Nearly Minimax Optimal Adversarial Imitation Learning with Known and Unknown Transitions
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This paper is dedicated to designing provably efficient adversarial imitation learning (AIL) algorithms that directly optimize policies from expert demonstrations. Firstly, we develop a transition-aware AIL algorithm named TAIL with an expert sample complexity of Õ(H^3/2 |S|/ε) under the known transition setting, where H is the planning horizon, |S| is the state space size and ε is desired policy value gap. This improves upon the previous best bound of Õ(H^2 |S| / ε^2) for AIL methods and matches the lower bound of Ω̃ (H^3/2 |S|/ε) in [Rajaraman et al., 2021] up to a logarithmic factor. The key ingredient of TAIL is a fine-grained estimator for expert state-action distribution, which explicitly utilizes the transition function information. Secondly, considering practical settings where the transition functions are usually unknown but environment interaction is allowed, we accordingly develop a model-based transition-aware AIL algorithm named MB-TAIL. In particular, MB-TAIL builds an empirical transition model by interacting with the environment and performs imitation under the recovered empirical model. The interaction complexity of MB-TAIL is Õ (H^3 |S|^2 |A| / ε^2), which improves the best known result of Õ (H^4 |S|^2 |A| / ε^2) in [Shani et al., 2021]. Finally, our theoretical results are supported by numerical evaluation and detailed analysis on two challenging MDPs.
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