mlsanityData to 7 Oct 2026

The Tamed Unadjusted Langevin Algorithm

arXiv 1710.05559 ↗First posted 16 Oct 2017stat.MEcited by 31

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Abstract (arXiv)

In this article, we consider the problem of sampling from a probability measure π having a density on ℝd known up to a normalizing constant, xmapsto e-U(x) / intℝd e-U(y) d y. The Euler discretization of the Langevin stochastic differential equation (SDE) is known to be unstable in a precise sense, when the potential U is superlinear, i.e. liminfVert x Vert→+∞ Vert nabla U(x) Vert / Vert x Vert = +∞. Based on previous works on the taming of superlinear drift coefficients for SDEs, we introduce the Tamed Unadjusted Langevin Algorithm (TULA) and obtain non-asymptotic bounds in V-total variation norm and Wasserstein distance of order 2 between the iterates of TULA and π, as well as weak error bounds. Numerical experiments are presented which support our findings.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Oct 2017.

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Citing papers per year: 2021: 4; 2022: 3; 2023: 5; 2024: 5; 2025: 5; 2026: 9.

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  1. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priorscited by 28
  2. 2023Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimationcited by 17
  3. 2024Diffusion posterior sampling for simulation-based inference in tall data settingscited by 17
  4. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  5. 2023Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Casecited by 12
  6. 2021Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networkscited by 11
  7. 2021Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimensioncited by 11
  8. 2022Lagrangian Manifold Monte Carlo on Monge Patchescited by 11
  9. 2021Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation functioncited by 10
  10. 2023Taming under isoperimetrycited by 7
  11. 2024Tamed Langevin sampling under weaker conditionscited by 7
  12. 2024Kinetic Interacting Particle Langevin Monte Carlocited by 7
19 more
  1. 2022Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradientcited by 5
  2. 2025From Global to Local: A Scalable Benchmark for Local Posterior Samplingcited by 5
  3. 2025The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptionscited by 4
  4. 2021Unadjusted Langevin algorithm for sampling a mixture of weakly smooth potentialscited by 3
  5. 2024Taming the Interacting Particle Langevin Algorithm: The Superlinear casecited by 3
  6. 2025kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradientscited by 2
  7. 2026Deterministic Envelopes for Tamed SGLD: Decoupling Stochastic Gradient Noise and Localizing Tamingcited by 2
  8. 2025Contractive kinetic Langevin samplers beyond global Lipschitz continuitycited by 1
  9. 2026Error estimates for tamed Euler and Randomized Euler schemes for SDEs with locally Lipschitz drift with applications to non-logconcave sampling and optimizationcited by 1
  10. 2026Deterministic Denominator Design for Localized Tamed Stochastic Gradient Langevin Dynamicscited by 1
  11. 2023Non-asymptotic analysis of Langevin-type Monte Carlo algorithmscited by 0
  12. 2023STANLEY: Stochastic Gradient Anisotropic Langevin Dynamics for Learning Energy-Based Modelscited by 0
  13. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a surveycited by 0
  14. 2026Time-Inhomogeneous Preconditioned Langevin Dynamicscited by 0
  15. 2026Theoretical guidelines for annealed Langevin dynamics in compositional simulation-based inferencecited by 0
  16. 2026Event Generation with Parallel Langevin Sampling and Learned Stein Diagnosticscited by 0
  17. 2026RELTA-SGLD: Relative-Growth Localized Taming for Nonconvex Stochastic-Gradient Langevin Learningcited by 0
  18. 2026Stability of Finite-Batch Particle Mean-Field Variational Inference Beyond Strong Convexitycited by 0
  19. 2026Muon meets Tamed Langevin: Momentum Preconditioning beyond Convex and gradient-Lipschitz Potentialscited by 0