  This paper focuses on stochastic proximal gradient methods for optimizing a
smooth non-convex loss function with a non-smooth non-convex regularizer and
convex constraints. To the best of our knowledge we present the first
non-asymptotic convergence results for this class of problem. We present two
simple stochastic proximal gradient algorithms, for general stochastic and
finite-sum optimization problems, which have the same or superior convergence
complexities compared to the current best results for the unconstrained problem
setting. In a numerical experiment we compare our algorithms with the current
state-of-the-art deterministic algorithm and find our algorithms to exhibit
superior convergence.
