On Efficient Online Imitation Learning via Classification

TL;DR

This paper investigates the limits and possibilities of classification-based online imitation learning, proposing new algorithms that improve sample efficiency and analyzing fundamental computational barriers in the nonrealizable setting.

Contribution

It introduces the Logger framework for improper online learning in COIL, designs two oracle-efficient algorithms, and establishes theoretical limitations on dynamic regret minimization.

Findings

Proper online algorithms cannot guarantee sublinear regret in general.

The Logger framework reduces COIL to online linear optimization.

Proposed algorithms outperform naive behavior cloning in finite-sample settings.

Abstract

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.