Title: Stochastic Methods for Composite and Weakly Convex Optimization Problems,
Abstract: We consider minimization of stochastic functionals that are compositions of a
(potentially) non-smooth convex function $h$ and smooth function $c$ and, more
generally, stochastic weakly-convex functionals. We develop a family of
stochastic methods---including a stochastic prox-linear algorithm and a
stochastic (generalized) sub-gradient procedure---and prove that, under mild
technical conditions, each converges to first-order stationary points of the
stochastic objective. We provide experiments further investigating our methods
on non-smooth phase retrieval problems; the experiments indicate the practical
effectiveness of the procedures.