We introduce Wasserstein Adversarial Proximal Policy Optimization (WAPPO), a novel algorithm for visual transfer in Reinforcement Learning that explicitly learns to align the distributions of extracted features between a source and target task. WAPPO approximates and minimizes the Wasserstein-1 distance between the distributions of features from source and target domains via a novel Wasserstein Confusion objective. WAPPO outperforms the prior state-of-the-art in visual transfer and successfully transfers policies across Visual Cartpole and two instantiations of 16 OpenAI Procgen environments.
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Baidu Inc.（百度公司）
Robust Reinforcement Learning aims to find the optimal policy with some extent of robustness to environmental dynamics. Existing learning algorithms usually enable the robustness through disturbing the current state or simulating environmental parameters in a heuristic way, which lack quantified robustness to the system dynamics (i.e. transition probability). To overcome this issue, we leverage Wasserstein distance to measure the disturbance to the reference transition kernel. With Wasserstein distance, we are able to connect transition kernel disturbance to the state disturbance, i.e. reduce …
Gatsby Unit, UCL（伦敦大学学院盖茨比计算神经科学单元）；University of Cambridge（剑桥大学）
A novel optimization approach is proposed for application to policy gradient methods and evolution strategies for reinforcement learning (RL). The procedure uses a computationally efficient Wasserstein natural gradient (WNG) descent that takes advantage of the geometry induced by a Wasserstein penalty to speed optimization. This method follows the recent theme in RL of including a divergence penalty in the objective to establish a trust region. Experiments on challenging tasks demonstrate improvements in both computational cost and performance over advanced baselines.
Huawei R&D UK（华为英国研发中心）；Imperial College London（帝国理工学院）；University College London（伦敦大学学院）；University of Cambridge（剑桥大学）
Reinforcement learning algorithms, though successful, tend to over-fit to training environments hampering their application to the real-world. This paper proposes $\text{W}\text{R}^{2}\text{L}$ -- a robust reinforcement learning algorithm with significant robust performance on low and high-dimensional control tasks. Our method formalises robust reinforcement learning as a novel min-max game with a Wasserstein constraint for a correct and convergent solver. Apart from the formulation, we also propose an efficient and scalable solver following a novel zero-order optimisation method that we belie…
Learning a generative model is a key component of model-based reinforcement learning. Though learning a good model in the tabular setting is a simple task, learning a useful model in the approximate setting is challenging. In this context, an important question is the loss function used for model learning as varying the loss function can have a remarkable impact on effectiveness of planning. Recently Farahmand et al. (2017) proposed a value-aware model learning (VAML) objective that captures the structure of value function during model learning. Using tools from Asadi et al. (2018), we show th…
We describe an application of Wasserstein distance to Reinforcement Learning. The Wasserstein distance in question is between the distribution of mappings of trajectories of a policy into some metric space, and some other fixed distribution (which may, for example, come from another policy). Different policies induce different distributions, so given an underlying metric, the Wasserstein distance quantifies how different policies are. This can be used to learn multiple polices which are different in terms of such Wasserstein distances by using a Wasserstein regulariser. Changing the sign of th…
Despite notable results in various fields over the recent years, deep reinforcement learning (DRL) algorithms lack transparency, affecting user trust and hindering their deployment to high-risk tasks. Causal confusion refers to a phenomenon where an agent learns spurious correlations between features which might not hold across the entire state space, preventing safe deployment to real tasks where such correlations might be broken. In this work, we examine whether an agent relies on spurious correlations in critical states, and propose an alternative subset of features on which it should base …
