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arXiv · 2511.13093

Convergence rate of randomized midpoint Langevin Monte Carlo

Ruinan Li·Tian Shen·Zhonggen Su
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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 $\pi$. 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.

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Ruinan Li, Tian Shen, Zhonggen Su. 2025-11-17. Convergence rate of randomized midpoint Langevin Monte Carlo. https://arxiv.org/abs/2511.13093

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