mlsanityData to 14 Oct 2026

Efficient constrained sampling via the mirror-Langevin algorithm

arXiv 2010.16212 ↗First posted 30 Oct 2020math.ST cs.LG stat.THcited by 55

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Abstract (arXiv)

We propose a new discretization of the mirror-Langevin diffusion and give a crisp proof of its convergence. Our analysis uses relative convexity/smoothness and self-concordance, ideas which originated in convex optimization, together with a new result in optimal transport that generalizes the displacement convexity of the entropy. Unlike prior works, our result both (1) requires much weaker assumptions on the mirror map and the target distribution, and (2) has vanishing bias as the step size tends to zero. In particular, for the task of sampling from a log-concave distribution supported on a compact set, our theoretical results are significantly better than the existing guarantees.

Key facts. Cited by 55 papers in the map (data through 14 Oct 2026). First posted on arXiv 30 Oct 2020.

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Citing papers per year: 2021: 5; 2022: 15; 2023: 8; 2024: 10; 2025: 9; 2026: 8.

55 papers.

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  1. 2022Improved analysis for a proximal algorithm for samplingcited by 73
  2. 2023Mirror Diffusion Models for Constrained and Watermarked Generationcited by 42
  3. 2021KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Supportcited by 37
  4. 2021The Mirror Langevin Algorithm Converges with Vanishing Biascited by 37
  5. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  6. 2021Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descentcited by 32
  7. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  8. 2022Convergence of the Riemannian Langevin Algorithmcited by 25
  9. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 22
  10. 2024In-and-Out: Algorithmic Diffusion for Sampling Convex Bodiescited by 19
  11. 2021Sampling with Mirrored Stein Operatorscited by 17
  12. 2022Sampling with Mollified Interaction Energy Descentcited by 17
38 more
  1. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  2. 2022Private Convex Optimization in General Normscited by 13
  3. 2023Query lower bounds for log-concave samplingcited by 12
  4. 2023Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithmcited by 11
  5. 2022Condition-number-independent convergence rate of Riemannian Hamiltonian Monte Carlo with numerical integratorscited by 10
  6. 2023Algorithmic Aspects of the Log-Laplace Transform and a Non-Euclidean Proximal Samplercited by 10
  7. 2024Constrained Sampling with Primal-Dual Langevin Monte Carlocited by 10
  8. 2025Constrained Diffusers for Safe Planning and Controlcited by 10
  9. 2022Bregman Proximal Langevin Monte Carlo via Bregman--Moreau Envelopescited by 7
  10. 2024Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamicscited by 7
  11. 2025Non-Reversible Langevin Algorithms for Constrained Samplingcited by 7
  12. 2021The entropic barrier is n-self-concordantcited by 6
  13. 2022Constrained Langevin Algorithms with L-mixing External Random Variablescited by 6
  14. 2024Efficient Sampling on Riemannian Manifolds via Langevin MCMCcited by 6
  15. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
  16. 2022A Note on the Convergence of Mirrored Stein Variational Gradient Descent under (L0,L1)-Smoothness Conditioncited by 4
  17. 2023Mean-Square Analysis of Discretized Ito Diffusions for Heavy-tailed Samplingcited by 4
  18. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  19. 2025Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysiscited by 4
  20. 2022Bregman Power k-Means for Clustering Exponential Family Datacited by 3
  21. 2023Learning Rate Free Sampling in Constrained Domainscited by 3
  22. 2024R'enyi-infinity constrained sampling with d3 membership queriescited by 3
  23. 2025Mirror Mean-Field Langevin Dynamicscited by 3
  24. 2025Oracle-based Uniform Sampling from Convex Bodiescited by 3
  25. 2026Polynomial Convergence of Riemannian Diffusion Modelscited by 3
  26. 2022A Particle-Based Algorithm for Distributional Optimization on textitConstrained Domains via Variational Transport and Mirror Descentcited by 2
  27. 2022A Dynamical System View of Langevin-Based Non-Convex Samplingcited by 2
  28. 2024Randomized Midpoint Method for Log-Concave Sampling under Constraintscited by 2
  29. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
  30. 2025Accelerating Constrained Sampling: A Large Deviations Approachcited by 2
  31. 2026Learning Flow Distributions via Projection-Constrained Diffusion on Manifoldscited by 2
  32. 2026Decentralized Proximal Stochastic Gradient Langevin Dynamicscited by 2
  33. 2026Improved Guarantees for Langevin Monte Carlo with Average Smoothnesscited by 2
  34. 2026Safe, Scalable, and Accurate Bayes Posterior Sampling for Large-Data Generalized Linear Mixed Modelscited by 1
  35. 2026Mirror Langevin diffusions: Convergence rates and Markov chain approximationscited by 1
  36. 2022Sampling Constrained Continuous Probability Distributions: A Reviewcited by 0
  37. 2024Families of costs with zero and nonnegative MTW tensor in optimal transport and the c-divergencescited by 0
  38. 2024Provable Accuracy Bounds for Hybrid Dynamical Optimization and Samplingcited by 0

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