Sliced Distribution Matching based on Cumulative Distribution Functions with Applications to Control
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.
Cite
@article{arxiv.2412.06220,
title = {Sliced Distribution Matching based on Cumulative Distribution Functions with Applications to Control},
author = {Alexandros E. Tzikas and Arec Jamgochian and Nazim Kemal Ure and Mykel J. Kochenderfer and Stephen P. Boyd},
journal= {arXiv preprint arXiv:2412.06220},
year = {2025}
}
Comments
Submitted to the 2026 American Control Conference