Unsupervised reinforcement learning aims to train agents to learn a handful of policies or skills in environments without external reward. These pre-trained policies can accelerate learning when endowed with external reward, and can also be used as primitive options in hierarchical reinforcement learning. Conventional approaches of unsupervised skill discovery feed a latent variable to the agent and shed its empowerment on agent's behavior by mutual information (MI) maximization. However, the policies learned by MI-based methods cannot sufficiently explore the state space, despite they can be …
Data Science Institute（数据科学研究所）；Imperial College（帝国理工学院）；Institute of Security Science and Technology（安全科学与技术研究所）
Policy gradients methods often achieve better performance when the change in policy is limited to a small Kullback-Leibler divergence. We derive policy gradients where the change in policy is limited to a small Wasserstein distance (or trust region). This is done in the discrete and continuous multi-armed bandit settings with entropy regularisation. We show that in the small steps limit with respect to the Wasserstein distance $W_2$, policy dynamics are governed by the Fokker-Planck (heat) equation, following the Jordan-Kinderlehrer-Otto result. This means that policies undergo diffusion and a…
Bosch Center for Artificial Intelligence（博世人工智能中心）；Robert Bosch GmbH（罗伯特·博世有限公司）
Imitation Learning describes the problem of recovering an expert policy from demonstrations. While inverse reinforcement learning approaches are known to be very sample-efficient in terms of expert demonstrations, they usually require problem-dependent reward functions or a (task-)specific reward-function regularization. In this paper, we show a natural connection between inverse reinforcement learning approaches and Optimal Transport, that enables more general reward functions with desirable properties (e.g., smoothness). Based on our observation, we propose a novel approach called Wasserstei…
University of Cambridge（剑桥大学）；Columbia University（哥伦比亚大学）；Google Brain（谷歌大脑）；Google Research（谷歌研究院）；The Alan Turing Institute（艾伦·图灵研究所）
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In this paper, we propose a new variant of sliced Wasserstein distance, study the use of orthogonal coupling in Monte Carlo estimation of Wasserstein distances and draw connections with stratified sampling, and evaluate our approaches experimentally in a range of large-scale experiments in generative modelling and reinforcement learning.
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Sony AI（索尼人工智能）
Learning with an objective to minimize the mismatch with a reference distribution has been shown to be useful for generative modeling and imitation learning. In this paper, we investigate whether one such objective, the Wasserstein-1 distance between a policy's state visitation distribution and a target distribution, can be utilized effectively for reinforcement learning (RL) tasks. Specifically, this paper focuses on goal-conditioned reinforcement learning where the idealized (unachievable) target distribution has full measure at the goal. This paper introduces a quasimetric specific to Marko…
Wasserstein Distributionally Robust Regret Optimization for Reinforcement Learning from Human Feedback
Department of Statistics and Operations Research, University of North Carolina（统计与运筹学系，北卡罗来纳大学）；Imperial Business School, Imperial College London（帝国理工学院伦敦商学院）；Department of Management Science and Engineering, Stanford University（管理科学与工程系，斯坦福大学）
Duke University（杜克大学）；SUNY at Buffalo（纽约州立大学布法罗分校）
Policy optimization is a core component of reinforcement learning (RL), and most existing RL methods directly optimize parameters of a policy based on maximizing the expected total reward, or its surrogate. Though often achieving encouraging empirical success, its underlying mathematical principle on {\em policy-distribution} optimization is unclear. We place policy optimization into the space of probability measures, and interpret it as Wasserstein gradient flows. On the probability-measure space, under specified circumstances, policy optimization becomes a convex problem in terms of distribu…
Distributional reinforcement learning (DRL) extends the value-based approach by approximating the full distribution over future returns instead of the mean only, providing a richer signal that leads to improved performances. Quantile Regression (QR) based methods like QR-DQN project arbitrary distributions into a parametric subset of staircase distributions by minimizing the 1-Wasserstein distance. However, due to biases in the gradients, the quantile regression loss is used instead for training, guaranteeing the same minimizer and enjoying unbiased gradients. Non-crossing constraints on the q…
