Finite-Particle Rates for Regularized Stein Variational Gradient Descent
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866916023266967552 |
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| author | He, Ye Balasubramanian, Krishnakumar Banerjee, Sayan Ghosal, Promit |
| author_facet | He, Ye Balasubramanian, Krishnakumar Banerjee, Sayan Ghosal, Promit |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05172 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite-Particle Rates for Regularized Stein Variational Gradient Descent He, Ye Balasubramanian, Krishnakumar Banerjee, Sayan Ghosal, Promit Machine Learning Statistics Theory 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. |
| title | Finite-Particle Rates for Regularized Stein Variational Gradient Descent |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2602.05172 |