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

TL;DR

This paper introduces a new model-based algorithm for offline robust two-player zero-sum Markov games that achieves near-optimal sample complexity and sets a new benchmark in the field.

Contribution

It proposes RTZ-VI-LCB, the first algorithm to attain optimal sample complexity for offline robust two-player zero-sum Markov games, validated both theoretically and experimentally.

Findings

Establishes near-optimal sample complexity guarantees.

Develops an information-theoretic lower bound confirming tightness.

Validates the algorithm's effectiveness through experiments.

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 (\textit{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.