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Offline Learning in Markov Games with General Function Approximation
Yuheng Zhang · Yu Bai · Nan Jiang

Thu Jul 27 01:30 PM -- 03:00 PM (PDT) @ Exhibit Hall 1 #437

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.

Author Information

Yuheng Zhang (University of Illinois at Urbana-Champaign)
Yu Bai (Salesforce Research)
Nan Jiang (University of Illinois at Urbana-Champaign)

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