  Despite the recent success of reinforcement learning in various domains,
these approaches remain, for the most part, deterringly sensitive to
hyper-parameters and are often riddled with essential engineering feats
allowing their success. We consider the case of off-policy generative
adversarial imitation learning, and perform an in-depth review, qualitative and
quantitative, of the method. We show that forcing the learned reward function
to be local Lipschitz-continuous is a sine qua non condition for the method to
perform well. We then study the effects of this necessary condition and provide
several theoretical results involving the local Lipschitzness of the
state-value function. We complement these guarantees with empirical evidence
attesting to the strong positive effect that the consistent satisfaction of the
Lipschitzness constraint on the reward has on imitation performance. Finally,
we tackle a generic pessimistic reward preconditioning add-on spawning a large
class of reward shaping methods, which makes the base method it is plugged into
provably more robust, as shown in several additional theoretical guarantees. We
then discuss these through a fine-grained lens and share our insights.
Crucially, the guarantees derived and reported in this work are valid for any
reward satisfying the Lipschitzness condition, nothing is specific to
imitation. As such, these may be of independent interest.
