mlsanityData to 7 Oct 2026

Global Non-convex Optimization with Discretized Diffusions

arXiv 1810.12361 ↗First posted 29 Oct 2018stat.ML cs.LG stat.COcited by 44

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Abstract (arXiv)

An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different diffusions are suitable for optimizing different classes of convex and non-convex functions. This allows us to design diffusions suitable for globally optimizing convex and non-convex functions not covered by the existing Langevin theory. Our non-asymptotic analysis delivers computable optimization and integration error bounds based on easily accessed properties of the objective and chosen diffusion. Central to our approach are new explicit Stein factor bounds on the solutions of Poisson equations. We complement these results with improved optimization guarantees for targets other than the standard Gibbs measure.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Oct 2018.

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Citing papers per year: 2021: 5; 2022: 16; 2023: 12; 2024: 5; 2025: 3; 2026: 3.

44 papers.

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  1. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
  2. 2023Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequalitycited by 31
  3. 2023Improved Discretization Analysis for Underdamped Langevin Monte Carlocited by 26
  4. 2022A Finite-Particle Convergence Rate for Stein Variational Gradient Descentcited by 22
  5. 2022Resolving the Mixing Time of the Langevin Algorithm to its Stationary Distribution for Log-Concave Samplingcited by 21
  6. 2021On Learnability via Gradient Method for Two-Layer ReLU Neural Networks in Teacher-Student Settingcited by 16
  7. 2023Algorithmic Stability of Heavy-Tailed SGD with General Loss Functionscited by 15
  8. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
  9. 2021Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networkscited by 11
  10. 2022Generalization Bounds for Stochastic Gradient Descent via Localized varepsilon-Coverscited by 11
  11. 2022Excess Risk of Two-Layer ReLU Neural Networks in Teacher-Student Settings and its Superiority to Kernel Methodscited by 10
  12. 2023Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisitedcited by 10
32 more
  1. 2022Interacting Contour Stochastic Gradient Langevin Dynamicscited by 9
  2. 2022Generalisation under gradient descent via deterministic PAC-Bayescited by 9
  3. 2024Parallelized Midpoint Randomization for Langevin Monte Carlocited by 9
  4. 2022Heavy-tailed Sampling via Transformed Unadjusted Langevin Algorithmcited by 6
  5. 2022Constrained Langevin Algorithms with L-mixing External Random Variablescited by 6
  6. 2023Stochastic Methods in Variational Inequalities: Ergodicity, Bias and Refinementscited by 6
  7. 2024A Separation in Heavy-Tailed Sampling: Gaussian vs. Stable Oracles for Proximal Samplerscited by 5
  8. 2021A Unifying and Canonical Description of Measure-Preserving Diffusionscited by 4
  9. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  10. 2023Langevin Quasi-Monte Carlocited by 4
  11. 2021Unadjusted Langevin algorithm for sampling a mixture of weakly smooth potentialscited by 3
  12. 2023Generalization Bounds for Label Noise Stochastic Gradient Descentcited by 3
  13. 2024Privacy of SGD under Gaussian or Heavy-Tailed Noise: Guarantees without Gradient Clippingcited by 3
  14. 2026Probabilistic Inference and Learning with Stein's Methodcited by 3
  15. 2022Global convergence of optimized adaptive importance samplerscited by 2
  16. 2022On Uniform Boundedness Properties of SGD and its Momentum Variantscited by 2
  17. 2022Weak Convergence of Approximate reflection coupling and its Application to Non-convex Optimizationcited by 2
  18. 2022A Dynamical System View of Langevin-Based Non-Convex Samplingcited by 2
  19. 2024Stein Boltzmann Sampling: A Variational Approach for Global Optimizationcited by 2
  20. 2024Randomized Midpoint Method for Log-Concave Sampling under Constraintscited by 2
  21. 2021Higher Order Generalization Error for First Order Discretization of Langevin Diffusioncited by 1
  22. 2025Langevin Monte-Carlo Provably Learns Depth Two Neural Nets at Any Size and Datacited by 1
  23. 2025Restricted Spectral Gap Decomposition for Simulated Tempering Targeting Mixture Distributionscited by 1
  24. 2022Uniform Generalization Bound on Time and Inverse Temperature for Gradient Descent Algorithm and its Application to Analysis of Simulated Annealingcited by 0
  25. 2022Concentration analysis of multivariate elliptic diffusion processescited by 0
  26. 2023Non-asymptotic analysis of Langevin-type Monte Carlo algorithmscited by 0
  27. 2023Accelerating Convergence in Global Non-Convex Optimization with Reversible Diffusioncited by 0
  28. 2023Ito Diffusion Approximation of Universal Ito Chains for Sampling, Optimization and Boostingcited by 0
  29. 2023Adam-like Algorithm with Smooth Clipping Attains Global Minima: Analysis Based on Ergodicity of Functional SDEscited by 0
  30. 2025Central Limit Theorems for Stochastic Gradient Descent Quantile Estimatorscited by 0
  31. 2026Shuffling the Data, Stretching the Step-size: Sharper Bias in constant step-size SGDcited by 0
  32. 2026Quantifying Multimodal Capabilities: Formal Generalization Guarantees in Pairwise Metric Learningcited by 0