Uniform-in-time propagation-of-chaos bounds for SVGD are obtained via cutoff for distributional metrics (logarithmic rates) and via finite-dimensional closure plus conjugacy for Gaussian targets (parametric N^{-1/2} rates).
Finite-Particle Rates for Regularized Stein Variational Gradient Descent
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abstract
We derive finite-particle rates for the regularized Stein variational gradient descent (R-SVGD) algorithm introduced by He et al. (2024) that corrects the constant-order bias of the SVGD by applying a resolvent-type preconditioner to the kernelized Wasserstein gradient. For the resulting interacting $N$-particle system, we establish explicit non-asymptotic bounds for time-averaged (annealed) empirical measures, illustrating convergence in the \emph{true} (non-kernelized) Fisher information and, under a $\mathrm{W}_1\mathrm{I}$ condition on the target, corresponding $\mathrm{W}_1$ convergence for a large class of smooth kernels. Our analysis covers both continuous- and discrete-time dynamics and yields principled tuning rules for the regularization parameter, step size, and averaging horizon that quantify the trade-off between approximating the Wasserstein gradient flow and controlling finite-particle estimation error.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
SVGD dynamics with concentrating kernels converge to a local Wasserstein gradient flow with quadratic mobility.
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Uniform-in-time Propagation-of-Chaos for Stein Variational Gradient Descent
Uniform-in-time propagation-of-chaos bounds for SVGD are obtained via cutoff for distributional metrics (logarithmic rates) and via finite-dimensional closure plus conjugacy for Gaussian targets (parametric N^{-1/2} rates).
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Stein Variational Gradient Descent dynamics for highly concentrated kernels
SVGD dynamics with concentrating kernels converge to a local Wasserstein gradient flow with quadratic mobility.