Dimension-free convergence rates for gradient Langevin dynamics in RKHS
Abstract
Gradient Langevin dynamics (GLD) and stochastic GLD (SGLD) have attracted considerable attention lately, as a way to provide convergence guarantees in a non-convex setting. However, the known rates grow exponentially with the dimension of the space. In this work, we provide a convergence analysis of GLD and SGLD when the optimization space is an infinite dimensional Hilbert space. More precisely, we derive non-asymptotic, dimension-free convergence rates for GLD/SGLD when performing regularized non-convex optimization in a reproducing kernel Hilbert space. Amongst others, the convergence analysis relies on the properties of a stochastic differential equation, its discrete time Galerkin approximation and the geometric ergodicity of the associated Markov chains.
Keywords
Cite
@article{arxiv.2003.00306,
title = {Dimension-free convergence rates for gradient Langevin dynamics in RKHS},
author = {Boris Muzellec and Kanji Sato and Mathurin Massias and Taiji Suzuki},
journal= {arXiv preprint arXiv:2003.00306},
year = {2020}
}