Corruption-Robust Offline Two-Player Zero-Sum Markov Games
This addresses data corruption robustness in multi-agent reinforcement learning, offering theoretical guarantees for scenarios with adversarial data modifications.
The paper tackles the problem of learning approximate Nash Equilibrium policies in offline two-player zero-sum Markov games when an adversary corrupts a fraction of the data, providing information-theoretic lower bounds and proposing robust algorithms that achieve near-optimal suboptimality gap bounds with respect to the corruption level.
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 $ε$-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 $ε$. 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.