mlsanityData to 7 Oct 2026

The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptions

arXiv 2502.03458 ↗First posted 5 Feb 2025stat.ML math.OC math.PRcited by 4

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Abstract (arXiv)

In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor logconcave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging techniques, such as the Moreau-Yosida envelope or Gaussian smoothing, and show consequently that the performance of samplers like ULA does not necessarily degenerate arbitrarily with low regularity. In particular, we show that the Lipschitz or H"older continuity assumption can be replaced by a geometric one-sided Lipschitz condition that allows even for discontinuous log-gradients. We derive non-asymptotic guarantees for the convergence of the algorithm to the target distribution in Wasserstein distances. Non-asymptotic bounds are also provided for the performance of the algorithm as an optimizer, specifically for the solution of associated excess risk optimization problems.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 32 of its 55 references that are in the map. First posted on arXiv 5 Feb 2025.

Builds on

32 of 55 references.

References · 32

  1. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 242
  2. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  3. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  4. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  5. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
  6. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 96
  7. 2018Sharp convergence rates for Langevin dynamics in the nonconvex settingcited by 67
  8. 2020On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothnesscited by 55
  9. 2013Proximal Markov chain Monte Carlo algorithmscited by 46
  10. 2017Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlocited by 43
  11. 2020Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergencecited by 42
  12. 2019Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexitycited by 38
20 more
  1. 2019Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimizationcited by 38
  2. 2018Non-asymptotic bounds for sampling algorithms without log-concavitycited by 35
  3. 2017The Tamed Unadjusted Langevin Algorithmcited by 31
  4. 2023Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequalitycited by 31
  5. 2019Langevin Monte Carlo without smoothnesscited by 27
  6. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distancecited by 27
  7. 2021The Langevin Monte Carlo algorithm in the non-smooth log-concave casecited by 26
  8. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 26
  9. 2020Taming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithmscited by 21
  10. 2018On stochastic gradient Langevin dynamics with dependent data streams in the logconcave casecited by 20
  11. 2023Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Casecited by 12
  12. 2021Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networkscited by 11
  13. 2021Proximal nested sampling for high-dimensional Bayesian model selectioncited by 11
  14. 2023Subgradient Langevin Methods for Sampling from Non-smooth Potentialscited by 11
  15. 2022Non-asymptotic convergence bounds for modified tamed unadjusted Langevin algorithm in non-convex settingcited by 10
  16. 2023Fractal Landscapes in Policy Optimizationcited by 8
  17. 2023Taming under isoperimetrycited by 7
  18. 2024Tamed Langevin sampling under weaker conditionscited by 7
  19. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  20. 2024Ergodicity of Langevin Dynamics and its Discretizations for Non-smooth Potentialscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 2.

4 papers.

  1. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradientscited by 15
  2. 2025Gradient Flow Sampler-based Distributionally Robust Optimizationcited by 2
  3. 2026DC-LA: Difference-of-Convex Langevin Algorithmcited by 1
  4. 2026Muon meets Tamed Langevin: Momentum Preconditioning beyond Convex and gradient-Lipschitz Potentialscited by 0