We provide the first finite-particle convergence rate for Stein variational gradient descent (SVGD), a popular algorithm for approximating a probability distribution with a collection of particles. 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：我们首次给出了斯坦变分梯度下降（SVGD）的有限粒子收敛速率。SVGD是一种通过粒子集合近似概率分布的流行算法。具体而言，当目标分布为次高斯分布且其得分函数满足利普希茨条件时，采用n个粒子和适当步长序列的SVGD能够以1/sqrt(log log n)阶速率将核斯坦离散度驱动至零。我们推测该速率对n的依赖关系仍可改进，并希望本文显式且非渐近的证明策略能为后续改进提供可参照的模板。