Proximal Point Imitation Learning
This work addresses imitation learning for robotics or AI agents by providing more efficient algorithms without restrictive assumptions, though it appears incremental in its optimization approach.
The paper tackles infinite horizon imitation learning with linear function approximation by developing algorithms based on the proximal-point method and dual smoothing, avoiding nested updates and achieving theoretical guarantees for both online and offline settings, with convincing empirical performance.
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.