mlsanityData to 7 Oct 2026

Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descent

arXiv 2409.08469 ↗First posted 13 Sep 2024math.ST cs.LG math.PRcited by 13

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Abstract (arXiv)

We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy (mathsfKSD) and Wasserstein-2 metrics. Our key insight is that the time derivative of the relative entropy between the joint density of N particle locations and the N-fold product target measure, starting from a regular initial distribution, splits into a dominant `negative part' proportional to N times the expected mathsfKSD2 and a smaller `positive part'. This observation leads to mathsfKSD rates of order 1/√N, in both continuous and discrete time, providing a near optimal (in the sense of matching the corresponding i.i.d. rates) double exponential improvement over the recent result by Shi and Mackey (2024). Under mild assumptions on the kernel and potential, these bounds also grow polynomially in the dimension d. By adding a bilinear component to the kernel, the above approach is used to further obtain Wasserstein-2 convergence in continuous time. For the case of `bilinear + Mat'ern' kernels, we derive Wasserstein-2 rates that exhibit a curse-of-dimensionality similar to the i.i.d. setting. We also obtain marginal convergence and long-time propagation of chaos results for the time-averaged particle laws.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 27 of its 49 references that are in the map. First posted on arXiv 13 Sep 2024.

Builds on

27 of 49 references.

References · 27

  1. 2016Variational Inference: A Review for Statisticianscited by 1,466
  2. 2017Reinforcement Learning with Deep Energy-Based Policiescited by 659
  3. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  4. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 242
  5. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  6. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
  7. 2017Stein Variational Gradient Descent as Gradient Flowcited by 149
  8. 2016A Kernel Test of Goodness of Fitcited by 143
  9. 2017Measuring Sample Quality with Kernelscited by 119
  10. 2015Measuring Sample Quality with Stein's Methodcited by 94
  11. 2019On the geometry of Stein variational gradient descentcited by 82
  12. 2020SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergencecited by 64
15 more
  1. 2020A Non-Asymptotic Analysis for Stein Variational Gradient Descentcited by 61
  2. 2018Scaling limit of the Stein variational gradient descent: the mean field regimecited by 35
  3. 2020Stochastic Stein Discrepanciescited by 30
  4. 2020Stein Variational Model Predictive Controlcited by 29
  5. 2017Learning to Draw Samples with Amortized Stein Variational Gradient Descentcited by 26
  6. 2022A Finite-Particle Convergence Rate for Stein Variational Gradient Descentcited by 22
  7. 2021A Convergence Theory for SVGD in the Population Limit under Talagrand's Inequality T1cited by 21
  8. 2022Regularized Stein Variational Gradient Flowcited by 18
  9. 2022Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Conditioncited by 16
  10. 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
  11. 2022Controlling Moments with Kernel Stein Discrepanciescited by 13
  12. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  13. 2024Minimax Optimal Goodness-of-Fit Testing with Kernel Stein Discrepancycited by 9
  14. 2023Provably Fast Finite Particle Variants of SVGD via Virtual Particle Stochastic Approximationcited by 6
  15. 2024Long-time asymptotics of noisy SVGD outside the population limitcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 9.

13 papers.

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  1. 2026Finite-Particle Rates for Regularized Stein Variational Gradient Descentcited by 3
  2. 2026Sobolev Regularized MMD Gradient Flowcited by 3
  3. 2026Minimax Estimation of Kernel Stein Discrepancy: Trace versus Hilbert-Schmidt Scalescited by 3
  4. 2025Stationary MMD Pointscited by 2
  5. 2026Finite-Particle Convergence Rates for Conservative and Non-Conservative Drifting Modelscited by 2
  6. 2025Beyond Propagation of Chaos: A Stochastic Algorithm for Mean Field Optimizationcited by 1
  7. 2026Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensionscited by 1
  8. 2026Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flowcited by 1
  9. 2026To discretize continually: Mean shift interacting particle systems for Bayesian inferencecited by 1
  10. 2025Branching Stein Variational Gradient Descent for sampling multimodal distributionscited by 0
  11. 2025Adaptive Kernel Selection for Stein Variational Gradient Descentcited by 0
  12. 2026Complexity of Non-Log-Concave Sampling in Fisher Informationcited by 0
1 more
  1. 2026Riesz-Kernel Stein Variational Gradient Descent: Renormalized Entropy and Long-Time Particle Limitscited by 0