累積分布関数に基づくスライス分布マッチングと制御への応用
Sliced Distribution Matching based on Cumulative Distribution Functions with Applications to Control
確率分布間の距離を累積分布関数の一次元射影の差で定義し、制御問題に応用した研究。
著者: Alexandros E. Tzikas, Arec Jamgochian, Nazim Kemal Ure, Mykel J. Kochenderfer, Stephen P. Boyd
分類: eess.SY, cs.RO, cs.SY
原文アブストラクト
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.
