Parallelized Midpoint Randomization for Langevin Monte Carlo
This provides incremental improvements to sampling algorithms for researchers in computational statistics and machine learning.
The paper tackles the problem of sampling from smooth, strongly log-concave probability densities by parallelizing the randomized midpoint method for Langevin Monte Carlo, deriving Wasserstein distance bounds that show significant runtime improvements through parallel processing.
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.