mlsanityData to 14 Oct 2026

Improved Convergence Rate of Stochastic Gradient Langevin Dynamics with Variance Reduction and its Application to Optimization

arXiv 2203.16217 ↗First posted 30 Mar 2022cs.LG math.PR stat.MLcited by 16

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Abstract (arXiv)

The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have nowadays gained particular attention. In this paper, we study two variants of this kind, namely, the Stochastic Variance Reduced Gradient Langevin Dynamics and the Stochastic Recursive Gradient Langevin Dynamics. We prove their convergence to the objective distribution in terms of KL-divergence under the sole assumptions of smoothness and Log-Sobolev inequality which are weaker conditions than those used in prior works for these algorithms. With the batch size and the inner loop length set to √n, the gradient complexity to achieve an ε-precision is tildeO((n+dn1/2ε-1)γ2 L2α-2), which is an improvement from any previous analyses. We also show some essential applications of our result to non-convex optimization.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Builds on 15 of its 50 references that are in the map. First posted on arXiv 30 Mar 2022.

Builds on

15 of 50 references.

References · 15

  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. 2017SARAH: A Novel Method for Machine Learning Problems Using Stochastic Recursive Gradientcited by 220
  4. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 208
  5. 2018Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problemcited by 123
  6. 2017Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimizationcited by 97
  7. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  8. 2019ProxSARAH: An Efficient Algorithmic Framework for Stochastic Composite Nonconvex Optimizationcited by 37
  9. 2020Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Samplingcited by 32
  10. 2019SSRGD: Simple Stochastic Recursive Gradient Descent for Escaping Saddle Pointscited by 25
  11. 2020Riemannian Langevin Algorithm for Solving Semidefinite Programscited by 22
  12. 2017Stochastic Recursive Gradient Algorithm for Nonconvex Optimizationcited by 20
3 more
  1. 2018On the Theory of Variance Reduction for Stochastic Gradient Monte Carlocited by 19
  2. 2021Stochastic Gradient Langevin Dynamics with Variance Reductioncited by 7
  3. 2021Approximation to stochastic variance reduced gradient Langevin dynamics by stochastic delay differential equationscited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 7; 2024: 3; 2025: 4; 2026: 1.

16 papers.

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  1. 2023Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reductioncited by 20
  2. 2023Algorithmic Stability of Heavy-Tailed SGD with General Loss Functionscited by 15
  3. 2023Time-Independent Information-Theoretic Generalization Bounds for SGLDcited by 12
  4. 2022Utilising the CLT Structure in Stochastic Gradient based Sampling : Improved Analysis and Faster Algorithmscited by 7
  5. 2023Provably Fast Finite Particle Variants of SVGD via Virtual Particle Stochastic Approximationcited by 6
  6. 2024On Divergence Measures for Training GFlowNetscited by 6
  7. 2025Quantum Speedups for Sampling and Non-convex Optimization with Stochastic Oraclescited by 2
  8. 2023Improved Langevin Monte Carlo for stochastic optimization via landscape modificationcited by 1
  9. 2023Subsampling Error in Stochastic Gradient Langevin Diffusionscited by 1
  10. 2024Isoperimetry is All We Need: Langevin Posterior Sampling for RL with Sublinear Regretcited by 1
  11. 2025Beyond Propagation of Chaos: A Stochastic Algorithm for Mean Field Optimizationcited by 1
  12. 2023Accelerating Convergence in Global Non-Convex Optimization with Reversible Diffusioncited by 0
4 more
  1. 2024Continuous-time Riemannian SGD and SVRG Flows on Wasserstein Probabilistic Spacecited by 0
  2. 2025Langevin Multiplicative Weights Update with Applications in Polynomial Portfolio Managementcited by 0
  3. 2025Flatness-Aware Stochastic Gradient Langevin Dynamicscited by 0
  4. 2026Generative Bayesian Filtering for State Estimationcited by 0