Geometric Entropy: When Trajectory Diversity Helps and Hurts in Imitation Learning

2026-06-18

AI Summary

This work investigates the impact of geometric diversity in demonstration trajectories on imitation learning performance, with a focus on the trade-off between policy ambiguity and robustness. To this end, the authors propose a task-agnostic geometric entropy metric (\(H_G\)) that quantifies the intrinsic diversity of trajectories after factoring out extrinsic variations. Through systematic experiments across diverse imitation learning architectures and contact-rich tasks in both simulation and real-world robotic settings, they uncover an inverted U-shaped relationship between geometric diversity and learning performance. Moreover, the optimal entropy level is found to vary dynamically with task difficulty, dataset size, and model priors. The findings demonstrate that geometric entropy serves as an effective tool for pre-training auditing of demonstration datasets and provides practical calibration guidelines for constructing high-quality demonstrations.

Abstract

We study how trajectory-shape diversity in demonstrations affects imitation learning (IL) performance across models, tasks, and data scales. We introduce Geometric Entropy (H_G), a task-agnostic metric that quantifies the intrinsic diversity of transit trajectories after normalizing away extrinsic variation, such as goal pose and workspace scale, via target-frame alignment. Across multiple IL architectures and both simulated and real-robot contact-rich manipulation tasks, we observe a consistent inverted-U relationship between success and H_G: increasing geometric diversity improves robustness in low-diversity regimes but degrades performance once diversity induces strategy ambiguity. Moreover, the optimal entropy shifts toward lower values as task mastery increases through more data, easier tasks, or stronger priors, and for a pretrained vision-language-action model the trend becomes effectively monotonic decreasing. Practically, H_G enables fast pre-training auditing of demonstration datasets and offers a simple guideline for calibrating demonstrations toward the learnable regime.

Problem

• Imitation Learning
• Trajectory Diversity
• Geometric Entropy
• Demonstration Quality
• Strategy Ambiguity

Innovation

• Geometric Entropy
• Imitation Learning
• Trajectory Diversity
• Demonstration Quality
• Strategy Ambiguity