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arXiv · 2412.06220

Sliced Distribution Matching based on Cumulative Distribution Functions with Applications to Control

Alexandros E. Tzikas·Arec Jamgochian·Nazim Kemal Ure·Mykel J. Kochenderfer·Stephen P. Boyd
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Abstract

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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Alexandros E. Tzikas, Arec Jamgochian, Nazim Kemal Ure, Mykel J. Kochenderfer, Stephen P. Boyd. 2024-12-09. Sliced Distribution Matching based on Cumulative Distribution Functions with Applications to Control. https://arxiv.org/abs/2412.06220

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