A Stochastic Non-monotone DR-Submodular Maximization Problem over a Convex Set

In this paper, we concentrate on a stochastic non-monotone DR-submodular maximization problem over a convex constraint C, where the objective function arises as an expectation of a set of stochastic functions. We develop an algorithm named SPIDER-FW, which is a stochastic version of the classical Frank-Wolfe algorithm with 1/4 (1- min(x epsilon C) parallel to x parallel to(infinity))F(x*) - epsilon (in expectation) approximation guarantee, the best guarantee so far for the above setting, achieved with O(1/epsilon) iterations, and O(1/epsilon(2)) first-order oracle calls.