  This work develops new algorithms with rigorous efficiency guarantees for
infinite horizon imitation learning (IL) with linear function approximation
without restrictive coherence assumptions. We begin with the minimax
formulation of the problem and then outline how to leverage classical tools
from optimization, in particular, the proximal-point method (PPM) and dual
smoothing, for online and offline IL, respectively. Thanks to PPM, we avoid
nested policy evaluation and cost updates for online IL appearing in the prior
literature. In particular, we do away with the conventional alternating updates
by the optimization of a single convex and smooth objective over both cost and
Q-functions. When solved inexactly, we relate the optimization errors to the
suboptimality of the recovered policy. As an added bonus, by re-interpreting
PPM as dual smoothing with the expert policy as a center point, we also obtain
an offline IL algorithm enjoying theoretical guarantees in terms of required
expert trajectories. Finally, we achieve convincing empirical performance for
both linear and neural network function approximation.
