mlsanityData to 14 Oct 2026

Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo

arXiv 1705.08964 ↗First posted 24 May 2017stat.MEcited by 43

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Abstract (arXiv)

This paper presents a detailed theoretical analysis of the Langevin Monte Carlo sampling algorithm recently introduced in Durmus et al. (Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau, 2016) when applied to log-concave probability distributions that are restricted to a convex body mathsfK. This method relies on a regularisation procedure involving the Moreau-Yosida envelope of the indicator function associated with mathsfK. Explicit convergence bounds in total variation norm and in Wasserstein distance of order 1 are established. In particular, we show that the complexity of this algorithm given a first order oracle is polynomial in the dimension of the state space. Finally, some numerical experiments are presented to compare our method with competing MCMC approaches from the literature.

Key facts. Cited by 43 papers in the map (data through 14 Oct 2026). First posted on arXiv 24 May 2017.

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Citing papers per year: 2021: 3; 2022: 5; 2023: 8; 2024: 8; 2025: 8; 2026: 11.

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  1. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  2. 2023Mirror Diffusion Models for Constrained and Watermarked Generationcited by 42
  3. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 22
  4. 2025Training-Free Constrained Generation With Stable Diffusion Modelscited by 20
  5. 2024In-and-Out: Algorithmic Diffusion for Sampling Convex Bodiescited by 19
  6. 2024Reflected Schr"odinger Bridge for Constrained Generative Modelingcited by 12
  7. 2023Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithmcited by 11
  8. 2023Algorithmic Aspects of the Log-Laplace Transform and a Non-Euclidean Proximal Samplercited by 10
  9. 2023Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisitedcited by 10
  10. 2021Sampling from Log-Concave Distributions with Infinity-Distance Guaranteescited by 8
  11. 2022Bregman Proximal Langevin Monte Carlo via Bregman--Moreau Envelopescited by 7
  12. 2024Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamicscited by 7
31 more
  1. 2025Non-Reversible Langevin Algorithms for Constrained Samplingcited by 7
  2. 2022Constrained Langevin Algorithms with L-mixing External Random Variablescited by 6
  3. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
  4. 2021Sensing Cox Processes via Posterior Sampling and Positive Basescited by 4
  5. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  6. 2025The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptionscited by 4
  7. 2025Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysiscited by 4
  8. 2022Convergence Error Analysis of Reflected Gradient Langevin Dynamics for Globally Optimizing Non-Convex Constrained Problemscited by 3
  9. 2024R'enyi-infinity constrained sampling with d3 membership queriescited by 3
  10. 2025Oracle-based Uniform Sampling from Convex Bodiescited by 3
  11. 2025PSI3D: Plug-and-Play 3D Stochastic Inference with Slice-wise Latent Diffusion Priorcited by 3
  12. 2024Randomized Midpoint Method for Log-Concave Sampling under Constraintscited by 2
  13. 2025Accelerating Constrained Sampling: A Large Deviations Approachcited by 2
  14. 2026Decentralized Proximal Stochastic Gradient Langevin Dynamicscited by 2
  15. 2026Improved Guarantees for Langevin Monte Carlo with Average Smoothnesscited by 2
  16. 2026Active-Trace Complexity Bounds for Moreau--Yosida Unadjusted Langevin Samplingcited by 2
  17. 2022Sampling from Log-Concave Distributions over Polytopes via a Soft-Threshold Dikin Walkcited by 1
  18. 2023Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Modelscited by 1
  19. 2024Faster Sampling from Log-Concave Densities over Polytopes via Efficient Linear Solverscited by 1
  20. 2026Alternating Diffusion for Proximal Sampling with Zeroth Order Queriescited by 1
  21. 2026Shuffling the Data, Stretching the Step-size: Sharper Bias in constant step-size SGDcited by 1
  22. 2026A proximal gradient algorithm for composite log-concave samplingcited by 1
  23. 2021Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlocited by 0
  24. 2023Efficiently handling constraints with Metropolis-adjusted Langevin algorithmcited by 0
  25. 2024Scalable Monte Carlo for Bayesian Learningcited by 0
  26. 2024Functional Gradient Flows for Constrained Samplingcited by 0
  27. 2026Functional Stochastic Localizationcited by 0
  28. 2026Mean Estimation from Coarse Data: Characterizations and Efficient Algorithmscited by 0
  29. 2026Kinetic Langevin Splitting Schemes for Constrained Samplingcited by 0
  30. 2026MINTS: Minimalist Thompson Samplingcited by 0
  31. 2026Fast rates in Bayesian online learning with approximate posteriorscited by 0