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Zero Order Stochastic Weakly Convex Composite Optimization

In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient estimate of the smoothed function. We prove convergence at a similar rate as state of the art methods, however with a larger constant, and report some numerical results showing the effectiveness of the approach.