  Stein Variational Gradient Descent (SVGD) is an algorithm for sampling from a
target density which is known up to a multiplicative constant. Although SVGD is
a popular algorithm in practice, its theoretical study is limited to a few
recent works. We study the convergence of SVGD in the population limit, (i.e.,
with an infinite number of particles) to sample from a non-logconcave target
distribution satisfying Talagrand's inequality T1. We first establish the
convergence of the algorithm. Then, we establish a dimension-dependent
complexity bound in terms of the Kernelized Stein Discrepancy (KSD). Unlike
existing works, we do not assume that the KSD is bounded along the trajectory
of the algorithm. Our approach relies on interpreting SVGD as a gradient
descent over a space of probability measures.
