On Efficient Online Imitation Learning via Classification
This work addresses a foundational challenge in imitation learning for sequential decision-making, providing theoretical insights and algorithmic improvements, though it is incremental in advancing the field's understanding.
The paper tackles the problem of classification-based online imitation learning (COIL) in the nonrealizable case, showing that proper algorithms cannot guarantee sublinear regret and proposing an improper framework called Logger that reduces COIL to online linear optimization, with two oracle-efficient algorithms offering improved sample and round complexity over naive behavior cloning.
Imitation learning (IL) is a general learning paradigm for tackling sequential decision-making problems. Interactive imitation learning, where learners can interactively query for expert demonstrations, has been shown to achieve provably superior sample efficiency guarantees compared with its offline counterpart or reinforcement learning. In this work, we study classification-based online imitation learning (abbrev. $\textbf{COIL}$) and the fundamental feasibility to design oracle-efficient regret-minimization algorithms in this setting, with a focus on the general nonrealizable case. We make the following contributions: (1) we show that in the $\textbf{COIL}$ problem, any proper online learning algorithm cannot guarantee a sublinear regret in general; (2) we propose $\textbf{Logger}$, an improper online learning algorithmic framework, that reduces $\textbf{COIL}$ to online linear optimization, by utilizing a new definition of mixed policy class; (3) we design two oracle-efficient algorithms within the $\textbf{Logger}$ framework that enjoy different sample and interaction round complexity tradeoffs, and conduct finite-sample analyses to show their improvements over naive behavior cloning; (4) we show that under the standard complexity-theoretic assumptions, efficient dynamic regret minimization is infeasible in the $\textbf{Logger}$ framework. Our work puts classification-based online imitation learning, an important IL setup, into a firmer foundation.