mlsanityData to 14 Oct 2026

Contractive kinetic Langevin samplers beyond global Lipschitz continuity

arXiv 2509.12031 ↗First posted 15 Sep 2025math.PR cs.NA math.NAcited by 1

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Abstract (arXiv)

In this paper, we examine the problem of sampling from log-concave distributions with (possibly) superlinear gradient growth under kinetic (underdamped) Langevin algorithms. Using a carefully tailored taming scheme, we propose two novel discretizations of the kinetic Langevin SDE, and we show that they are both contractive and satisfy a log-Sobolev inequality. Building on this, we establish a series of non-asymptotic bounds in 2-Wasserstein distance between the law reached by each algorithm and the underlying target measure.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 25 of its 37 references that are in the map. First posted on arXiv 15 Sep 2025.

Builds on

25 of 37 references.

References · 25

  1. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 243
  2. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
  3. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 208
  4. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 197
  5. 2016High-dimensional Bayesian inference via the Unadjusted Langevin Algorithmcited by 146
  6. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 133
  7. 2018Sharp convergence rates for Langevin dynamics in the nonconvex settingcited by 68
  8. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  9. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 62
  10. 2020On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothnesscited by 55
  11. 2023Faster high-accuracy log-concave sampling via algorithmic warm startscited by 45
  12. 2020Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergencecited by 42
13 more
  1. 2019Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimizationcited by 38
  2. 2018Non-asymptotic bounds for sampling algorithms without log-concavitycited by 35
  3. 2017The Tamed Unadjusted Langevin Algorithmcited by 31
  4. 2018Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Accelerationcited by 31
  5. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 28
  6. 2020Taming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithmscited by 21
  7. 2018On stochastic gradient Langevin dynamics with dependent data streams in the logconcave casecited by 20
  8. 2020Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimizationcited by 13
  9. 2018Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimizationcited by 12
  10. 2023Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Casecited by 12
  11. 2022Non-asymptotic convergence bounds for modified tamed unadjusted Langevin algorithm in non-convex settingcited by 10
  12. 2019Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Learningcited by 8
  13. 2023Taming under isoperimetrycited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Error estimates for tamed Euler and Randomized Euler schemes for SDEs with locally Lipschitz drift with applications to non-logconcave sampling and optimizationcited by 2