We provide a first finite-particle convergence rate for Stein variational gradient descent (SVGD). Specifically, whenever the target distribution is sub-Gaussian with a Lipschitz score, SVGD with n particles and an appropriate step size sequence drives the kernel Stein discrepancy to zero at an order 1/sqrt(log log n) rate. 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.

翻译：我们给出了斯坦变分梯度下降（SVGD）的首个有限粒子收敛速率。具体而言，当目标分布为具有Lipschitz分数的次高斯分布时，采用n个粒子和适当步长序列的SVGD能够以1/sqrt(log log n)的阶数将核斯坦差异驱至零。我们推测对n的依赖关系可进一步优化，并希望本文明确的非渐近证明策略能为后续改进提供参考模板。