  We provide a unifying view of a large family of previous imitation learning
algorithms through the lens of moment matching. At its core, our classification
scheme is based on whether the learner attempts to match (1) reward or (2)
action-value moments of the expert's behavior, with each option leading to
differing algorithmic approaches. By considering adversarially chosen
divergences between learner and expert behavior, we are able to derive bounds
on policy performance that apply for all algorithms in each of these classes,
the first to our knowledge. We also introduce the notion of moment
recoverability, implicit in many previous analyses of imitation learning, which
allows us to cleanly delineate how well each algorithmic family is able to
mitigate compounding errors. We derive three novel algorithm templates (AdVIL,
AdRIL, and DAeQuIL) with strong guarantees, simple implementation, and
competitive empirical performance.
