Random sampling: Billiard Walk algorithm

TL;DR

This paper introduces a billiard walk algorithm for random sampling that converges faster to uniform distribution than traditional Hit-and-Run methods, demonstrated through numerical experiments.

Contribution

The paper proposes a novel billiard walk algorithm that improves convergence speed over existing hit-and-run methods for random sampling.

Findings

Faster convergence to uniform distribution in numerical tests

Billiard walk outperforms traditional hit-and-run in practice

Abstract

Hit-and-Run is known to be one of the best random sampling algorithms, its mixing time is polynomial in dimension. Nevertheless, in practice the number of steps required to achieve uniformly distributed samples is rather high. We propose new random walk algorithm based on billiard trajectories. Numerical experiments demonstrate much faster convergence to uniform distribution.