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 . 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}
}