In multi-agent systems, the agent behavior is highly influenced by its utility function, as these utilities shape both individual goals as well as interactions with the other agents. Inverse Reinforcement Learning (IRL) is a well-established approach to inferring the utility function by observing an expert behavior within a given environment. In this paper, we extend the IRL framework to the multi-agent setting, assuming to observe agents who are following Nash Equilibrium (NE) policies. We theoretically investigate the set of utilities that explain the behavior of NE experts. Specifically, we provide an explicit characterization of the feasible reward set and analyze how errors in estimating the transition dynamics and expert behavior impact the recovered rewards. Building on these findings, we provide the first sample complexity analysis for the multi-agent IRL problem. Finally, we provide a numerical evaluation of our theoretical results.

翻译：在多智能体系统中，智能体的行为深受其效用函数影响，因为效用函数不仅决定个体目标，也塑造其与其他智能体的交互。逆强化学习（IRL）是一种成熟的方法，可通过观察给定环境中专家行为来推断效用函数。本文将IRL框架扩展至多智能体场景，假设观测到的智能体遵循纳什均衡（NE）策略。我们从理论上研究了能够解释NE专家行为的效用函数集合，具体给出了可行奖励集的显式表征，并分析了转移动力学与专家行为估计误差对恢复奖励的影响。基于这些发现，我们首次对多智能体IRL问题进行了样本复杂度分析。最后，通过数值实验对我们的理论结果进行了验证。