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.

本文利用潜在变量模型将层次化模仿学习问题转化为参数推断，理论上表征了Daniel等人（2016）提出的EM方法。研究了种群水平算法作为中间步骤的性能保证，证明了该算法在一定的正则条件下以高概率收敛于真实参数周围的范数球上。据我们所知，这是第一个仅观察原始状态-动作对的层次化模仿学习算法的性能保证。

基于EM的可证明分层模仿学习