mlsanityData to 14 Oct 2026

Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis

arXiv 2503.19066 ↗First posted 24 Mar 2025math.PR stat.MLcited by 4

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Abstract (arXiv)

Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped Langevin dynamics. There are many variants of Langevin dynamics that often show superior performance in practice. In this paper, we provide a unified approach to study the acceleration of the variants of the overdamped Langevin dynamics through the lens of large deviations theory. Numerical experiments using both synthetic and real data are provided to illustrate the efficiency of these variants.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 34 of its 59 references that are in the map. First posted on arXiv 24 Mar 2025.

Builds on

34 of 59 references.

References · 34

  1. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 243
  2. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 208
  3. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 197
  4. 2015A Complete Recipe for Stochastic Gradient MCMCcited by 146
  5. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 146
  6. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 133
  7. 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
  8. 2017Convergence of Langevin MCMC in KL-divergencecited by 88
  9. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 84
  10. 2018Sharp convergence rates for Langevin dynamics in the nonconvex settingcited by 68
  11. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 62
  12. 2018Mirrored Langevin Dynamicscited by 61
22 more
  1. 2020Efficient constrained sampling via the mirror-Langevin algorithmcited by 55
  2. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
  3. 2017Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlocited by 43
  4. 2020Exponential ergodicity of mirror-Langevin diffusionscited by 37
  5. 2021The Mirror Langevin Algorithm Converges with Vanishing Biascited by 37
  6. 2019High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithmcited by 36
  7. 2020Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithmcited by 35
  8. 2020Non-convex Learning via Replica Exchange Stochastic Gradient MCMCcited by 34
  9. 2020Fractional Underdamped Langevin Dynamics: Retargeting SGD with Momentum under Heavy-Tailed Gradient Noisecited by 33
  10. 2020Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learningcited by 33
  11. 2018Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Accelerationcited by 31
  12. 2017Deep Learning: A Bayesian Perspectivecited by 20
  13. 2020Decentralized Stochastic Gradient Langevin Dynamics and Hamiltonian Monte Carlocited by 19
  14. 2020Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusioncited by 16
  15. 2017Fractional Langevin Monte Carlo: Exploring L'evy Driven Stochastic Differential Equations for Markov Chain Monte Carlocited by 13
  16. 2022Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Samplingcited by 13
  17. 2018Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimizationcited by 12
  18. 2024Generalized EXTRA stochastic gradient Langevin dynamicscited by 9
  19. 2017Nonreversible Langevin Samplers: Splitting Schemes, Analysis and Implementationcited by 8
  20. 2025Non-Reversible Langevin Algorithms for Constrained Samplingcited by 7
  21. 2020Non-Convex Optimization via Non-Reversible Stochastic Gradient Langevin Dynamicscited by 6
  22. 2022Constrained Langevin Algorithms with L-mixing External Random Variablescited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2025Accelerating Constrained Sampling: A Large Deviations Approachcited by 2
  2. 2026Decentralized Proximal Stochastic Gradient Langevin Dynamicscited by 2
  3. 2026Particle-based Generalised Stochastic Optimisationcited by 0
  4. 2026Accelerating Non-Smooth and Heavy-Tailed Samplingcited by 0