mlsanityData to 7 Oct 2026

Analysis of Langevin Monte Carlo via convex optimization

arXiv 1802.09188 ↗First posted 26 Feb 2018stat.CO stat.MLcited by 126

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Abstract (arXiv)

In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order 2. Using this interpretation and techniques borrowed from convex optimization, we give a non-asymptotic analysis of this method to sample from logconcave smooth target distribution on ℝd. Based on this interpretation, we propose two new methods for sampling from a non-smooth target distribution, which we analyze as well. Besides, these new algorithms are natural extensions of the Stochastic Gradient Langevin Dynamics (SGLD) algorithm, which is a popular extension of the Unadjusted Langevin Algorithm. Similar to SGLD, they only rely on approximations of the gradient of the target log density and can be used for large-scale Bayesian inference.

Key facts. Cited by 126 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Feb 2018.

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Citing papers per year: 2021: 16; 2022: 26; 2023: 20; 2024: 27; 2025: 19; 2026: 18.

126 papers.

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  1. 2022Variational inference via Wasserstein gradient flowscited by 84
  2. 2022Improved analysis for a proximal algorithm for samplingcited by 72
  3. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  4. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
  5. 2021Kernel Stein Discrepancy Descentcited by 57
  6. 2022Private Convex Optimization via Exponential Mechanismcited by 47
  7. 2021KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Supportcited by 37
  8. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  9. 2023Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequalitycited by 31
  10. 2023Improved dimension dependence of a proximal algorithm for samplingcited by 29
  11. 2021QLSD: Quantised Langevin stochastic dynamics for Bayesian federated learningcited by 26
  12. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
38 more
  1. 2021Sqrt(d) Dimension Dependence of Langevin Monte Carlocited by 25
  2. 2021A Proximal Algorithm for Sampling from Non-smooth Potentialscited by 23
  3. 2022Convergence of the Riemannian Langevin Algorithmcited by 23
  4. 2024Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Samplingcited by 23
  5. 2024Implicit Diffusion: Efficient Optimization through Stochastic Samplingcited by 22
  6. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  7. 2022A Proximal Algorithm for Samplingcited by 21
  8. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 21
  9. 2023Sampling via Gradient Flows in the Space of Probability Measurescited by 20
  10. 2021Lower Bounds on Metropolized Sampling Methods for Well-Conditioned Distributionscited by 19
  11. 2021The query complexity of sampling from strongly log-concave distributions in one dimensioncited by 18
  12. 2024In-and-Out: Algorithmic Diffusion for Sampling Convex Bodiescited by 18
  13. 2022Sampling with Mollified Interaction Energy Descentcited by 17
  14. 2023Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimationcited by 17
  15. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  16. 2023An Explicit Expansion of the Kullback-Leibler Divergence along its Fisher-Rao Gradient Flowcited by 16
  17. 2023A connection between Tempering and Entropic Mirror Descentcited by 16
  18. 2021On Convergence of Federated Averaging Langevin Dynamicscited by 14
  19. 2024Convergence of coordinate ascent variational inference for log-concave measures via optimal transportcited by 13
  20. 2021When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpointcited by 12
  21. 2023Query lower bounds for log-concave samplingcited by 12
  22. 2024More Efficient Randomized Exploration for Reinforcement Learning via Approximate Samplingcited by 12
  23. 2021Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimensioncited by 11
  24. 2025Mixing Time of the Proximal Sampler in Relative Fisher Information via Strong Data Processing Inequalitycited by 11
  25. 2021Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation functioncited by 10
  26. 2022Condition-number-independent convergence rate of Riemannian Hamiltonian Monte Carlo with numerical integratorscited by 10
  27. 2023Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisitedcited by 10
  28. 2024Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamicscited by 10
  29. 2024Constrained Sampling with Primal-Dual Langevin Monte Carlocited by 10
  30. 2022Sampling Approximately Low-Rank Ising Models: MCMC meets Variational Methodscited by 9
  31. 2023Algorithmic Aspects of the Log-Laplace Transform and a Non-Euclidean Proximal Samplercited by 9
  32. 2024Regularization by denoising: Bayesian model and Langevin-within-split Gibbs samplingcited by 9
  33. 2024Parallelized Midpoint Randomization for Langevin Monte Carlocited by 9
  34. 2021Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equationscited by 8
  35. 2021Sampling from Log-Concave Distributions with Infinity-Distance Guaranteescited by 8
  36. 2022Quantum Algorithms for Sampling Log-Concave Distributions and Estimating Normalizing Constantscited by 8
  37. 2023Coin Sampling: Gradient-Based Bayesian Inference without Learning Ratescited by 8
  38. 2024Proximal Interacting Particle Langevin Algorithmscited by 8

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