A Natural Actor-Critic Framework for Zero-Sum Markov Games

Ahmet Alacaoglu · Luca Viano · Niao He · Volkan Cevher

Room 318 - 320
[ Abstract ] [ Livestream: Visit Miscellaneous Aspects of Machine Learning/Reinforcement Learning ]
Wed 20 Jul 2:40 p.m. — 2:45 p.m. PDT
[ Slides [ Paper PDF

We introduce algorithms based on natural actor-critic and analyze their sample complexity for solving two player zero-sum Markov games in the tabular case. Our results improve the best-known sample complexities of policy gradient/actor-critic methods for convergence to Nash equilibrium in the multi-agent setting. We use the error propagation scheme in approximate dynamic programming, recent advances for global convergence of policy gradient methods, temporal difference learning, and techniques from stochastic primal-dual optimization. Our algorithms feature two stages, requiring agents to agree on an etiquette before starting their interactions, which is feasible for instance in self-play. However, the agents only access to joint reward and joint next state and not to each other's actions or policies. Our complexity results match the best-known results for global convergence of policy gradient algorithms for single agent RL. We provide numerical verification of our methods for a two player bandit environment and a two player game, Alesia. We observe improved empirical performance as compared to the recently proposed optimistic gradient descent-ascent variant for Markov games.

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