提出基于累积分布的分布匹配新方法，可用于控制中的梯度优化。
Sliced Distribution Matching based on Cumulative Distribution Functions with Applications to Control
- 通过随机线性投影的累积分布差异定义新距离
- 样本估计具渐近理论保证，可微且计算简单
- 适合需要梯度的控制任务如分布引导与遍历控制
在控制领域中，计算两个概率分布之间的相似性是一个常见问题。本文提出了一类统一的距离度量，基于两个随机变量的随机线性一维投影的累积分布函数之间的差异。所提距离具有可解释性、计算简便性，并支持可微近似。我们为基于样本的估计器建立了渐近理论保证。通过两样本检验的实证研究，验证了该距离区分不同分布的能力。最后，我们展示了该距离在控制中的应用潜力：可用于实现分布引导和遍历控制的简单梯度求解方案。
原文摘要 · Abstract (English)
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy between the cumulative distribution functions of random linear one-dimensional projections of the random variables. Our proposed distance is interpretable, computationally simple, and admits a differentiable approximation. We establish asymptotic theoretical guarantees for sample-based estimators of the distance. We empirically study the use of the distance in a two-sample test and demonstrate its ability to distinguish different distributions. Finally, we show that the distance allows for simple gradient-based solutions in control by studying distribution steering and ergodic control.
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