mlsanityData to 7 Oct 2026

A Proximal Algorithm for Sampling

arXiv 2202.13975 ↗First posted 28 Feb 2022cs.LG stat.MLcited by 21

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Abstract (arXiv)

We study sampling problems associated with potentials that lack smoothness. The potentials can be either convex or non-convex. Departing from the standard smooth setting, the potentials are only assumed to be weakly smooth or non-smooth, or the summation of multiple such functions. We develop a sampling algorithm that resembles proximal algorithms in optimization for this challenging sampling task. Our algorithm is based on a special case of Gibbs sampling known as the alternating sampling framework (ASF). The key contribution of this work is a practical realization of the ASF based on rejection sampling for both non-convex and convex potentials that are not necessarily smooth. In almost all the cases of sampling considered in this work, our proximal sampling algorithm achieves better complexity than all existing methods.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 32 of its 70 references that are in the map. First posted on arXiv 28 Feb 2022.

Builds on

32 of 70 references.

References · 32

  1. 2021What Are Bayesian Neural Network Posteriors Really Like?cited by 307
  2. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 242
  3. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  4. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  5. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 131
  6. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 126
  7. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  8. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 117
  9. 2017Convergence of Langevin MCMC in KL-divergencecited by 86
  10. 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 85
  11. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 83
  12. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
20 more
  1. 2022Improved analysis for a proximal algorithm for samplingcited by 72
  2. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  3. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 61
  4. 2020On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothnesscited by 55
  5. 2019Fast mixing of Metropolized Hamiltonian Monte Carlo: Benefits of multi-step gradientscited by 51
  6. 2019Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexitycited by 38
  7. 2020Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithmcited by 34
  8. 2017Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computationcited by 32
  9. 2019Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetrycited by 31
  10. 2019Langevin Monte Carlo without smoothnesscited by 27
  11. 2021The Langevin Monte Carlo algorithm in the non-smooth log-concave casecited by 26
  12. 2021A Proximal Algorithm for Sampling from Non-smooth Potentialscited by 23
  13. 2019An Efficient Sampling Algorithm for Non-smooth Composite Potentialscited by 19
  14. 2017Fast MCMC sampling algorithms on polytopescited by 17
  15. 2019Bounding the error of discretized Langevin algorithms for non-strongly log-concave targetscited by 16
  16. 2016Eldan's Stochastic Localization and the KLS Conjecture: Isoperimetry, Concentration and Mixingcited by 13
  17. 2021When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpointcited by 12
  18. 2020Composite Logconcave Sampling with a Restricted Gaussian Oraclecited by 8
  19. 2020A proximal bundle variant with optimal iteration-complexity for a large range of prox stepsizescited by 7
  20. 2021A unified analysis of a class of proximal bundle methods for solving hybrid convex composite optimization problemscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 5; 2024: 5; 2025: 6; 2026: 4.

21 papers.

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  1. 2023The probability flow ODE is provably fastcited by 145
  2. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 44
  3. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Modelscited by 39
  4. 2023Improved dimension dependence of a proximal algorithm for samplingcited by 29
  5. 2024Provable Benefit of Annealed Langevin Monte Carlo for Non-log-concave Samplingcited by 23
  6. 2024Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusioncited by 19
  7. 2025Mixing Time of the Proximal Sampler in Relative Fisher Information via Strong Data Processing Inequalitycited by 11
  8. 2024Efficient Statistics With Unknown Truncation, Polynomial Time Algorithms, Beyond Gaussianscited by 6
  9. 2024Characterizing Dependence of Samples along the Langevin Dynamics and Algorithms via Contraction of Phi-Mutual Informationcited by 5
  10. 2024Proximal Oracles for Optimization and Samplingcited by 5
  11. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  12. 2025Beyond Scores: Proximal Diffusion Modelscited by 3
9 more
  1. 2025Oracle-based Uniform Sampling from Convex Bodiescited by 3
  2. 2022A Proximal Algorithm for Sampling from Non-convex Potentialscited by 2
  3. 2025Entropy-Guided Sampling of Flat Modes in Discrete Spacescited by 1
  4. 2026Alternating Diffusion for Proximal Sampling with Zeroth Order Queriescited by 1
  5. 2026A proximal gradient algorithm for composite log-concave samplingcited by 1
  6. 2025Improved sampling algorithms and functional inequalities for non-log-concave distributionscited by 0
  7. 2025Sampling on Metric Graphscited by 0
  8. 2026The Geometry of Efficient Nonconvex Samplingcited by 0
  9. 2026Local Geometric Mixing via Dobrushin Contraction with Applications to Diffusion Path Monte Carlo and the Proximal Samplercited by 0