Parallelized midpoint randomization for Langevin Monte Carlo

Lu Yu; Arnak Dalalyan

doi:10.1016/j.spa.2025.104764

Parallelized midpoint randomization for Langevin Monte Carlo

Lu Yu^*
, Arnak Dalalyan

^*Corresponding author for this work

Department of Data Science

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Abstract

We study the problem of sampling from a target probability density function in frameworks where parallel evaluations of the log-density gradient are feasible. Focusing on smooth and strongly log-concave densities, we revisit the parallelized randomized midpoint method and investigate its properties using recently developed techniques for analyzing its sequential version. Through these techniques, we derive upper bounds on the Wasserstein distance between sampling and target densities. These bounds quantify the substantial runtime improvements achieved through parallel processing. © 2025 The Authors

Original language	English
Article number	104764
Number of pages	27
Journal	Stochastic Processes and their Applications
Volume	190
Online published	21 Aug 2025
DOIs	https://doi.org/10.1016/j.spa.2025.104764
Publication status	Published - Dec 2025

Funding

This work was supported by the center Hi! PARIS and the grant Investissements d’Avenir (ANR-11-IDEX0003/Labex Ecodec/ANR-11-LABX-0047).

Research Keywords

Langevin algorithm
Markov Chain Monte Carlo
Midpoint randomization
Mixing rate
Parallel computing

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This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/

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AU - Dalalyan, Arnak

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N2 - We study the problem of sampling from a target probability density function in frameworks where parallel evaluations of the log-density gradient are feasible. Focusing on smooth and strongly log-concave densities, we revisit the parallelized randomized midpoint method and investigate its properties using recently developed techniques for analyzing its sequential version. Through these techniques, we derive upper bounds on the Wasserstein distance between sampling and target densities. These bounds quantify the substantial runtime improvements achieved through parallel processing. © 2025 The Authors

AB - We study the problem of sampling from a target probability density function in frameworks where parallel evaluations of the log-density gradient are feasible. Focusing on smooth and strongly log-concave densities, we revisit the parallelized randomized midpoint method and investigate its properties using recently developed techniques for analyzing its sequential version. Through these techniques, we derive upper bounds on the Wasserstein distance between sampling and target densities. These bounds quantify the substantial runtime improvements achieved through parallel processing. © 2025 The Authors

KW - Langevin algorithm

KW - Markov Chain Monte Carlo

KW - Midpoint randomization

KW - Mixing rate

KW - Parallel computing

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DO - 10.1016/j.spa.2025.104764

M3 - RGC 21 - Publication in refereed journal

SN - 0304-4149

VL - 190

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

M1 - 104764

ER -

Parallelized midpoint randomization for Langevin Monte Carlo

Abstract

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Research Keywords

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