  Stein variational gradient decent (SVGD) has been shown to be a powerful
approximate inference algorithm for complex distributions. However, the
standard SVGD requires calculating the gradient of the target density and
cannot be applied when the gradient is unavailable. In this work, we develop a
gradient-free variant of SVGD (GF-SVGD), which replaces the true gradient with
a surrogate gradient, and corrects the induced bias by re-weighting the
gradients in a proper form. We show that our GF-SVGD can be viewed as the
standard SVGD with a special choice of kernel, and hence directly inherits the
theoretical properties of SVGD. We shed insights on the empirical choice of the
surrogate gradient and propose an annealed GF-SVGD that leverages the idea of
simulated annealing to improve the performance on high dimensional complex
distributions. Empirical studies show that our method consistently outperforms
a number of recent advanced gradient-free MCMC methods.
