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Parallelized Midpoint Randomization for Langevin Monte Carlo

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arxiv 2402.14434 v4 pith:T7QCQ3F7 submitted 2024-02-22 math.ST cs.LGmath.PRstat.COstat.TH

Lu Yu , Arnak Dalalyan This is my paper · ORCID
classification math.STcs.LGmath.PRstat.COstat.TH
keywords boundsdensitiesmidpointparallelparallelizedsamplingtargettechniques
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Shifted Composition III: Local Error Framework for KL Divergence

    math.ST 2024-12 conditional novelty 7.0 of 10

    A new local-error framework converts Wasserstein coupling estimates into KL divergence bounds and yields the first KL rates for randomized midpoint Langevin Monte Carlo under strong-log-concavity, weak-log-concavity, ...

  2. Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Acceleration

    stat.ML 2025-02 conditional novelty 6.0 of 10

    A second-order local linearization sampler is shown to reach O~(1/ε) Wasserstein-2 accuracy for strongly log-concave score-based diffusion models, improving on the O~(1/ε²) rate of Euler and exponential integrator schemes.

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