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In this paper we analyze a zeroth-order proximal stochastic gradient methodsuitable for the minimization of weakly convex stochastic optimizationproblems. We consider nonsmooth and nonlinear stochastic composite problems,for which (sub-)gradient information might be unavailable. The proposedalgorithm utilizes the well-known Gaussian smoothing technique, which yieldsunbiased zeroth-order gradient estimators of a related partially smoothsurrogate problem (in which one of the two nonsmooth terms in the originalproblem's objective is replaced by a smooth approximation). This allows us toemploy a standard proximal stochastic gradient scheme for the approximatesolution of the surrogate problem, which is determined by a single smoothingparameter, and without the utilization of first-order information. We providestate-of-the-art convergence rates for the proposed zeroth-order method usingminimal assumptions. The proposed scheme is numerically compared againstalternative zeroth-order methods as well as a stochastic sub-gradient scheme ona standard phase retrieval problem. Further, we showcase the usefulness andeffectiveness of our method for the unique setting of automated hyper-parametertuning. In particular, we focus on automatically tuning the parameters ofoptimization algorithms by minimizing a novel heuristic model. The proposedapproach is tested on a proximal alternating direction method of multipliersfor the solution of $\mathcal{L}_1/\mathcal{L}_2$-regularized PDE-constrainedoptimal control problems, with evident empirical success.

A Zeroth-order Proximal Stochastic Gradient Method for Weakly Convex Stochastic Optimization