English

Optimal Ricci curvature Markov chain Monte Carlo methods on finite states

Optimization and Control 2023-02-06 v1 Probability

Abstract

We construct a new Markov chain Monte Carlo method on finite states with optimal choices of acceptance-rejection ratio functions. We prove that the constructed continuous time Markov jumping process has a global in-time convergence rate in L1L^1 distance. The convergence rate is no less than one-half and is independent of the target distribution. For example, our method recovers the Metropolis-Hastings algorithm on a two-point state. And it forms a new algorithm for sampling general target distributions. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.

Keywords

Cite

@article{arxiv.2302.01378,
  title  = {Optimal Ricci curvature Markov chain Monte Carlo methods on finite states},
  author = {Wuchen Li and Linyuan Lu},
  journal= {arXiv preprint arXiv:2302.01378},
  year   = {2023}
}