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We develop an implementable stochastic proximal point (SPP) method for aclass of weakly convex, composite optimization problems. The proposedstochastic proximal point algorithm incorporates a variance reduction mechanismand the resulting SPP updates are solved using an inexact semismooth Newtonframework. We establish detailed convergence results that take the inexactnessof the SPP steps into account and that are in accordance with existingconvergence guarantees of (proximal) stochastic variance-reduced gradientmethods. Numerical experiments show that the proposed algorithm competesfavorably with other state-of-the-art methods and achieves higher robustnesswith respect to the step size selection.

A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction