Causal Imitation for Markov Decision Processes: a Partial Identification Approach

Imitation learning enables an agent to learn from expert demonstrations when the performance measure is unknown and the reward signal is not specified. Standard imitation methods do not generally apply when the learner and the expert's sensory capabilities mismatch and demonstrations are contaminated with unobserved confounding bias. To address these challenges, recent advancements in causal imitation learning have been pursued. However, these methods often require access to underlying causal structures that might not always be available, posing practical challenges.In this paper, we investigate robust imitation learning within the framework of canonical Markov Decision Processes (MDPs) using partial identification, allowing the agent to achieve expert performance even when the system dynamics are not uniquely determined from the confounded expert demonstrations. Specifically, first, we theoretically demonstrate that when unobserved confounders (UCs) exist in an MDP, the learner is generally unable to imitate expert performance. We then explore imitation learning in partially identifiable settings --- either transition distribution or reward function is non-identifiable from the available data and knowledge. Augmenting the celebrated GAIL method (Ho \& Ermon, 2016), our analysis leads to two novel causal imitation algorithms that can obtain effective policies guaranteed to achieve expert performance.