Offline Learning in Markov Games with General Function Approximation

TL;DR

This paper introduces a unified, sample-efficient offline learning framework for Markov games with general function approximation, capable of handling multiple equilibrium concepts and improving data coverage requirements.

Contribution

It provides the first unified approach for offline RL in Markov games with general function approximation, handling all three equilibria and improving data coverage conditions.

Findings

Handles multiple equilibria simultaneously

Requires weaker data coverage than previous methods

Generalizes to two-player zero-sum games

Abstract

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.