Proximally Guided Stochastic Subgradient Method for Nonsmooth, Nonconvex Problems
Abstract
In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a high-level, the method is an inexact proximal point iteration in which the strongly convex proximal subproblems are quickly solved with a specialized stochastic projected subgradient method. The primary contribution of this paper is a simple proof that the proposed algorithm converges at the same rate as the stochastic gradient method for smooth nonconvex problems. This result appears to be the first convergence rate analysis of a stochastic (or even deterministic) subgradient method for the class of weakly convex functions.
Cite
@article{arxiv.1707.03505,
title = {Proximally Guided Stochastic Subgradient Method for Nonsmooth, Nonconvex Problems},
author = {Damek Davis and Benjamin Grimmer},
journal= {arXiv preprint arXiv:1707.03505},
year = {2018}
}
Comments
Updated 9/17/2018: Major Revision -added high probability bounds, improved convergence analysis in general, new experimental results. Updated 7/26/2017: Added references to introduction and a couple simple extensions as Sections 3.2 and 4. Updated 8/23/2017: Added NSF acknowledgements. Updated 10/16/2017: Added experimental results