We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium -- such as Nash equilibrium and (Coarse) Correlated Equilibrium -- from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies' returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed "unilateral concentrability". Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.
We study what dataset assumption permits solving offline two-player zero-sum Markov games. In stark contrast to the offline single-agent Markov decision process, we show that the single strategy concentration assumption is insufficient for learning the Nash equilibrium (NE) strategy in offline two-player zero-sum Markov games. On the other hand, we propose a new assumption named unilateral concentration and design a pessimism-type algorithm that is provably efficient under this assumption. In addition, we show that the unilateral concentration assumption is necessary for learning an NE strateg…
The Hong Kong University of Science Technology（香港科技大学）；Peking University（北京大学）；University of Virginia（弗吉尼亚大学）
Offline reinforcement learning (RL) aims at learning an optimal strategy using a pre-collected dataset without further interactions with the environment. While various algorithms have been proposed for offline RL in the previous literature, the minimax optimality has only been (nearly) established for tabular Markov decision processes (MDPs). In this paper, we focus on offline RL with linear function approximation and propose a new pessimism-based algorithm for offline linear MDP. At the core of our algorithm is the uncertainty decomposition via a reference function, which is new in the litera…
The combination of Formal Methods with Reinforcement Learning (RL) has recently attracted interest as a way for single-agent RL to learn multiple-task specifications. In this paper we extend this convergence to multi-agent settings and formally define Extended Markov Games as a general mathematical model that allows multiple RL agents to concurrently learn various non-Markovian specifications. To introduce this new model we provide formal definitions and proofs as well as empirical tests of RL algorithms running on this framework. Specifically, we use our model to train two different logic-bas…
Microsoft Research（微软研究院）；University of Toronto（多伦多大学）；Hamilton Health Sciences（汉密尔顿健康科学中心）；Population Health Research Institute（人口健康研究所）；Duke University（杜克大学）；Massachusetts Institute of Technology（麻省理工学院）
Reinforcement learning (RL) tasks are typically framed as Markov Decision Processes (MDPs), assuming that decisions are made at fixed time intervals. However, many applications of great importance, including healthcare, do not satisfy this assumption, yet they are commonly modelled as MDPs after an artificial reshaping of the data. In addition, most healthcare (and similar) problems are offline by nature, allowing for only retrospective studies. To address both challenges, we begin by discussing the Semi-MDP (SMDP) framework, which formally handles actions of variable timings. We next present …
Scaling Offline Model-Based RL via Jointly-Optimized World-Action Model Pretraining
State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences（多模态人工智能系统国家重点实验室，自动化研究所，中国科学院）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；Alibaba Group（阿里巴巴集团）
Massachusetts Institute of Technology（麻省理工学院）；Princeton University（普林斯顿大学）
We study online learning in unknown Markov games, a problem that arises in episodic multi-agent reinforcement learning where the actions of the opponents are unobservable. We show that in this challenging setting, achieving sublinear regret against the best response in hindsight is statistically hard. We then consider a weaker notion of regret by competing with the \emph{minimax value} of the game, and present an algorithm that achieves a sublinear $\tilde{\mathcal{O}}(K^{2/3})$ regret after $K$ episodes. This is the first sublinear regret bound (to our knowledge) for online learning in unknow…
We consider the problem of decentralized multi-agent reinforcement learning in Markov games. A fundamental question is whether there exist algorithms that, when adopted by all agents and run independently in a decentralized fashion, lead to no-regret for each player, analogous to celebrated convergence results in normal-form games. While recent work has shown that such algorithms exist for restricted settings (notably, when regret is defined with respect to deviations to Markovian policies), the question of whether independent no-regret learning can be achieved in the standard Markov game fram…
University of South Carolina（南卡罗来纳大学）；Virginia Tech（弗吉尼亚理工大学）
We study the performance of policy gradient methods for the subclass of Markov games known as Markov potential games (MPGs), which extends the notion of normal-form potential games to the stateful setting and includes the important special case of the fully cooperative setting where the agents share an identical reward function. Our focus in this paper is to study the convergence of the policy gradient method for solving MPGs under softmax policy parameterization, both tabular and parameterized with general function approximators such as neural networks. We first show the asymptotic convergenc…
