2017

Proximally Guided Stochastic Subgradient Method for Nonsmooth, Nonconvex Problems

Davis, Damek, Grimmer, Benjamin

Understand

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.

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