  Imitation learning (IL) aims to learn a policy from expert demonstrations
that minimizes the discrepancy between the learner and expert behaviors.
Various imitation learning algorithms have been proposed with different
pre-determined divergences to quantify the discrepancy. This naturally gives
rise to the following question: Given a set of expert demonstrations, which
divergence can recover the expert policy more accurately with higher data
efficiency? In this work, we propose $f$-GAIL, a new generative adversarial
imitation learning (GAIL) model, that automatically learns a discrepancy
measure from the $f$-divergence family as well as a policy capable of producing
expert-like behaviors. Compared with IL baselines with various predefined
divergence measures, $f$-GAIL learns better policies with higher data
efficiency in six physics-based control tasks.
