Complexity Analysis of Stein Variational Gradient Descent Under Talagrand's Inequality T1

We study the complexity of Stein Variational Gradient Descent (SVGD), which is an algorithm to sample from $\pi(x) \propto \exp(-F(x))$ where $F$ smooth and nonconvex. We provide a clean complexity bound for SVGD in the population limit in terms of the Stein Fisher Information (or squared Kernelized Stein Discrepancy), as a function of the dimension of the problem $d$ and the desired accuracy $\varepsilon$. Unlike existing work, we do not make any assumption on the trajectory of the algorithm. Instead, our key assumption is that the target distribution satisfies Talagrand's inequality T1.