mlsanityData to 14 Oct 2026

The Langevin Monte Carlo algorithm in the non-smooth log-concave case

arXiv 2101.10695 ↗First posted 26 Jan 2021math.ST cs.DS math.PRcited by 26

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Abstract (arXiv)

We prove non asymptotic polynomial bounds on the convergence of the Langevin Monte Carlo algorithm in the case where the potential is a convex function which is globally Lipschitz on its domain, typically the maximum of a finite number of affine functions on an arbitrary convex set. In particular the potential is not assumed to be gradient Lipschitz, in contrast with most existing works on the topic.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). First posted on arXiv 26 Jan 2021.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 7; 2023: 5; 2024: 5; 2025: 4; 2026: 2.

26 papers.

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  1. 2023Improved dimension dependence of a proximal algorithm for samplingcited by 30
  2. 2021Sqrt(d) Dimension Dependence of Langevin Monte Carlocited by 25
  3. 2021A Proximal Algorithm for Sampling from Non-smooth Potentialscited by 24
  4. 2022A Proximal Algorithm for Samplingcited by 22
  5. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 22
  6. 2024In-and-Out: Algorithmic Diffusion for Sampling Convex Bodiescited by 19
  7. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  8. 2022Bregman Proximal Langevin Monte Carlo via Bregman--Moreau Envelopescited by 7
  9. 2022Heavy-tailed Sampling via Transformed Unadjusted Langevin Algorithmcited by 6
  10. 2022Constrained Langevin Algorithms with L-mixing External Random Variablescited by 6
  11. 2023NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problemscited by 4
  12. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
14 more
  1. 2024Convergence of Unadjusted Langevin in High Dimensions: Delocalization of Biascited by 4
  2. 2025The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptionscited by 4
  3. 2024R'enyi-infinity constrained sampling with d3 membership queriescited by 3
  4. 2025Oracle-based Uniform Sampling from Convex Bodiescited by 3
  5. 2022A Proximal Algorithm for Sampling from Non-convex Potentialscited by 2
  6. 2024Randomized Midpoint Method for Log-Concave Sampling under Constraintscited by 2
  7. 2024Covariance estimation using Markov chain Monte Carlocited by 2
  8. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
  9. 2026Improved Guarantees for Langevin Monte Carlo with Average Smoothnesscited by 2
  10. 2021Fast Scalable Image Restoration using Total Variation Priors and Expectation Propagationcited by 1
  11. 2023Non-asymptotic analysis of Langevin-type Monte Carlo algorithmscited by 0
  12. 2023Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterationscited by 0
  13. 2025Mixing Times and Privacy Analysis for the Projected Langevin Algorithm under a Modulus of Continuitycited by 0
  14. 2026Muon meets Tamed Langevin: Momentum Preconditioning beyond Convex and gradient-Lipschitz Potentialscited by 0