Explaining Fast Improvement in Online Imitation Learning

TL;DR

This paper explains why online imitation learning often improves policies faster than theory predicts, showing that expressive policy classes enhance both speed and accuracy of learning.

Contribution

The paper provides a theoretical analysis demonstrating that expressive policy classes accelerate policy improvement in online imitation learning.

Findings

Policy improvement speed is $ ilde{O}(1/N + \sqrt{\xi/N})$ after N rounds.

Expressive policy classes reduce bias and increase learning speed.

Theoretical results align with empirical observations of fast policy improvement.

Abstract

Online imitation learning (IL) is an algorithmic framework that leverages interactions with expert policies for efficient policy optimization. Here policies are optimized by performing online learning on a sequence of loss functions that encourage the learner to mimic expert actions, and if the online learning has no regret, the agent can provably learn an expert-like policy. Online IL has demonstrated empirical successes in many applications and interestingly, its policy improvement speed observed in practice is usually much faster than existing theory suggests. In this work, we provide an explanation of this phenomenon. Let $\xi$ denote the policy class bias and assume the online IL loss functions are convex, smooth, and non-negative. We prove that, after $N$ rounds of online IL with stochastic feedback, the policy improves in $\tilde{O}(1/N + \sqrt{\xi/N})$ in both expectation and high probability. In other words, we show that adopting a sufficiently expressive policy class in online IL has two benefits: both the policy improvement speed increases and the performance bias decreases.