Stein Variational Gradient Descent Without Gradient
This work addresses a bottleneck for practitioners needing approximate inference in complex distributions without gradient access, though it is incremental as it builds directly on SVGD.
The authors tackled the problem of applying Stein variational gradient descent (SVGD) to distributions where gradients are unavailable by developing a gradient-free variant (GF-SVGD) that uses surrogate gradients and re-weighting, and they showed it outperforms recent gradient-free MCMC methods in empirical studies.
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.