Convergence of a model-free entropy-regularized inverse reinforcement learning algorithm

Given a dataset of expert demonstrations, inverse reinforcement learning (IRL) aims to recover a reward for which the expert is optimal. This work proposes a model-free algorithm to solve the entropy-regularized IRL problem. In particular, we employ a stochastic gradient descent update for the reward and a stochastic soft policy iteration update for the policy. Assuming access to a generative model, we prove that our algorithm is guaranteed to recover a reward for which the expert is $\varepsilon$-optimal using an expected number of $\mathcal{O}\left(1 / \varepsilon^{2}\right)$ samples of the Markov decision process (MDP). Furthermore, with an expected number of $\mathcal{O}\left(1 / \varepsilon^{4}\right)$ samples we prove that the optimal policy corresponding to the recovered reward is $\varepsilon$-close to the expert policy in total variation distance.