  Stein Variational Gradient Descent (SVGD) is an important alternative to the
Langevin-type algorithms for sampling from probability distributions of the
form $\pi(x) \propto \exp(-V(x))$. In the existing theory of Langevin-type
algorithms and SVGD, the potential function $V$ is often assumed to be
$L$-smooth. However, this restrictive condition excludes a large class of
potential functions such as polynomials of degree greater than $2$. Our paper
studies the convergence of the SVGD algorithm for distributions with
$(L_0,L_1)$-smooth potentials. This relaxed smoothness assumption was
introduced by Zhang et al. [2019a] for the analysis of gradient clipping
algorithms. With the help of trajectory-independent auxiliary conditions, we
provide a descent lemma establishing that the algorithm decreases the
$\mathrm{KL}$ divergence at each iteration and prove a complexity bound for
SVGD in the population limit in terms of the Stein Fisher information.
