Finite-Particle Rates for Regularized Stein Variational Gradient Descent

• URL: http://arxiv.org/abs/2602.05172v1
• Date: Thu, 05 Feb 2026 01:00:00 GMT
• Title: Finite-Particle Rates for Regularized Stein Variational Gradient Descent
• Authors: Ye He, Krishnakumar Balasubramanian, Sayan Banerjee, Promit Ghosal,
• Abstract summary: We derive finite-particle rates for the regularized Stein variational descent gradient (R-SVGD) algorithm introduced by He et al.<n>For the resulting interacting $N$-particle system, we establish explicit non-asymptotic bounds for time-averaged (annealed) empirical measures.<n>Our analysis covers both continuous- and discrete-time dynamics and yields principled tuning rules for the regularization parameter, step size, and averaging horizon.
• Score: 9.824622287505454
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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