  Deep Reinforcement Learning (DRL) has achieved impressive success in many
applications. A key component of many DRL models is a neural network
representing a Q function, to estimate the expected cumulative reward following
a state-action pair. The Q function neural network contains a lot of implicit
knowledge about the RL problems, but often remains unexamined and
uninterpreted. To our knowledge, this work develops the first mimic learning
framework for Q functions in DRL. We introduce Linear Model U-trees (LMUTs) to
approximate neural network predictions. An LMUT is learned using a novel
on-line algorithm that is well-suited for an active play setting, where the
mimic learner observes an ongoing interaction between the neural net and the
environment. Empirical evaluation shows that an LMUT mimics a Q function
substantially better than five baseline methods. The transparent tree structure
of an LMUT facilitates understanding the network's learned knowledge by
analyzing feature influence, extracting rules, and highlighting the
super-pixels in image inputs.
