mlsanityData to 7 Oct 2026

Sampling from a log-concave distribution with Projected Langevin Monte Carlo

arXiv 1507.02564 ↗First posted 9 Jul 2015math.PR cs.DS cs.LGcited by 52

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Abstract (arXiv)

We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (projected) LMC allows to sample in polynomial time from a log-concave distribution with smooth potential. This gives a new Markov chain to sample from a log-concave distribution. Our main result shows in particular that when the target distribution is uniform, LMC mixes in tildeO(n7) steps (where n is the dimension). We also provide preliminary experimental evidence that LMC performs at least as well as hit-and-run, for which a better mixing time of tildeO(n4) was proved by Lov'asz and Vempala.

Key facts. Cited by 52 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Jul 2015.

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Citing papers per year: 2021: 7; 2022: 11; 2023: 4; 2024: 8; 2025: 10; 2026: 12.

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  2. 2022Private Convex Optimization via Exponential Mechanismcited by 47
  3. 2021KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Supportcited by 37
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  5. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 21
  6. 2024In-and-Out: Algorithmic Diffusion for Sampling Convex Bodiescited by 18
  7. 2021Lazy OCO: Online Convex Optimization on a Switching Budgetcited by 14
  8. 2021Mixability made efficient: Fast online multiclass logistic regressioncited by 12
  9. 2024Reflected Schr"odinger Bridge for Constrained Generative Modelingcited by 12
  10. 2023Fast sampling from constrained spaces using the Metropolis-adjusted Mirror Langevin algorithmcited by 11
  11. 2024Shifted Interpolation for Differential Privacycited by 10
  12. 2024Constrained Sampling with Primal-Dual Langevin Monte Carlocited by 10
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  5. 2024Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamicscited by 7
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  8. 2022Optimal Regularization for a Data Sourcecited by 6
  9. 2025FlowLPS: Langevin-Proximal Sampling for Flow-based Inverse Problem Solverscited by 5
  10. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  11. 2025Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysiscited by 4
  12. 2021Contrastive learning of strong-mixing continuous-time stochastic processescited by 3
  13. 2022Convergence Error Analysis of Reflected Gradient Langevin Dynamics for Globally Optimizing Non-Convex Constrained Problemscited by 3
  14. 2022Differentially Private Sampling from Rashomon Sets, and the Universality of Langevin Diffusion for Convex Optimizationcited by 3
  15. 2025Oracle-based Uniform Sampling from Convex Bodiescited by 3
  16. 2022A Dynamical System View of Langevin-Based Non-Convex Samplingcited by 2
  17. 2024Randomized Midpoint Method for Log-Concave Sampling under Constraintscited by 2
  18. 2025Accelerating Constrained Sampling: A Large Deviations Approachcited by 2
  19. 2025A Simple, Optimal and Efficient Algorithm for Online Exp-Concave Optimizationcited by 2
  20. 2026Decentralized Proximal Stochastic Gradient Langevin Dynamicscited by 2
  21. 2026Improved Guarantees for Langevin Monte Carlo with Average Smoothnesscited by 2
  22. 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Modelscited by 1
  23. 2025Learning High-dimensional Gaussians from Censored Datacited by 1
  24. 2026Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solverscited by 1
  25. 2026Alternating Diffusion for Proximal Sampling with Zeroth Order Queriescited by 1
  26. 2026Manifold Sampling via Entropy Maximizationcited by 1
  27. 2026A proximal gradient algorithm for composite log-concave samplingcited by 1
  28. 2021Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlocited by 0
  29. 2021The Effects of Invertibility on the Representational Complexity of Encoders in Variational Autoencoderscited by 0
  30. 2023Towards Optimal Randomized Strategies in Adversarial Example Gamecited by 0
  31. 2024Provable Accuracy Bounds for Hybrid Dynamical Optimization and Samplingcited by 0
  32. 2024Functional Gradient Flows for Constrained Samplingcited by 0
  33. 2025Mixing Times and Privacy Analysis for the Projected Langevin Algorithm under a Modulus of Continuitycited by 0
  34. 2025Sampling with Shielded Langevin Monte Carlo Using Navigation Potentialscited by 0
  35. 2026Mean Estimation from Coarse Data: Characterizations and Efficient Algorithmscited by 0
  36. 2026Efficient Logistic Regression with Mixture of Sigmoidscited by 0
  37. 2026Shuffling the Data, Stretching the Step-size: Sharper Bias in constant step-size SGDcited by 0
  38. 2026MINTS: Minimalist Thompson Samplingcited by 0

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