Stochastic Proximal Methods for Non-Smooth Non-Convex Constrained Sparse Optimization

Abstract: 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.