Clustered KL-barycenter design for policy evaluation

In the context of stochastic bandit models, this article examines how to design sample-efficient behavior policies for the importance sampling evaluation of multiple target policies. From importance sampling theory, it is well established that sample efficiency is highly sensitive to the KL divergence between the target and importance sampling distributions. We first analyze a single behavior policy defined as the KL-barycenter of the target policies. Then, we refine this approach by clustering the target policies into groups with small KL divergences and assigning each cluster its own KL-barycenter as a behavior policy. This clustered KL-based policy evaluation (CKL-PE) algorithm provides a novel perspective on optimal policy selection. We prove upper bounds on the sample complexity of our method and demonstrate its effectiveness with numerical validation.

On Multi-Agent Inverse Reinforcement Learning

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.