Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning

TL;DR

This paper analyzes the horizon dependence in imitation learning, showing conditions under which offline behavior cloning can achieve horizon-independent sample complexity and comparing it to online methods.

Contribution

It provides a new theoretical analysis of behavior cloning with logarithmic loss, revealing conditions for horizon-independent sample complexity in offline IL and clarifying the offline-online gap.

Findings

Offline IL can achieve horizon-independent sample complexity under certain conditions.

The gap between offline and online IL is smaller than previously thought, especially with dense rewards.

Online IL cannot outperform offline IL with logarithmic loss in benign MDPs without additional assumptions.

Abstract

Imitation learning (IL) aims to mimic the behavior of an expert in a sequential decision making task by learning from demonstrations, and has been widely applied to robotics, autonomous driving, and autoregressive text generation. The simplest approach to IL, behavior cloning (BC), is thought to incur sample complexity with unfavorable quadratic dependence on the problem horizon, motivating a variety of different online algorithms that attain improved linear horizon dependence under stronger assumptions on the data and the learner's access to the expert. We revisit the apparent gap between offline and online IL from a learning-theoretic perspective, with a focus on the realizable/well-specified setting with general policy classes up to and including deep neural networks. Through a new analysis of behavior cloning with the logarithmic loss, we show that it is possible to achieve horizon-independent sample complexity in offline IL whenever (i) the range of the cumulative payoffs is controlled, and (ii) an appropriate notion of supervised learning complexity for the policy class is controlled. Specializing our results to deterministic, stationary policies, we show that the gap between offline and online IL is smaller than previously thought: (i) it is possible to achieve linear dependence on horizon in offline IL under dense rewards (matching what was previously only known to be achievable in online IL); and (ii) without further assumptions on the policy class, online IL cannot improve over offline IL with the logarithmic loss, even in benign MDPs. We complement our theoretical results with experiments on standard RL tasks and autoregressive language generation to validate the practical relevance of our findings.