mlsanityData to 7 Oct 2026

Taming under isoperimetry

arXiv 2311.09003 ↗First posted 15 Nov 2023math.PR cs.NA math.NAcited by 7

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Abstract (arXiv)

In this article we propose a novel taming Langevin-based scheme called sTULA to sample from distributions with superlinearly growing log-gradient which also satisfy a Log-Sobolev inequality. We derive non-asymptotic convergence bounds in KL and consequently total variation and Wasserstein-2 distance from the target measure. Non-asymptotic convergence guarantees are provided for the performance of the new algorithm as an optimizer. Finally, some theoretical results on isoperimertic inequalities for distributions with superlinearly growing gradients are provided. Key findings are a Log-Sobolev inequality with constant independent of the dimension, in the presence of a higher order regularization and a Poincare inequality with constant independent of temperature and dimension under a novel non-convex theoretical framework.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 21 of its 43 references that are in the map. First posted on arXiv 15 Nov 2023.

Builds on

21 of 43 references.

References · 21

  1. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 242
  2. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  3. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 206
  4. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 195
  5. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 144
  6. 2018Sampling Can Be Faster Than Optimizationcited by 68
  7. 2018Sharp convergence rates for Langevin dynamics in the nonconvex settingcited by 67
  8. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  9. 2020On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothnesscited by 55
  10. 2020Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergencecited by 42
  11. 2019Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexitycited by 38
  12. 2019Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimizationcited by 38
9 more
  1. 2018Non-asymptotic bounds for sampling algorithms without log-concavitycited by 35
  2. 2017The Tamed Unadjusted Langevin Algorithmcited by 31
  3. 2020Riemannian Langevin Algorithm for Solving Semidefinite Programscited by 22
  4. 2020Taming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithmscited by 21
  5. 2018On stochastic gradient Langevin dynamics with dependent data streams in the logconcave casecited by 20
  6. 2023Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Casecited by 12
  7. 2021Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networkscited by 11
  8. 2021Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation functioncited by 10
  9. 2022Non-asymptotic convergence bounds for modified tamed unadjusted Langevin algorithm in non-convex settingcited by 10

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 4; 2026: 2.

7 papers.

  1. 2024Tamed Langevin sampling under weaker conditionscited by 7
  2. 2025The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptionscited by 4
  3. 2025kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradientscited by 2
  4. 2025Contractive kinetic Langevin samplers beyond global Lipschitz continuitycited by 1
  5. 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
  6. 2025When Langevin Monte Carlo Meets Randomization: New Sampling Algorithms with Non-asymptotic Error Bounds beyond Log-Concavity and Gradient Lipschitznesscited by 0
  7. 2026RELTA-SGLD: Relative-Growth Localized Taming for Nonconvex Stochastic-Gradient Langevin Learningcited by 0