Provable Hierarchical Imitation Learning via EM
This provides a theoretical guarantee for hierarchical imitation learning algorithms, addressing a gap in performance analysis for methods that only observe primitive state-action pairs, which is incremental but important for the reinforcement learning community.
The paper tackles the problem of hierarchical imitation learning by learning an options-type hierarchical policy from expert demonstrations, proving that the proposed EM algorithm converges with high probability to a norm ball around the true parameter under certain conditions.
Due to recent empirical successes, the options framework for hierarchical reinforcement learning is gaining increasing popularity. Rather than learning from rewards which suffers from the curse of dimensionality, we consider learning an options-type hierarchical policy from expert demonstrations. Such a problem is referred to as hierarchical imitation learning. Converting this problem to parameter inference in a latent variable model, we theoretically characterize the EM approach proposed by Daniel et al. (2016). The population level algorithm is analyzed as an intermediate step, which is nontrivial due to the samples being correlated. If the expert policy can be parameterized by a variant of the options framework, then under regularity conditions, we prove that the proposed algorithm converges with high probability to a norm ball around the true parameter. To our knowledge, this is the first performance guarantee for an hierarchical imitation learning algorithm that only observes primitive state-action pairs.