mlsanityData to 14 Oct 2026

Non-Reversible Langevin Algorithms for Constrained Sampling

arXiv 2501.11743 ↗First posted 20 Jan 2025cs.LG math.PR stat.COcited by 7

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Abstract (arXiv)

We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD), a continuous-time stochastic differential equation with skew-reflected boundary. We obtain non-asymptotic convergence rate of SRNLD to the target distribution in both total variation and 1-Wasserstein distances. By breaking reversibility, we show that the convergence is faster than the special case of the reversible dynamics. Based on the discretization of SRNLD, we propose skew-reflected non-reversible Langevin Monte Carlo (SRNLMC), and obtain non-asymptotic discretization error from SRNLD, and convergence guarantees to the target distribution in 1-Wasserstein distance. We show better performance guarantees than the projected Langevin Monte Carlo in the literature that is based on the reversible dynamics. Numerical experiments are provided for both synthetic and real datasets to show efficiency of the proposed algorithms.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 18 of its 44 references that are in the map. First posted on arXiv 20 Jan 2025.

Builds on

18 of 44 references.

References · 18

  1. 2014Consistency and fluctuations for stochastic gradient Langevin dynamicscited by 65
  2. 2018Mirrored Langevin Dynamicscited by 61
  3. 2020Wasserstein Control of Mirror Langevin Monte Carlocited by 55
  4. 2020Efficient constrained sampling via the mirror-Langevin algorithmcited by 55
  5. 2015Sampling from a log-concave distribution with Projected Langevin Monte Carlocited by 52
  6. 2017Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlocited by 43
  7. 2020Exponential ergodicity of mirror-Langevin diffusionscited by 37
  8. 2021The Mirror Langevin Algorithm Converges with Vanishing Biascited by 37
  9. 2020Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithmcited by 35
  10. 2020Projected Stochastic Gradient Langevin Algorithms for Constrained Sampling and Non-Convex Learningcited by 33
  11. 2020Decentralized Stochastic Gradient Langevin Dynamics and Hamiltonian Monte Carlocited by 19
  12. 2022Penalized Overdamped and Underdamped Langevin Monte Carlo Algorithms for Constrained Samplingcited by 13
6 more
  1. 2018Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimizationcited by 12
  2. 2024Generalized EXTRA stochastic gradient Langevin dynamicscited by 9
  3. 2016Improving the convergence of reversible samplerscited by 8
  4. 2024Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamicscited by 7
  5. 2020Non-Convex Optimization via Non-Reversible Stochastic Gradient Langevin Dynamicscited by 6
  6. 2022Constrained Langevin Algorithms with L-mixing External Random Variablescited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 5.

7 papers.

  1. 2025Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysiscited by 4
  2. 2025Accelerating Constrained Sampling: A Large Deviations Approachcited by 2
  3. 2026Decentralized Proximal Stochastic Gradient Langevin Dynamicscited by 2
  4. 2026Variance Reduction for Stochastic Gradient Generalized Non-reversible Langevin Monte Carlo Algorithmscited by 2
  5. 2026Reflected Anchored Langevin Algorithmscited by 1
  6. 2026Kinetic Langevin Splitting Schemes for Constrained Samplingcited by 0
  7. 2026Accelerating Non-Smooth and Heavy-Tailed Samplingcited by 0