mlsanityData to 14 Oct 2026

Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case

arXiv 2301.08039 ↗First posted 19 Jan 2023math.PR cs.LG cs.NAcited by 12

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Abstract (arXiv)

In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz. We propose two algorithms based on monotone polygonal (tamed) Euler schemes, to sample from a target measure, and provide non-asymptotic 2-Wasserstein distance bounds between the law of the process of each algorithm and the target measure. Finally, we apply these results to bound the excess risk optimization error of the associated optimization problem.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 18 of its 30 references that are in the map. First posted on arXiv 19 Jan 2023.

Builds on

18 of 30 references.

References · 18

  1. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 243
  2. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 197
  3. 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 133
  4. 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
  5. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 84
  6. 2018Sharp convergence rates for Langevin dynamics in the nonconvex settingcited by 68
  7. 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 62
  8. 2018The promises and pitfalls of Stochastic Gradient Langevin Dynamicscited by 56
  9. 2019Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimizationcited by 38
  10. 2017The Tamed Unadjusted Langevin Algorithmcited by 31
  11. 2018Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Accelerationcited by 31
  12. 2020Taming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithmscited by 21
6 more
  1. 2018On stochastic gradient Langevin dynamics with dependent data streams in the logconcave casecited by 20
  2. 2020Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimizationcited by 13
  3. 2018Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimizationcited by 12
  4. 2019Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Learningcited by 8
  5. 2020First-Order Algorithms Without Lipschitz Gradient: A Sequential Local Optimization Approachcited by 5
  6. 2019Proximal mappings and Moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functionscited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 3; 2025: 4; 2026: 2.

12 papers.

  1. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 28
  2. 2023Taming under isoperimetrycited by 7
  3. 2024Central Limit Theorem for Two-Timescale Stochastic Approximation with Markovian Noise: Theory and Applicationscited by 7
  4. 2024Tamed Langevin sampling under weaker conditionscited by 7
  5. 2024Kinetic Interacting Particle Langevin Monte Carlocited by 7
  6. 2025The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptionscited by 4
  7. 2025kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradientscited by 3
  8. 2023Mean-field underdamped Langevin dynamics and its spacetime discretizationcited by 2
  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 2
  10. 2025Contractive kinetic Langevin samplers beyond global Lipschitz continuitycited by 1
  11. 2025Analysis of kinetic Langevin Monte Carlo under the stochastic exponential Euler discretization from underdamped all the way to overdampedcited by 0
  12. 2026Muon meets Tamed Langevin: Momentum Preconditioning beyond Convex and gradient-Lipschitz Potentialscited by 0