Distributionally Robust Optimization (DRO) has enabled to prove the equivalence between robustness and regularization in classification and regression, thus providing an analytical reason why regularization generalizes well in statistical learning. Although DRO's extension to sequential decision-making overcomes $\textit{external uncertainty}$ through the robust Markov Decision Process (MDP) setting, the resulting formulation is hard to solve, especially on large domains. On the other hand, existing regularization methods in reinforcement learning only address $\textit{internal uncertainty}$ d…
Inverse reinforcement learning (IRL) is used to infer the reward function from the actions of an expert running a Markov Decision Process (MDP). A novel approach using variational inference for learning the reward function is proposed in this research. Using this technique, the intractable posterior distribution of the continuous latent variable (the reward function in this case) is analytically approximated to appear to be as close to the prior belief while trying to reconstruct the future state conditioned on the current state and action. The reward function is derived using a well-known dee…
Quantile-Coupled Flow Matching for Distributional Reinforcement Learning
Oxford Robotics Institute, University of Oxford（牛津大学机器人研究所）；Bristol Robotics Laboratory, University of the West of England（布里斯托尔机器人实验室，西英格兰大学）；Dyson Institute of Engineering & Technology（戴森工程与技术研究院）
Zhiyuan College, Shanghai Jiao Tong University, Shanghai 200240, China（上海交通大学紫阳学院）；School of Data Science, The Chinese University of Hong Kong, Shenzhen, Guangdong, China（香港中文大学（深圳）数据科学学院）；McCombs School of Business, The University of Texas at Austin, Austin, TX, USA（德克萨斯大学奥斯汀分校麦克拉姆商学院）
We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the Wasserstein metric. We go on to prove an error bound for the value-function estimate arising from Lipschitz models and show that the estimated value function is itself Lipschitz. We conclude with empirical results that show the benefits of controlling the Lipschitz constant of neural-network models.
Duke University（杜克大学）；University at Buffalo（布法罗大学）；Microsoft Dynamics 365 AI Research（微软Dynamics 365人工智能研究院）；DeepMind（深度思维）
Reinforcement learning (RL) has been widely studied for improving sequence-generation models. However, the conventional rewards used for RL training typically cannot capture sufficient semantic information and therefore render model bias. Further, the sparse and delayed rewards make RL exploration inefficient. To alleviate these issues, we propose the concept of nested-Wasserstein distance for distributional semantic matching. To further exploit it, a novel nested-Wasserstein self-imitation learning framework is developed, encouraging the model to exploit historical high-rewarded sequences for…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；University of Illinois, Urbana–Champaign（伊利诺伊大学厄巴纳-香槟分校）
Recent studies have shown that reinforcement learning (RL) models are vulnerable in various noisy scenarios. For instance, the observed reward channel is often subject to noise in practice (e.g., when rewards are collected through sensors), and is therefore not credible. In addition, for applications such as robotics, a deep reinforcement learning (DRL) algorithm can be manipulated to produce arbitrary errors by receiving corrupted rewards. In this paper, we consider noisy RL problems with perturbed rewards, which can be approximated with a confusion matrix. We develop a robust RL framework th…
We describe a new approach for managing aleatoric uncertainty in the Reinforcement Learning (RL) paradigm. Instead of selecting actions according to a single statistic, we propose a distributional method based on the second-order stochastic dominance (SSD) relation. This compares the inherent dispersion of random returns induced by actions, producing a more comprehensive and robust evaluation of the environment's uncertainty. The necessary conditions for SSD require estimators to predict accurate second moments. To accommodate this, we map the distributional RL problem to a Wasserstein gradien…
Building on the framework introduced by Xu and Raginksy [1] for supervised learning problems, we study the best achievable performance for model-based Bayesian reinforcement learning problems. With this purpose, we define minimum Bayesian regret (MBR) as the difference between the maximum expected cumulative reward obtainable either by learning from the collected data or by knowing the environment and its dynamics. We specialize this definition to reinforcement learning problems modeled as Markov decision processes (MDPs) whose kernel parameters are unknown to the agent and whose uncertainty i…
