Corruption-Robust Offline Two-Player Zero-Sum Markov Games

TL;DR

This paper addresses the challenge of learning approximate Nash Equilibria in offline two-player zero-sum Markov games when the data is partially corrupted, proposing robust algorithms with near-optimal guarantees.

Contribution

It introduces the first characterization of learning approximate Nash Equilibria in corrupted offline Markov games and develops robust algorithms with theoretical guarantees.

Findings

Established an information-theoretic lower bound on suboptimality gap.

Designed robust algorithms achieving near-optimal suboptimality bounds.

Provided the first analysis of corruption-robust learning in offline Markov games.

Abstract

We study data corruption robustness in offline two-player zero-sum Markov games. Given a dataset of realized trajectories of two players, an adversary is allowed to modify an $\epsilon$-fraction of it. The learner's goal is to identify an approximate Nash Equilibrium policy pair from the corrupted data. We consider this problem in linear Markov games under different degrees of data coverage and corruption. We start by providing an information-theoretic lower bound on the suboptimality gap of any learner. Next, we propose robust versions of the Pessimistic Minimax Value Iteration algorithm, both under coverage on the corrupted data and under coverage only on the clean data, and show that they achieve (near)-optimal suboptimality gap bounds with respect to $\epsilon$. We note that we are the first to provide such a characterization of the problem of learning approximate Nash Equilibrium policies in offline two-player zero-sum Markov games under data corruption.