几何熵：轨迹多样性在模仿学习中的利弊
Geometric Entropy: When Trajectory Diversity Helps and Hurts in Imitation Learning
AI总结：
提出几何熵（H_G）量化演示轨迹的几何多样性，发现成功率与H_G呈倒U型关系，且最优熵随任务掌握度增加而降低，可用于数据集审计与校准。
摘要：
我们研究了演示中的轨迹形状多样性如何影响不同模型、任务和数据规模下的模仿学习（IL）性能。我们引入了几何熵（H_G），这是一种与任务无关的度量，通过目标帧对齐归一化外在变化（如目标姿态和工作空间尺度）后，量化过渡轨迹的内在多样性。在多种IL架构以及模拟和真实机器人接触丰富的操作任务中，我们观察到成功率与H_G之间一致的倒U型关系：增加几何多样性在低多样性区域提高了鲁棒性，但一旦多样性导致策略模糊，性能就会下降。此外，随着任务掌握度的提高（通过更多数据、更简单的任务或更强的先验），最优熵向较低值移动，而对于预训练的视觉-语言-动作模型，趋势实际上变为单调递减。实际上，H_G能够快速对演示数据集进行预训练审计，并为将演示校准到可学习区域提供简单的指导原则。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