Northwestern University（西北大学）；George Washington University（乔治华盛顿大学）；Yale University（耶鲁大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
We study the offline reinforcement learning (RL) in the face of unmeasured confounders. Due to the lack of online interaction with the environment, offline RL is facing the following two significant challenges: (i) the agent may be confounded by the unobserved state variables; (ii) the offline data collected a prior does not provide sufficient coverage for the environment. To tackle the above challenges, we study the policy learning in the confounded MDPs with the aid of instrumental variables. Specifically, we first establish value function (VF)-based and marginalized importance sampling (MIS…
University of Southern California（南加州大学）；Massachusetts Institute of Technology（麻省理工学院）
We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space and/or the number of players can be very large, we propose new independent policy gradient algorithms that are run by all players in tandem. When there is no uncertainty in the gradient evaluation, we show that our algorithm finds an $ε$-Nash equilibrium with $O(1/ε^2)$ iteration complexity which does not explicitly depend on the state space size. When the e…
Oxford Robotics Institute（牛津机器人研究所）；University of Oxford（牛津大学）
Offline reinforcement learning (RL) aims to find performant policies from logged data without further environment interaction. Model-based algorithms, which learn a model of the environment from the dataset and perform conservative policy optimisation within that model, have emerged as a promising approach to this problem. In this work, we present Robust Adversarial Model-Based Offline RL (RAMBO), a novel approach to model-based offline RL. We formulate the problem as a two-player zero sum game against an adversarial environment model. The model is trained to minimise the value function while …
This paper presents a theoretical framework for probably approximately correct (PAC) multi-agent reinforcement learning (MARL) algorithms for Markov games. The paper offers an extension to the well-known Nash Q-learning algorithm, using the idea of delayed Q-learning, in order to build a new PAC MARL algorithm for general-sum Markov games. In addition to guiding the design of a provably PAC MARL algorithm, the framework enables checking whether an arbitrary MARL algorithm is PAC. Comparative numerical results demonstrate performance and robustness.
Yale University（耶鲁大学）；Princeton University（普林斯顿大学）；Northwestern University（西北大学）；University of Washington（华盛顿大学）
As one of the most popular methods in the field of reinforcement learning, Q-learning has received increasing attention. Recently, there have been more theoretical works on the regret bound of algorithms that belong to the Q-learning class in different settings. In this paper, we analyze the cumulative regret when conducting Nash Q-learning algorithm on 2-player turn-based stochastic Markov games (2-TBSG), and propose the very first gap dependent logarithmic upper bounds in the episodic tabular setting. This bound matches the theoretical lower bound only up to a logarithmic term. Furthermore, …
University of California, Berkeley（加州大学伯克利分校）；University of California, Los Angeles（加州大学洛杉矶分校）
We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS). The key challenge is how to do exploration in the high-dimensional function space. We propose a novel online learning algorithm to find a Nash equilibrium by minimizing the duality gap. At the core of our algorithms are upper and lower confidence bounds that are derived based on the principle of optimism in the face of uncertainty. We prove that our algorithm is able to attain …
We study reinforcement learning for two-player zero-sum Markov games with simultaneous moves in the finite-horizon setting, where the transition kernel of the underlying Markov games can be parameterized by a linear function over the current state, both players' actions and the next state. In particular, we assume that we can control both players and aim to find the Nash Equilibrium by minimizing the duality gap. We propose an algorithm Nash-UCRL based on the principle "Optimism-in-Face-of-Uncertainty". Our algorithm only needs to find a Coarse Correlated Equilibrium (CCE), which is computatio…
High-Probability Nash Regret for Decentralized Learning in Markov $α$-Potential Games: Episodic and Fully Online Asynchronous Algorithms with Applications to Markov Congestion Games
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
University of California, Irvine（加州大学欧文分校）；Carnegie Mellon University（卡内基梅隆大学）；Columbia University（哥伦比亚大学）；University of California, Santa Cruz（加州大学圣克鲁兹分校）
Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully competitive or cooperative scenarios or impose strong assumptions that are difficult to meet in most practical applications. In this work, we depart from those prior results by investigating infinite-horizon \emph{adversarial team Markov games}, a natural and well-motivated class of games in which a team of identically-interested players -- in the absence of an…
