mlsanityData to 14 Oct 2026

Parallelized Midpoint Randomization for Langevin Monte Carlo

arXiv 2402.14434 ↗First posted 22 Feb 2024math.ST cs.LG math.PRcited by 9

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Abstract (arXiv)

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.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 23 of its 46 references that are in the map. First posted on arXiv 22 Feb 2024.

Builds on

23 of 46 references.

References · 23

  1. 2016TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systemscited by 664
  2. 2017Large Batch Training of Convolutional Networkscited by 535
  3. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 243
  4. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
  5. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 208
  6. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 197
  7. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 146
  8. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 133
  9. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 127
  10. 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
  11. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 84
  12. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 78
11 more
  1. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 62
  2. 2020On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothnesscited by 55
  3. 2018Global Non-convex Optimization with Discretized Diffusionscited by 44
  4. 2020Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergencecited by 42
  5. 2019Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexitycited by 39
  6. 2023Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequalitycited by 31
  7. 2013Asymptotically Exact, Embarrassingly Parallel MCMCcited by 30
  8. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 28
  9. 2020On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Methodcited by 23
  10. 2024Fast parallel sampling under isoperimetrycited by 12
  11. 2023Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisitedcited by 10

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 4; 2025: 3; 2026: 2.

9 papers.

  1. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  2. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  3. 2025Accelerated Diffusion Models via Speculative Samplingcited by 31
  4. 2024Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallelcited by 29
  5. 2025Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Accelerationcited by 17
  6. 2024Parallel Simulation for Log-concave Sampling and Score-based Diffusion Modelscited by 6
  7. 2026Accelerating Discrete Diffusion Models with Parallel-In-Time Samplingcited by 4
  8. 2024Randomized Midpoint Method for Log-Concave Sampling under Constraintscited by 2
  9. 2026Improved Guarantees for Langevin Monte Carlo with Average Smoothnesscited by 2