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In this paper, we design and analyze a new family of adaptive subgradientmethods for solving an important class of weakly convex (possibly nonsmooth)stochastic optimization problems. Adaptive methods that use exponential movingaverages of past gradients to update search directions and learning rates haverecently attracted a lot of attention for solving optimization problems thatarise in machine learning. Nevertheless, their convergence analysis almostexclusively requires smoothness and/or convexity of the objective function. Incontrast, we establish non-asymptotic rates of convergence of first andzeroth-order adaptive methods and their proximal variants for a reasonablybroad class of nonsmooth \& nonconvex optimization problems. Experimentalresults indicate how the proposed algorithms empirically outperform stochasticgradient descent and its zeroth-order variant for solving such optimizationproblems.

Adaptive First-and Zeroth-order Methods for Weakly Convex Stochastic Optimization Problems