Parallelized Midpoint Randomization for Langevin Monte Carlo

Understand

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.