mlsanityData to 14 Oct 2026

Beyond Propagation of Chaos: A Stochastic Algorithm for Mean Field Optimization

arXiv 2503.13115 ↗First posted 17 Mar 2025cs.LG cs.AI math.PRcited by 1

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Abstract (arXiv)

Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with n particles. Analyzing these algorithms requires showing (a) that the finite-particle system converges and/or (b) that the resultant empirical distribution of the particles closely approximates the optimal distribution (i.e., propagation of chaos). However, establishing efficient sufficient conditions can be challenging, as the finite particle system may produce heavily dependent random variables. In this work, we study the virtual particle stochastic approximation, originally introduced for Stein Variational Gradient Descent. This method can be viewed as a form of stochastic gradient descent in the Wasserstein space and can be implemented efficiently. In popular settings, we demonstrate that our algorithm's output converges to the optimal distribution under conditions similar to those for the infinite particle limit, and it produces i.i.d. samples without the need to explicitly establish propagation of chaos bounds.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 21 of its 51 references that are in the map. First posted on arXiv 17 Mar 2025.

Builds on

21 of 51 references.

References · 21

  1. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 507
  2. 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 426
  3. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 243
  4. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
  5. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 127
  6. 2022Variational inference via Wasserstein gradient flowscited by 85
  7. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 78
  8. 2022Mean-Field Langevin Dynamics: Exponential Convergence and Annealingcited by 61
  9. 2022Convex Analysis of the Mean Field Langevin Dynamicscited by 55
  10. 2017Stochastic Particle Gradient Descent for Infinite Ensemblescited by 52
  11. 2021SGD Generalizes Better Than GD (And Regularization Doesn't Help)cited by 38
  12. 2022Uniform-in-time propagation of chaos for mean field Langevin dynamicscited by 23
9 more
  1. 2022Improved Convergence Rate of Stochastic Gradient Langevin Dynamics with Variance Reduction and its Application to Optimizationcited by 16
  2. 2024Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descentcited by 14
  3. 2023Independent projections of diffusions: Gradient flows for variational inference and optimal mean field approximationscited by 12
  4. 2024Improved Particle Approximation Error for Mean Field Neural Networkscited by 12
  5. 2023Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisitedcited by 10
  6. 2022Utilising the CLT Structure in Stochastic Gradient based Sampling : Improved Analysis and Faster Algorithmscited by 7
  7. 2023Provably Fast Finite Particle Variants of SVGD via Virtual Particle Stochastic Approximationcited by 6
  8. 2021Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Streaming Datacited by 5
  9. 2024Faster Sampling via Stochastic Gradient Proximal Samplercited by 5

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Citing papers per year: 2025: 1.

1 paper.

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