Regime-Switching Langevin Monte Carlo Algorithms

Fuente: arXiv
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Main Authors: Wang, Xiaoyu, Wang, Yingli, Zhu, Lingjiong
Format: Preprint
Published: 2025
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author Wang, Xiaoyu
Wang, Yingli
Zhu, Lingjiong
author_facet Wang, Xiaoyu
Wang, Yingli
Zhu, Lingjiong
contents Langevin Monte Carlo (LMC) algorithms are popular Markov Chain Monte Carlo (MCMC) methods to sample a target probability distribution, which arises in many applications in machine learning. Inspired by regime-switching stochastic differential equations in the probability literature, we propose and study regime-switching Langevin dynamics (RS-LD) and regime-switching kinetic Langevin dynamics (RS-KLD). Based on their discretizations, we introduce regime-switching Langevin Monte Carlo (RS-LMC) and regime-switching kinetic Langevin Monte Carlo (RS-KLMC) algorithms, which can also be viewed as LMC and KLMC algorithms with random stepsizes. We also propose frictional-regime-switching kinetic Langevin dynamics (FRS-KLD) and its associated algorithm frictional-regime-switching kinetic Langevin Monte Carlo (FRS-KLMC), which can also be viewed as the KLMC algorithm with random frictional coefficients. We provide their 2-Wasserstein non-asymptotic convergence guarantees to the target distribution, and analyze the iteration complexities. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of our proposed algorithms.
format Preprint
id arxiv_https___arxiv_org_abs_2509_00941
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Regime-Switching Langevin Monte Carlo Algorithms
Wang, Xiaoyu
Wang, Yingli
Zhu, Lingjiong
Computation
Machine Learning
Probability
Langevin Monte Carlo (LMC) algorithms are popular Markov Chain Monte Carlo (MCMC) methods to sample a target probability distribution, which arises in many applications in machine learning. Inspired by regime-switching stochastic differential equations in the probability literature, we propose and study regime-switching Langevin dynamics (RS-LD) and regime-switching kinetic Langevin dynamics (RS-KLD). Based on their discretizations, we introduce regime-switching Langevin Monte Carlo (RS-LMC) and regime-switching kinetic Langevin Monte Carlo (RS-KLMC) algorithms, which can also be viewed as LMC and KLMC algorithms with random stepsizes. We also propose frictional-regime-switching kinetic Langevin dynamics (FRS-KLD) and its associated algorithm frictional-regime-switching kinetic Langevin Monte Carlo (FRS-KLMC), which can also be viewed as the KLMC algorithm with random frictional coefficients. We provide their 2-Wasserstein non-asymptotic convergence guarantees to the target distribution, and analyze the iteration complexities. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of our proposed algorithms.
title Regime-Switching Langevin Monte Carlo Algorithms
topic Computation
Machine Learning
Probability
url https://arxiv.org/abs/2509.00941