brittle in high-dimensional state/action space due to increased number of low-performing actions. In this work, we consider risk-averse exploration in approximate RL setting. To ensure safety during learning, we propose the distributionally robust policy iteration scheme that provides lower bound guarantee on state-values. Our approach induces a dynamic level of risk to preve…
Generalized Advantage Estimation for Distributional Policy Gradients
Mechanical Engineering Department, Clemson University（克莱姆斯大学机械工程系）；Ground Vehicle Systems Center U.S. Army CCDC（美国陆军地面车辆系统中心）；Automotive Research Center (ARC) at the University of Michigan, Ann Arbor（密歇根大学安娜堡分校汽车研究中心）
University of Liège（列日大学）；Institut Polytechnique de Paris（巴黎理工学院）
Classical reinforcement learning (RL) techniques are generally concerned with the design of decision-making policies driven by the maximisation of the expected outcome. Nevertheless, this approach does not take into consideration the potential risk associated with the actions taken, which may be critical in certain applications. To address that issue, the present research work introduces a novel methodology based on distributional RL to derive sequential decision-making policies that are sensitive to the risk, the latter being modelled by the tail of the return probability distribution. The co…
Distributional Off-Policy Evaluation with Deep Quantile Process Regression
School of Statistics and Data Science, and Philosophy and Social Sciences Laboratory of Data Science in Finance and Economics at the Ministry of Education, Jiangxi University of Finance and Economics（统计学与数据科学学院，暨教育部金融与经济数据科学与社会科学实验室，江西财经大学）；School of Statistics and Data Science, Shanghai University of Finance and Economics（统计学与数据科学学院，上海财经大学）；School of Artificial Intelligence, and Hubei Key Laboratory of Computational Science, Wuhan University（人工智能学院，湖北省计算科学重点实验室，武汉大学）
KLATASDS - MOE School of Statistics East China Normal University（KLATASDS - 教育部统计学系华东师范大学）
Reliable uncertainty quantification is crucial for reinforcement learning (RL) in high-stakes settings. We propose a unified conformal prediction framework for infinite-horizon policy evaluation that constructs distribution-free prediction intervals {for returns} in both on-policy and off-policy settings. Our method integrates distributional RL with conformal calibration, addressing challenges such as unobserved returns, temporal dependencies, and distributional shifts. We propose a modular pseudo-return construction based on truncated rollouts and a time-aware calibration strategy using exper…
Carnegie Mellon University（卡内基梅隆大学）；Columbia University（哥伦比亚大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
One key challenge for multi-task Reinforcement learning (RL) in practice is the absence of task indicators. Robust RL has been applied to deal with task ambiguity, but may result in over-conservative policies. To balance the worst-case (robustness) and average performance, we propose Group Distributionally Robust Markov Decision Process (GDR-MDP), a flexible hierarchical MDP formulation that encodes task groups via a latent mixture model. GDR-MDP identifies the optimal policy that maximizes the expected return under the worst-possible qualified belief over task groups within an ambiguity set. …
Safety in reinforcement learning (RL) is a key property in both training and execution in many domains such as autonomous driving or finance. In this paper, we formalize it with a constrained RL formulation in the distributional RL setting. Our general model accepts various definitions of safety(e.g., bounds on expected performance, CVaR, variance, or probability of reaching bad states). To ensure safety during learning, we extend a safe policy optimization method to solve our problem. The distributional RL perspective leads to a more efficient algorithm while additionally catering for natural…
Vector-Valued Distributional Reinforcement Learning Policy Evaluation: A Hilbert Space Embedding Approach
Department of Statistics, University of Illinois Urbana-Champaign（统计系，伊利诺伊大学厄巴纳-香槟分校）；Department of Bioinformatics and Biostatistics, University of Louisville（生物信息学与生物统计学系，路易斯维尔大学）
Many real-world problems require trading off multiple competing objectives. However, these objectives are often in different units and/or scales, which can make it challenging for practitioners to express numerical preferences over objectives in their native units. In this paper we propose a novel algorithm for multi-objective reinforcement learning that enables setting desired preferences for objectives in a scale-invariant way. We propose to learn an action distribution for each objective, and we use supervised learning to fit a parametric policy to a combination of these distributions. We d…
On Generalization and Distributional Update for Mimicking Observations with Adequate Exploration
Shanghai Institute of Satellite Engineering（上海卫星工程研究所）；Department of Mathematics, College of Sciences, Shanghai University（上海大学数学系）；School of Computer Science, University of Bristol（布里斯托大学计算机科学学院）；Newtouch Center for Mathematics of Shanghai University（上海大学数学中心）
We introduce a distributional method for learning the optimal policy in risk averse Markov decision process with finite state action spaces, latent costs, and stationary dynamics. We assume sequential observations of states, actions, and costs and assess the performance of a policy using dynamic risk measures constructed from nested Kusuoka-type conditional risk mappings. For such performance criteria, randomized policies may outperform deterministic policies, therefore, the candidate policies lie in the d-dimensional simplex where d is the cardinality of the action space. Existing risk averse…
Actor-critic algorithms that make use of distributional policy evaluation have frequently been shown to outperform their non-distributional counterparts on many challenging control tasks. Examples of this behavior include the D4PG and DMPO algorithms as compared to DDPG and MPO, respectively [Barth-Maron et al., 2018; Hoffman et al., 2020]. However, both agents rely on the C51 critic for value estimation.One major drawback of the C51 approach is its requirement of prior knowledge about the minimum andmaximum values a policy can attain as well as the number of bins used, which fixes the resolut…
We propose a framework based on distributional reinforcement learning and recent attempts to combine Bayesian parameter updates with deep reinforcement learning. We show that our proposed framework conceptually unifies multiple previous methods in exploration. We also derive a practical algorithm that achieves efficient exploration on challenging control tasks.
