  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.
