mlsanityData to 7 Oct 2026

Mirrored Langevin Dynamics

arXiv 1802.10174 ↗First posted 27 Feb 2018cs.LG math.OCcited by 61

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Abstract (arXiv)

We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror descent, to derive novel first-order sampling schemes. We prove that, for a general target distribution with strongly convex potential, our framework implies the existence of a first-order algorithm achieving tildeO(ε-2d) convergence, suggesting that the state-of-the-art tildeO(ε-6d5) can be vastly improved. With the important Latent Dirichlet Allocation (LDA) application in mind, we specialize our algorithm to sample from Dirichlet posteriors, and derive the first non-asymptotic tildeO(ε-2d2) rate for first-order sampling. We further extend our framework to the mini-batch setting and prove convergence rates when only stochastic gradients are available. Finally, we report promising experimental results for LDA on real datasets.

Key facts. Cited by 61 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Feb 2018.

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Citing papers per year: 2021: 7; 2022: 10; 2023: 15; 2024: 7; 2025: 13; 2026: 9.

61 papers.

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  1. 2021Bayesian Learning via Neural Schr"odinger-F"ollmer Flowscited by 56
  2. 2023Mirror Diffusion Models for Constrained and Watermarked Generationcited by 38
  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. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  6. 2022Convergence of the Riemannian Langevin Algorithmcited by 23
  7. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  8. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 21
  9. 2023Sampling via Gradient Flows in the Space of Probability Measurescited by 20
  10. 2021Sampling with Mirrored Stein Operatorscited by 17
  11. 2023Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariancecited by 16
  12. 2022Private Convex Optimization in General Normscited by 13
38 more
  1. 2024Reflected Schr"odinger Bridge for Constrained Generative Modelingcited by 12
  2. 2023Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithmcited by 11
  3. 2024Constrained Sampling with Primal-Dual Langevin Monte Carlocited by 10
  4. 2023Algorithmic Aspects of the Log-Laplace Transform and a Non-Euclidean Proximal Samplercited by 9
  5. 2022Bregman Proximal Langevin Monte Carlo via Bregman--Moreau Envelopescited by 7
  6. 2023SMURF-THP: Score Matching-based UnceRtainty quantiFication for Transformer Hawkes Processcited by 7
  7. 2024Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamicscited by 7
  8. 2024Neural Approximate Mirror Maps for Constrained Diffusion Modelscited by 7
  9. 2025Non-Reversible Langevin Algorithms for Constrained Samplingcited by 7
  10. 2022Constrained Langevin Algorithms with L-mixing External Random Variablescited by 6
  11. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
  12. 2023Variational Principles for Mirror Descent and Mirror Langevin Dynamicscited by 5
  13. 2023Langevin Thompson Sampling with Logarithmic Communication: Bandits and Reinforcement Learningcited by 5
  14. 2025Unleashing High-Quality Image Generation in Diffusion Sampling Using Second-Order Levenberg-Marquardt-Langevincited by 5
  15. 2021Sensing Cox Processes via Posterior Sampling and Positive Basescited by 4
  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. 2021Unadjusted Langevin algorithm for sampling a mixture of weakly smooth potentialscited by 3
  21. 2022Convergence Error Analysis of Reflected Gradient Langevin Dynamics for Globally Optimizing Non-Convex Constrained Problemscited by 3
  22. 2023Learning Rate Free Sampling in Constrained Domainscited by 3
  23. 2025Mirror Mean-Field Langevin Dynamicscited by 3
  24. 2022A Particle-Based Algorithm for Distributional Optimization on textitConstrained Domains via Variational Transport and Mirror Descentcited by 2
  25. 2022A Dynamical System View of Langevin-Based Non-Convex Samplingcited by 2
  26. 2024Randomized Midpoint Method for Log-Concave Sampling under Constraintscited by 2
  27. 2025Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problemscited by 2
  28. 2025Variational Online Mirror Descent for Robust Learning in Schr"odinger Bridgecited by 2
  29. 2025Accelerating Constrained Sampling: A Large Deviations Approachcited by 2
  30. 2025Dale meets Langevin: A Multiplicative Denoising Diffusion Modelcited by 2
  31. 2026Decentralized Proximal Stochastic Gradient Langevin Dynamicscited by 2
  32. 2023Transport map unadjusted Langevin algorithms: learning and discretizing perturbed samplerscited by 1
  33. 2023Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Modelscited by 1
  34. 2023Score Matching-based Pseudolikelihood Estimation of Neural Marked Spatio-Temporal Point Process with Uncertainty Quantificationcited by 1
  35. 2025Preconditioned Regularized Wasserstein Proximal Samplingcited by 1
  36. 2026Safe, Scalable, and Accurate Bayes Posterior Sampling for Large-Data Generalized Linear Mixed Modelscited by 1
  37. 2026Mirror Langevin diffusions: Convergence rates and Markov chain approximationscited by 1
  38. 2023Efficiently handling constraints with Metropolis-adjusted Langevin algorithmcited by 0

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