On Feasible Rewards in Multi-Agent Inverse Reinforcement Learning

Giorgia Ramponi (Department of Informatics, University of Zurich, University of Zurich) · Till Freihaut (Department of Informatics, University of Zurich)

ambiguity in equilibriumentropy-regularized markov gamesexpert demonstrationslearned policy performancemarkov gamesmulti-agent inverse reinforcement learningmulti-agent systems nash equilibrium practical insights reward functionsreward structuressample complexity analysisstrategic incentivestheoretical foundationsunique equilibrium

Multi-agent inverse reinforcement learning (MAIRL) aims to recover agent reward functions from expert demonstrations. We characterize the feasible reward set in Markov games, identifying all reward functions that rationalize a given equilibrium. However, equilibrium-based observations are often ambiguous: a single Nash equilibrium can correspond to many reward structures, potentially changing the game's nature in multi-agent systems. We address this by introducing entropy-regularized Markov games, which yield a unique equilibrium while preserving strategic incentives. For this setting, we provide a sample complexity analysis detailing how errors affect learned policy performance. Our work establishes theoretical foundations and practical insights for MAIRL.