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

06/06/2021

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by   Adil Salim, et al.

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We study the complexity of Stein Variational Gradient Descent (SVGD), which is an algorithm to sample from π(x) ∝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 ε. 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.