  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.
