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A Finite-Particle Convergence Rate for Stein Variational Gradient Descent
Jiaxin Shi · Lester Mackey

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in OPT 2022: Optimization for Machine Learning »
Event URL: https://openreview.net/forum?id=AFSuiA7hLsx »
We provide a first finite-particle convergence rate for Stein variational gradient descent (SVGD). Specifically, with certain choices of step size sequences, SVGD with n particles drive the kernel Stein discrepancy to zero at the rate $O\left(\frac{1}{\sqrt{\log\log n}} \right)$. We suspect that the dependence on $n$ can be improved, and we hope that our explicit, non-asymptotic proof strategy will serve as a template for future refinements.

Author Information

Jiaxin Shi (Stanford University)
Lester Mackey (Microsoft Research)

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