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Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization

arXiv 1910.02008 ↗First posted 4 Oct 2019math.ST cs.LG math.PRcited by 38

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Abstract (arXiv)

In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserstein-1 and Wasserstein-2 distances for a popular class of algorithms called Stochastic Gradient Langevin Dynamics (SGLD). In addition, the aforementioned Wasserstein-2 convergence result can be applied to establish a non-asymptotic error bound for the expected excess risk. Crucially, these results are obtained under a local Lipschitz condition and a local dissipativity condition where we remove the uniform dependence in the data stream. We illustrate the importance of this relaxation by presenting examples from variational inference and from index tracking optimization.

Key facts. Cited by 38 papers in the map (data through 14 Oct 2026). First posted on arXiv 4 Oct 2019.

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Citing papers per year: 2021: 5; 2022: 7; 2023: 11; 2024: 4; 2025: 10; 2026: 1.

38 papers.

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  1. 2021Time-independent Generalization Bounds for SGLD in Non-convex Settingscited by 27
  2. 2023Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimationcited by 17
  3. 2023Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Casecited by 12
  4. 2023Time-Independent Information-Theoretic Generalization Bounds for SGLDcited by 12
  5. 2021Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networkscited by 11
  6. 2021Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation functioncited by 10
  7. 2024Proximal Interacting Particle Langevin Algorithmscited by 8
  8. 2021Convergence Analysis of Schr"odinger-F"ollmer Sampler without Convexitycited by 7
  9. 2022Utilising the CLT Structure in Stochastic Gradient based Sampling : Improved Analysis and Faster Algorithmscited by 7
  10. 2023Taming under isoperimetrycited by 7
  11. 2024Tamed Langevin sampling under weaker conditionscited by 7
  12. 2024Kinetic Interacting Particle Langevin Monte Carlocited by 7
26 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. 2025Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamicscited by 5
  4. 2021Statistical Finite Elements via Langevin Dynamicscited by 4
  5. 2022A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamicscited by 4
  6. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  7. 2025The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptionscited by 4
  8. 2025Uniform-in-time convergence bounds for Persistent Contrastive Divergence algorithmscited by 4
  9. 2023Generalization Bounds for Label Noise Stochastic Gradient Descentcited by 3
  10. 2025kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradientscited by 3
  11. 2025Regime-Switching Langevin Monte Carlo Algorithmscited by 3
  12. 2025Anchored Langevin Algorithmscited by 3
  13. 2022Global convergence of optimized adaptive importance samplerscited by 2
  14. 2022Weak Convergence of Approximate reflection coupling and its Application to Non-convex Optimizationcited by 2
  15. 2023Approximating Langevin Monte Carlo with ResNet-like Neural Network architecturescited by 2
  16. 2025Random Reshuffling for Stochastic Gradient Langevin Dynamicscited by 2
  17. 2023Geometric ergodicity of SGLD via reflection couplingcited by 1
  18. 2023Subsampling Error in Stochastic Gradient Langevin Diffusionscited by 1
  19. 2025Contractive kinetic Langevin samplers beyond global Lipschitz continuitycited by 1
  20. 2026Improved Analysis for Hessian-free High-resolution Monte Carlo Samplingcited by 1
  21. 2022Uniform Generalization Bound on Time and Inverse Temperature for Gradient Descent Algorithm and its Application to Analysis of Simulated Annealingcited by 0
  22. 2022Asynchronous Bayesian Learning over a Networkcited by 0
  23. 2023Non-asymptotic analysis of Langevin-type Monte Carlo algorithmscited by 0
  24. 2023Adam-like Algorithm with Smooth Clipping Attains Global Minima: Analysis Based on Ergodicity of Functional SDEscited by 0
  25. 2024Sampling from Boltzmann densities with physics informed low-rank formatscited by 0
  26. 2025Flatness-Aware Stochastic Gradient Langevin Dynamicscited by 0