mlsanityData to 7 Oct 2026

Constrained Langevin Algorithms with L-mixing External Random Variables

arXiv 2205.14192 ↗First posted 27 May 2022cs.LG math.OC math.PRcited by 6

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Abstract (arXiv)

Langevin algorithms are gradient descent methods augmented with additive noise, and are widely used in Markov Chain Monte Carlo (MCMC) sampling, optimization, and machine learning. In recent years, the non-asymptotic analysis of Langevin algorithms for non-convex learning has been extensively explored. For constrained problems with non-convex losses over a compact convex domain with IID data variables, the projected Langevin algorithm achieves a deviation of O(T-1/4 (log T)1/2) from its target distribution [27] in 1-Wasserstein distance. In this paper, we obtain a deviation of O(T-1/2 log T) in 1-Wasserstein distance for non-convex losses with L-mixing data variables and polyhedral constraints (which are not necessarily bounded). This improves on the previous bound for constrained problems and matches the best-known bound for unconstrained problems.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 27 of its 47 references that are in the map. First posted on arXiv 27 May 2022.

Builds on

27 of 47 references.

References · 27

  1. 2021Convex optimizationcited by 2,479
  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. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  6. 2017Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimizationcited by 96
  7. 2018Sampling Can Be Faster Than Optimizationcited by 68
  8. 2018Sharp convergence rates for Langevin dynamics in the nonconvex settingcited by 67
  9. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  10. 2018Mirrored Langevin Dynamicscited by 61
  11. 2020Wasserstein Control of Mirror Langevin Monte Carlocited by 55
  12. 2020Efficient constrained sampling via the mirror-Langevin algorithmcited by 55
15 more
  1. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
  2. 2018Global Non-convex Optimization with Discretized Diffusionscited by 44
  3. 2017Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlocited by 43
  4. 2020Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergencecited by 42
  5. 2018Non-asymptotic bounds for sampling algorithms without log-concavitycited by 35
  6. 2020Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learningcited by 33
  7. 2020Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Samplingcited by 32
  8. 2021The Langevin Monte Carlo algorithm in the non-smooth log-concave casecited by 26
  9. 2021Sqrt(d) Dimension Dependence of Langevin Monte Carlocited by 25
  10. 2018On stochastic gradient Langevin dynamics with dependent data streams in the logconcave casecited by 20
  11. 2020Fast Convergence of Langevin Dynamics on Manifold: Geodesics meet Log-Sobolevcited by 16
  12. 2019On Stationary-Point Hitting Time and Ergodicity of Stochastic Gradient Langevin Dynamicscited by 14
  13. 2019On stochastic gradient Langevin dynamics with dependent data streams: the fully non-convex casecited by 14
  14. 2017Acceleration and Averaging in Stochastic Mirror Descent Dynamicscited by 1
  15. 2021Wasserstein Contraction Bounds on Closed Convex Domains with Applications to Stochastic Adaptive Controlcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 0; 2025: 4; 2026: 1.

6 papers.

  1. 2025Non-Reversible Langevin Algorithms for Constrained Samplingcited by 7
  2. 2025Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysiscited by 4
  3. 2025Accelerating Constrained Sampling: A Large Deviations Approachcited by 2
  4. 2026Decentralized Proximal Stochastic Gradient Langevin Dynamicscited by 2
  5. 2023Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Modelscited by 1
  6. 2025Quantitative Convergence Analysis of Projected Stochastic Gradient Descent for Non-Convex Losses via the Goldstein Subdifferentialcited by 0