Imitation Learning as Return Distribution Matching

We study the problem of training a risk-sensitive reinforcement learning (RL) agent through imitation learning (IL). Unlike standard IL, our goal is not only to train an agent that matches the expert's expected return (i.e., its average performance) but also its risk attitude (i.e., other features of the return distribution, such as variance). We propose a general formulation of the risk-sensitive IL problem in which the objective is to match the expert's return distribution in Wasserstein distance. We focus on the tabular setting and assume the expert's reward is known. After demonstrating the limited expressivity of Markovian policies for this task, we introduce an efficient and sufficiently expressive subclass of non-Markovian policies tailored to it. Building on this subclass, we develop two provably efficient algorithms-RS-BC and RS-KT -for solving the problem when the transition model is unknown and known, respectively. We show that RS-KT achieves substantially lower sample complexity than RS-BC by exploiting dynamics information. We further demonstrate the sample efficiency of return distribution matching in the setting where the expert's reward is unknown by designing an oracle-based variant of RS-KT. Finally, we complement our theoretical analysis of RS-KT and RS-BC with numerical simulations, highlighting both their sample efficiency and the advantages of non-Markovian policies over standard sample-efficient IL algorithms. INTRODUCTION Imitation Learning (IL) (Abbeel & Ng, 2004; Osa et al., 2018) is the problem of training an agent to behave by mimicking demonstrations from an expert. By removing the need for designing a reward function for the task-which is often a difficult challenge (Hadfield-Menell et al., 2017) -IL has been successfully applied in diverse domains, including robotics (