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Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Sampling

arXiv 2010.09597 ↗First posted 19 Oct 2020cs.LG math.ST stat.MLcited by 32

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Abstract (arXiv)

We provide a new convergence analysis of stochastic gradient Langevin dynamics (SGLD) for sampling from a class of distributions that can be non-log-concave. At the core of our approach is a novel conductance analysis of SGLD using an auxiliary time-reversible Markov Chain. Under certain conditions on the target distribution, we prove that tilde O(d4ε-2) stochastic gradient evaluations suffice to guarantee ε-sampling error in terms of the total variation distance, where d is the problem dimension. This improves existing results on the convergence rate of SGLD (Raginsky et al., 2017; Xu et al., 2018). We further show that provided an additional Hessian Lipschitz condition on the log-density function, SGLD is guaranteed to achieve ε-sampling error within tilde O(d15/4ε-3/2) stochastic gradient evaluations. Our proof technique provides a new way to study the convergence of Langevin-based algorithms and sheds some light on the design of fast stochastic gradient-based sampling algorithms.

Key facts. Cited by 32 papers in the map (data through 14 Oct 2026). First posted on arXiv 19 Oct 2020.

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Citing papers per year: 2021: 3; 2022: 9; 2023: 8; 2024: 6; 2025: 4; 2026: 2.

32 papers.

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  1. 2021Differentiable Annealed Importance Sampling and the Perils of Gradient Noisecited by 36
  2. 2023Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlocited by 29
  3. 2022Langevin Monte Carlo for Contextual Banditscited by 22
  4. 2023Guiding Energy-based Models via Contrastive Latent Variablescited by 18
  5. 2022Improved Convergence Rate of Stochastic Gradient Langevin Dynamics with Variance Reduction and its Application to Optimizationcited by 16
  6. 2021Provable Compressed Sensing with Generative Priors via Langevin Dynamicscited by 14
  7. 2022Fisher information lower bounds for samplingcited by 12
  8. 2024More Efficient Randomized Exploration for Reinforcement Learning via Approximate Samplingcited by 12
  9. 2025Adaptive Defense against Harmful Fine-Tuning for Large Language Models via Bayesian Data Schedulercited by 12
  10. 2021Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networkscited by 11
  11. 2023Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimationcited by 10
  12. 2026EEO-TFV: Escape-Explore Optimizer for Web-Scale Time-Series Forecasting and Vision Analysiscited by 9
20 more
  1. 2022Utilising the CLT Structure in Stochastic Gradient based Sampling : Improved Analysis and Faster Algorithmscited by 7
  2. 2022Constrained Langevin Algorithms with L-mixing External Random Variablescited by 6
  3. 2023Provably Fast Finite Particle Variants of SVGD via Virtual Particle Stochastic Approximationcited by 6
  4. 2024Faster Sampling via Stochastic Gradient Proximal Samplercited by 5
  5. 2025From Global to Local: A Scalable Benchmark for Local Posterior Samplingcited by 5
  6. 2022Gradient Boosting Performs Gaussian Process Inferencecited by 4
  7. 2022A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamicscited by 4
  8. 2023Stochastic Quantum Sampling for Non-Logconcave Distributions and Estimating Partition Functionscited by 4
  9. 2024Bayesian Federated Learning with Hamiltonian Monte Carlo: Algorithm and Theorycited by 4
  10. 2022Convergence Error Analysis of Reflected Gradient Langevin Dynamics for Globally Optimizing Non-Convex Constrained Problemscited by 3
  11. 2024A Bayesian Approach to Data Point Selectioncited by 3
  12. 2022Global convergence of optimized adaptive importance samplerscited by 2
  13. 2025Quantum Speedups for Sampling and Non-convex Optimization with Stochastic Oraclescited by 2
  14. 2023Geometric ergodicity of SGLD via reflection couplingcited by 1
  15. 2023Improved Langevin Monte Carlo for stochastic optimization via landscape modificationcited by 1
  16. 2023Subsampling Error in Stochastic Gradient Langevin Diffusionscited by 1
  17. 2025Operator-Level Quantum Acceleration of Non-Logconcave Samplingcited by 1
  18. 2026Deterministic Denominator Design for Localized Tamed Stochastic Gradient Langevin Dynamicscited by 1
  19. 2024An Improved Analysis of Langevin Algorithms with Prior Diffusion for Non-Log-Concave Samplingcited by 0
  20. 2024Langevin Dynamics: A Unified Perspective on Optimization via Lyapunov Potentialscited by 0