Understanding Adversarial Imitation Learning in Small Sample Regime: A Stage-Coupled Analysis

Area of Science:

• Robotics and Artificial Intelligence
• Machine Learning Theory

Background:

• Imitation learning (IL) trains AI policies from expert examples, crucial for large language models and embodied AI.
• Sequential decision-making in IL faces challenges like error accumulation and distribution shift.
• Adversarial imitation learning (AIL) demonstrates strong performance, even with limited expert data.

Purpose of the Study:

• To theoretically explain AIL's effectiveness with few expert trajectories.
• To understand why AIL maintains performance over long decision horizons.
• To analyze a specific AIL variant, total-variation-distance-based AIL (TV-AIL).

Main Methods:

• Analysis of total-variation-distance-based AIL (TV-AIL).
• Derivation of a horizon-free imitation gap bound: ${\mathcal {O}}(\min \lbrace 1, \sqrt{|{\mathcal {S}}|/N} \rbrace )$.
• Development of a novel stage-coupled analysis for multi-stage policy optimization.

Main Results:

• The derived bound is valid for both small and large numbers of expert trajectories (N).
• The imitation gap does not increase with the decision horizon, explaining empirical successes.
• The analysis provides insights into AIL's handling of distribution shift issues.

Conclusions:

• The theoretical analysis explains AIL's strong empirical performance in scenarios like robotic locomotion.
• The findings offer a deeper understanding of imitation learning's capabilities and limitations.
• The stage-coupled analysis tool is applicable to worst-case scenarios in general Markov Decision Processes (MDPs).