Parallelized midpoint randomization for Langevin Monte Carlo

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Lu Yu, Arnak Dalalyan

Published: 01 Dec 2025, Last Modified: 25 Dec 2025Stochastic Processes and their ApplicationsEveryoneRevisionsBibTeXCC BY-SA 4.0
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