Informed and robust decision making in the face of uncertainty is critical for robots that perform physical tasks alongside people. We formulate this as Bayesian Reinforcement Learning over latent Markov Decision Processes (MDPs). While Bayes-optimality is theoretically the gold standard, existing algorithms do not scale well to continuous state and action spaces. Our proposal builds on the following insight: in the absence of uncertainty, each latent MDP is easier to solve. We first obtain an ensemble of experts, one for each latent MDP, and fuse their advice to compute a baseline policy. Nex…
A Distributional Analogue to the Successor Representation
McGill University（麦吉尔大学）；Mila - Québec AI Institute（米拉-魁北克人工智能研究所）；Google DeepMind（谷歌DeepMind）；University College London（伦敦大学学院）；CIFAR AI Chair（加拿大高级研究所人工智能主席职位）
McGill University（麦吉尔大学）；University of Alberta（阿尔伯塔大学）
Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors. PAC-Bayesian methods overcome this problem by providing bounds that hold regardless of the correctness of the prior distribution. This paper introduces the first PAC-Bayesian bound for the batch reinforcement learning problem with function approximation. We show how this bound can be used to perform model-selection in a transfer learning scenario. Our empirical …
We study the problem of obtaining accurate policy gradient estimates using a finite number of samples. Monte-Carlo methods have been the default choice for policy gradient estimation, despite suffering from high variance in the gradient estimates. On the other hand, more sample efficient alternatives like Bayesian quadrature methods have received little attention due to their high computational complexity. In this work, we propose deep Bayesian quadrature policy gradient (DBQPG), a computationally efficient high-dimensional generalization of Bayesian quadrature, for policy gradient estimation.…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳市人工智能与机器人研究院）
In a sequential decision-making problem, off-policy evaluation estimates the expected cumulative reward of a target policy using logged trajectory data generated from a different behavior policy, without execution of the target policy. Reinforcement learning in high-stake environments, such as healthcare and education, is often limited to off-policy settings due to safety or ethical concerns, or inability of exploration. Hence it is imperative to quantify the uncertainty of the off-policy estimate before deployment of the target policy. In this paper, we propose a novel framework that provides…
Paul G. Allen School of Computer Science & Engineering（保罗·G·艾伦计算机科学与工程学院）；University of Washington（华盛顿大学）
Addressing uncertainty is critical for autonomous systems to robustly adapt to the real world. We formulate the problem of model uncertainty as a continuous Bayes-Adaptive Markov Decision Process (BAMDP), where an agent maintains a posterior distribution over latent model parameters given a history of observations and maximizes its expected long-term reward with respect to this belief distribution. Our algorithm, Bayesian Policy Optimization, builds on recent policy optimization algorithms to learn a universal policy that navigates the exploration-exploitation trade-off to maximize the Bayesia…
We present a distributional approach to theoretical analyses of reinforcement learning algorithms for constant step-sizes. We demonstrate its effectiveness by presenting simple and unified proofs of convergence for a variety of commonly-used methods. We show that value-based methods such as TD($λ$) and $Q$-Learning have update rules which are contractive in the space of distributions of functions, thus establishing their exponentially fast convergence to a stationary distribution. We demonstrate that the stationary distribution obtained by any algorithm whose target is an expected Bellman upda…