We show that computing approximate stationary Markov coarse correlated equilibria (CCE) in general-sum stochastic games is computationally intractable, even when there are two players, the game is turn-based, the discount factor is an absolute constant, and the approximation is an absolute constant. Our intractability results stand in sharp contrast to normal-form games where exact CCEs are efficiently computable. A fortiori, our results imply that there are no efficient algorithms for learning stationary Markov CCE policies in multi-agent reinforcement learning (MARL), even when the interacti…
Multi-agent reinforcement learning has been successfully applied to fully-cooperative and fully-competitive environments, but little is currently known about mixed cooperative/competitive environments. In this paper, we focus on a particular class of multi-agent mixed cooperative/competitive stochastic games called Markov Potential Games (MPGs), which include cooperative games as a special case. Recent results have shown that independent policy gradient converges in MPGs but it was not known whether Independent Natural Policy Gradient converges in MPGs as well. We prove that Independent Natura…
Peking University（北京大学）；University of Groningen（格罗宁根大学）
In stochastic dynamic environments, team Markov games have emerged as a versatile paradigm for studying sequential decision-making problems of fully cooperative multi-agent systems. However, the optimality of the derived policies is usually sensitive to model parameters, which are typically unknown and required to be estimated from noisy data in practice. To mitigate the sensitivity of optimal policies to these uncertain parameters, we propose a robust model of team Markov games in this paper, where agents utilize robust optimization approaches to update strategies. This model extends team Mar…
We study multi-player general-sum Markov games with one of the players designated as the leader and the other players regarded as followers. In particular, we focus on the class of games where the followers are myopic, i.e., they aim to maximize their instantaneous rewards. For such a game, our goal is to find a Stackelberg-Nash equilibrium (SNE), which is a policy pair $(π^*, ν^*)$ such that (i) $π^*$ is the optimal policy for the leader when the followers always play their best response, and (ii) $ν^*$ is the best response policy of the followers, which is a Nash equilibrium of the followers…
Northwestern University（西北大学）；George Washington University（乔治华盛顿大学）；Yale University（耶鲁大学）；University of Miami（迈阿密大学）
Motivated by the human-machine interaction such as training chatbots for improving customer satisfaction, we study human-guided human-machine interaction involving private information. We model this interaction as a two-player turn-based game, where one player (Alice, a human) guides the other player (Bob, a machine) towards a common goal. Specifically, we focus on offline reinforcement learning (RL) in this game, where the goal is to find a policy pair for Alice and Bob that maximizes their expected total rewards based on an offline dataset collected a priori. The offline setting presents two…
Optimistic Policy Gradient in Multi-Player Markov Games with a Single Controller: Convergence Beyond the Minty Property
Meta AI；University of California Irvine（加州大学欧文分校）；Archimedes research unit（阿基米德研究单元）；Massachusetts Institute of Technology（麻省理工学院）；Strategy Robot, Inc.（战略机器人公司）；Strategic Machine, Inc.（战略机器公司）；Optimized Markets, Inc.（优化市场公司）；Carnegie Mellon University（卡内基梅隆大学）
Convergence of Decentralized Actor-Critic Algorithm in General-sum Markov Games
Electrical Engineering and Computer Sciences (EECS) at UC Berkeley（加州大学伯克利分校电子工程与计算机科学系）；Operations Research and Information Engineering (ORIE) at Cornell University（康奈尔大学运筹学与信息工程系）
Model-Based Reinforcement Learning for Offline Zero-Sum Markov Games
Institute for Data, Systems, and Society, MIT（麻省理工学院数据、系统与社会研究所）；Department of Statistics, The Chinese University of Hong Kong（香港中文大学统计系）；Department of Statistics and Data Science, Wharton School, University of Pennsylvania（宾夕法尼亚大学沃顿商学院统计与数据科学系）；Department of Operations Research and Financial Engineering, Princeton University（普林斯顿大学运筹学与金融工程系）
University of Pennsylvania（宾夕法尼亚大学）；Carnegie Mellon University（卡内基梅隆大学）
This paper studies multi-agent reinforcement learning in Markov games, with the goal of learning Nash equilibria or coarse correlated equilibria (CCE) sample-optimally. All prior results suffer from at least one of the two obstacles: the curse of multiple agents and the barrier of long horizon, regardless of the sampling protocol in use. We take a step towards settling this problem, assuming access to a flexible sampling mechanism: the generative model. Focusing on non-stationary finite-horizon Markov games, we develop a fast learning algorithm called \myalg~and an adaptive sampling scheme tha…
