English

Convergence rate of randomized midpoint Langevin Monte Carlo

Statistics Theory 2025-11-18 v1 Probability Statistics Theory

Abstract

The randomized midpoint Langevin Monte Carlo (RLMC), introduced by Shen and Lee (2019), is a variant of classical Unadjusted Langevin Algorithm. It was shown in the literature that the RLMC is an efficient algorithm for approximating high-dimensional probability distribution π\pi. In this paper, we establish the exponential ergodicity of RLMC with constant step-size. Moreover, we design a dereasing-step size RLMC and provide its convergence rate in terms of a functional class distance.

Keywords

Cite

@article{arxiv.2511.13093,
  title  = {Convergence rate of randomized midpoint Langevin Monte Carlo},
  author = {Ruinan Li and Tian Shen and Zhonggen Su},
  journal= {arXiv preprint arXiv:2511.13093},
  year   = {2025}
}