The generative adversarial imitation learning (GAIL) has provided an adversarial learning framework for imitating expert policy from demonstrations in high-dimensional continuous tasks. However, almost all GAIL and its extensions only design a kind of reward function of logarithmic form in the adversarial training strategy with the Jensen-Shannon (JS) divergence for all complex environments. The fixed logarithmic type of reward function may be difficult to solve all complex tasks, and the vanishing gradients problem caused by the JS divergence will harm the adversarial learning process. In thi…
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）
University of Bologna（博洛尼亚大学）；Politecnico di Milano（米兰理工大学）
Uncertainty quantification has been extensively used as a means to achieve efficient directed exploration in Reinforcement Learning (RL). However, state-of-the-art methods for continuous actions still suffer from high sample complexity requirements. Indeed, they either completely lack strategies for propagating the epistemic uncertainty throughout the updates, or they mix it with aleatoric uncertainty while learning the full return distribution (e.g., distributional RL). In this paper, we propose Wasserstein Actor-Critic (WAC), an actor-critic architecture inspired by the recent Wasserstein Q-…
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Microsoft Research Asia（微软亚洲研究院）
Behavioral cloning has proven to be effective for learning sequential decision-making policies from expert demonstrations. However, behavioral cloning often suffers from the causal confusion problem where a policy relies on the noticeable effect of expert actions due to the strong correlation but not the cause we desire. This paper presents Object-aware REgularizatiOn (OREO), a simple technique that regularizes an imitation policy in an object-aware manner. Our main idea is to encourage a policy to uniformly attend to all semantic objects, in order to prevent the policy from exploiting nuisanc…
University of Liège（列日大学）；Institut Polytechnique de Paris（巴黎理工学院）
The distributional reinforcement learning (RL) approach advocates for representing the complete probability distribution of the random return instead of only modelling its expectation. A distributional RL algorithm may be characterised by two main components, namely the representation of the distribution together with its parameterisation and the probability metric defining the loss. The present research work considers the unconstrained monotonic neural network (UMNN) architecture, a universal approximator of continuous monotonic functions which is particularly well suited for modelling differ…
Well-Posed KL-Regularized Control via Wasserstein and Kalman-Wasserstein KL Divergences
Department of Mathematics, Technical University of Munich \& Munich Center for Machine Learning, Germany. The majority of the work was conducted while at the Institute of Mathematics at the Technical University of Berlin, Germany \& the Berlin Mathematical School.；Institute for Data Science Foundations, Hamburg University of Technology, Germany；Santa Fe Institute, USA
Hierarchical Reinforcement Learning (HRL) exploits temporally extended actions, or options, to make decisions from a higher-dimensional perspective to alleviate the sparse reward problem, one of the most challenging problems in reinforcement learning. The majority of existing HRL algorithms require either significant manual design with respect to the specific environment or enormous exploration to automatically learn options from data. To achieve fast exploration without using manual design, we devise a multi-goal HRL algorithm, consisting of a high-level policy Manager and a low-level policy …
Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients
School of Mathematics University of Edinburgh, United Kingdom（爱丁堡大学数学学院）；Department of Industrial Engineering Ulsan National Institute of Science and Technology, Republic of Korea（釜山国立科学技术院工业工程系）；National Technical University of Athens, Greece（雅典国家技术大学）；Archimedes, Athena Research Center, Greece（阿提卡研究中心）
Shanghai Jiao Tong University（上海交通大学）；Georgia Institute of Technology（佐治亚理工学院）
Temporal point process is an expressive tool for modeling event sequences over time. In this paper, we take a reinforcement learning view whereby the observed sequences are assumed to be generated from a mixture of latent policies. The purpose is to cluster the sequences with different temporal patterns into the underlying policies while learning each of the policy model. The flexibility of our model lies in: i) all the components are networks including the policy network for modeling the intensity function of temporal point process; ii) to handle varying-length event sequences, we resort to i…
