  While deep reinforcement learning has successfully solved many challenging
control tasks, its real-world applicability has been limited by the inability
to ensure the safety of learned policies. We propose an approach to verifiable
reinforcement learning by training decision tree policies, which can represent
complex policies (since they are nonparametric), yet can be efficiently
verified using existing techniques (since they are highly structured). The
challenge is that decision tree policies are difficult to train. We propose
VIPER, an algorithm that combines ideas from model compression and imitation
learning to learn decision tree policies guided by a DNN policy (called the
oracle) and its Q-function, and show that it substantially outperforms two
baselines. We use VIPER to (i) learn a provably robust decision tree policy for
a variant of Atari Pong with a symbolic state space, (ii) learn a decision tree
policy for a toy game based on Pong that provably never loses, and (iii) learn
a provably stable decision tree policy for cart-pole. In each case, the
decision tree policy achieves performance equal to that of the original DNN
policy.
