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• W3005731428 abstract "We develop provably efficient reinforcement learning algorithms for two-player zero-sum finite-horizon Markov games with simultaneous moves. To incorporate function approximation, we consider a family of Markov games where the reward function and transition kernel possess a linear structure. Both the offline and online settings of the problems are considered. In the offline setting, we control both players and aim to find the Nash Equilibrium by minimizing the duality gap. In the online setting, we control a single player playing against an arbitrary opponent and aim to minimize the regret. For both settings, we propose an optimistic variant of the least-squares minimax value iteration algorithm. We show that our algorithm is computationally efficient and provably achieves an $tilde O(sqrt{d^3 H^3 T} )$ upper bound on the duality gap and regret, where $d$ is the linear dimension, $H$ the horizon and $T$ the total number of timesteps. Our results do not require additional assumptions on the sampling model. Our setting requires overcoming several new challenges that are absent in Markov decision processes or turn-based Markov games. In particular, to achieve optimism with simultaneous moves, we construct both upper and lower confidence bounds of the value function, and then compute the optimistic policy by solving a general-sum matrix game with these bounds as the payoff matrices. As finding the Nash Equilibrium of a general-sum game is computationally hard, our algorithm instead solves for a Coarse Correlated Equilibrium (CCE), which can be obtained efficiently. To our best knowledge, such a CCE-based scheme for optimism has not appeared in the literature and might be of interest in its own right." @default.
• W3005731428 created "2020-02-24" @default.
• W3005731428 creator A5008882694 @default.
• W3005731428 creator A5048272675 @default.
• W3005731428 creator A5060774236 @default.
• W3005731428 creator A5078210646 @default.
• W3005731428 date "2020-02-17" @default.
• W3005731428 modified "2023-09-26" @default.
• W3005731428 title "Learning Zero-Sum Simultaneous-Move Markov Games Using Function Approximation and Correlated Equilibrium" @default.
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• W3005731428 doi "https://doi.org/10.48550/arxiv.2002.07066" @default.
• W3005731428 hasPublicationYear "2020" @default.
• W3005731428 type Work @default.
• W3005731428 sameAs 3005731428 @default.

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