Sample-Efficient Tabular Self-Play for Offline Robust Reinforcement Learning

Na Li, Zewu Zheng, Wei Ni, Hangguan Shan, Wenjie Zhang, Xinyu Li

Keywords: robust Markov games, self-play, distribution shift, model uncertainty, reinforcement learning

TL;DR: We design an algorithm that first achieves the optimal sample complexity regarding both state and action spaces under partial coverage and environment uncertainty in robust two-player zero-sum Markov games.

Abstract: Multi-agent reinforcement learning (MARL), as a thriving field, explores how multiple agents independently make decisions in a shared dynamic environment. Due to environmental uncertainties, policies in MARL must remain robust to tackle the sim-to-real gap. We focus on robust two-player zero-sum Markov games (TZMGs) in offline settings, specifically on tabular robust TZMGs (RTZMGs). We propose a model-based algorithm (*RTZ-VI-LCB*) for offline RTZMGs, which is optimistic robust value iteration combined with a data-driven Bernstein-style penalty term for robust value estimation. By accounting for distribution shifts in the historical dataset, the proposed algorithm establishes near-optimal sample complexity guarantees under partial coverage and environmental uncertainty. An information-theoretic lower bound is developed to confirm the tightness of our algorithm's sample complexity, which is optimal regarding both state and action spaces. To the best of our knowledge, RTZ-VI-LCB is the first to attain this optimality, sets a new benchmark for offline RTZMGs, and is validated experimentally.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 5402