几何熵揭示演示轨迹多样性对模仿学习的双重影响。
Geometric Entropy: When Trajectory Diversity Helps and Hurts in Imitation Learning
- 提出几何熵（H_G）度量归一化后的轨迹内在多样性。
- 轨迹多样性与成功率呈倒U型关系，过犹不及。
- 适合评估数据集质量或指导演示数据优化。
我们研究了演示中轨迹形状多样性对模仿学习（IL）性能的影响，涵盖不同模型、任务和数据规模。提出一种与任务无关的几何熵（H_G）度量，通过目标帧对齐消除目标位姿和工作空间尺度等外在变化后，量化轨迹的内在多样性。在多种IL架构及模拟与真实机器人接触丰富操作任务中，均观察到成功与H_G之间存在一致的倒U型关系：在低多样性时提升鲁棒性，但过度多样性导致策略模糊反而降低性能。随着数据量增加、任务变简单或先验更强，最优几何熵趋向更低值；对于预训练视觉-语言-动作模型，该趋势近乎单调下降。实践中，H_G可快速审计预训练数据集，并为演示数据校准提供简单指导。
原文摘要 · Abstract (English)
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.
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