A Non-Asymptotic Analysis for Stein Variational Gradient Descent
Anna Korba, Adil Salim, Michael Arbel, Giulia Luise, Arthur Gretton
Abstract
We study the Stein Variational Gradient Descent (SVGD) algorithm, which optimises a set of particles to approximate a target probability distribution $\pi\propto e^{-V}$ on $\R^d$. In the population limit, SVGD performs gradient descent in the space of probability distributions on the KL divergence with respect to $\pi$, where the gradient is smoothed through a kernel integral operator. In this paper, we provide a novel finite time analysis for the SVGD algorithm. We provide a descent lemma establishing that the algorithm decreases the objective at each iteration, and rates of convergence. We also provide a convergence result of the finite particle system corresponding to the practical implementation of SVGD to its population version.
BibTeX
@inproceedings{NEURIPS2020_3202111c,
author = {Korba, Anna and Salim, Adil and Arbel, Michael and Luise, Giulia and Gretton, Arthur},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin},
pages = {4672--4682},
publisher = {Curran Associates, Inc.},
title = {A Non-Asymptotic Analysis for Stein Variational Gradient Descent},
url = {https://proceedings.neurips.cc/paper_files/paper/2020/file/3202111cf90e7c816a472aaceb72b0df-Paper.pdf},
volume = {33},
year = {2020}
}