Stochastic billiards for sampling from the boundary of a convex set

TL;DR

This paper analyzes the efficiency of stochastic billiards as an MCMC method for sampling uniformly from the boundary of convex sets with bounded curvature, providing polynomial-time guarantees.

Contribution

It establishes a polynomial-time algorithm for sampling from the boundary of convex sets with bounded curvature using stochastic billiards.

Findings

Polynomial-time sampling algorithm developed

Bounded curvature condition crucial for efficiency

Theoretical guarantees on mixing time provided

Abstract

Stochastic billiards can be used for approximate sampling from the boundary of a bounded convex set through the Markov Chain Monte Carlo (MCMC) paradigm. This paper studies how many steps of the underlying Markov chain are required to get samples (approximately) from the uniform distribution on the boundary of the set, for sets with an upper bound on the curvature of the boundary. Our main theorem implies a polynomial-time algorithm for sampling from the boundary of such sets.