Geometric Entropy: When Trajectory Diversity Helps and Hurts in Imitation Learning
Geometric Entropy: When Trajectory Diversity Helps and Hurts in Imitation Learning
This research paper introduces Geometric Entropy (H_G), a metric that quantifies the intrinsic diversity of transit trajectories in imitation learning by normalizing for extrinsic variations like goal pose. The study finds an inverted-U relationship between H_G and task success: while increasing geometric diversity improves robustness in low-diversity regimes, it degrades performance when diversity induces strategy ambiguity. Furthermore, the optimal entropy level shifts toward lower values as task mastery increases through more data, easier tasks, or stronger priors. The authors demonstrate that H_G can be used for fast pre-training auditing of demonstration datasets and provide guidelines for calibrating demonstrations to the learnable regime.
The authors introduce Geometric Entropy (H_G) as a metric to quantify trajectory diversity in imitation learning demonstrations, observing an inverted-U relationship between this diversity and task success across simulated and real-robot manipulation tasks.
Source: arXiv Robotics — research abstracts · Read original article ↗
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arXiv:2606.20871v2 Announce Type: replace 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 al
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ignment. 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 mor
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e 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.
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Geometric Entropy: When Trajectory Diversity Helps and Hurts in Imitation Learning
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Source：arXiv Robotics — research abstracts · arxiv.org