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This paper considers two-player zero-sum finite-horizon Markov games with simultaneous moves. The study focuses on the challenging settings where the value function or the model is parameterized by general function classes. Provably efficient algorithms for both decoupled and {coordinated} settings are developed. In the {decoupled} setting where the agent controls a single player and plays against an arbitrary opponent, we propose a new model-free algorithm. The sample complexity is governed by the Minimax Eluder dimension -- a new dimension of the function class in Markov games. As a special case, this method improves the state-of-the-art algorithm by a $sqrt{d}$ factor in the regret when the reward function and transition kernel are parameterized with $d$-dimensional linear features. In the {coordinated} setting where both players are controlled by the agent, we propose a model-based algorithm and a model-free algorithm. In the model-based algorithm, we prove that sample complexity can be bounded by a generalization of Witness rank to Markov games. The model-free algorithm enjoys a $sqrt{K}$-regret upper bound where $K$ is the number of episodes. Our algorithms are based on new techniques of alternate optimism.
We study multi-agent reinforcement learning (MARL) in infinite-horizon discounted zero-sum Markov games. We focus on the practical but challenging setting of decentralized MARL, where agents make decisions without coordination by a centralized contro
We present fictitious play dynamics for stochastic games and analyze its convergence properties in zero-sum stochastic games. Our dynamics involves players forming beliefs on opponent strategy and their own continuation payoff (Q-function), and playi
Similar to the role of Markov decision processes in reinforcement learning, Stochastic Games (SGs) lay the foundation for the study of multi-agent reinforcement learning (MARL) and sequential agent interactions. In this paper, we derive that computin
Zero-sum games have long guided artificial intelligence research, since they possess both a rich strategy space of best-responses and a clear evaluation metric. Whats more, competition is a vital mechanism in many real-world multi-agent systems capab
Despite the many recent practical and theoretical breakthroughs in computational game theory, equilibrium finding in extensive-form team games remains a significant challenge. While NP-hard in the worst case, there are provably efficient algorithms f