More Efficient Adversarial Imitation Learning Algorithms With Known and Unknown Transitions

In this work, we design provably (more) efficient imitation learning algorithms that directly optimize policies from expert demonstrations. Firstly, when the transition function is known, we build on the nearly minimax optimal algorithm MIMIC-MD and relax a projection operator in it. Based on this change, we develop an adversarial imitation learning (AIL) algorithm named \emph{TAIL} with a gradient-based optimization procedure. Accordingly, TAIL has the same sample complexity (i.e., the number of expert trajectories) $\widetilde{\mathcal{O}}(H^{3/2} |\mathcal{S}|/\varepsilon)$ with MIMIC-MD, where $H$ is the planning horizon, $|\mathcal{S}|$ is the state space size and $\varepsilon$ is desired policy value gap. In addition, TAIL is more practical than MIMIC-MD as the former has a space complexity $\mathcal{O} (|\mathcal{S}||\mathcal{A}|H)$ while the latter's is about $\mathcal{O} (|\mathcal{S}|^2 |\mathcal{A}|^2 H^2)$. Secondly, under the scenario where the transition function is unknown but the interaction is allowed, we present an extension of TAIL named \emph{MB-TAIL}. The sample complexity of MB-TAIL is still $\widetilde{\mathcal{O}}(H^{3/2} |\mathcal{S}|/\varepsilon)$ while the interaction complexity (i.e., the number of interaction episodes) is $\widetilde{\mathcal{O}} (H^3 |\mathcal{S}|^2 |\mathcal{A}| / \varepsilon^2)$. In particular, MB-TAIL is significantly better than the best-known OAL algorithm, which has a sample complexity $\widetilde{\mathcal{O}}(H^{2} |\mathcal{S}|/\varepsilon^2)$ and interaction complexity $\widetilde{\mathcal{O}} (H^4 |\mathcal{S}|^2 |\mathcal{A}| / \varepsilon^2)$. The advances in MB-TAIL are based on a new framework that connects reward-free exploration and AIL. To our understanding, MB-TAIL is the first algorithm that shifts the advances in the known transition setting to the unknown transition setting.