Zeroth-Order Stochastic Coordinate Methods for Decentralized Non-convex Optimization

Abstract: In this letter, we first propose a \underline{Z}eroth-\underline{O}rder c\underline{O}ordinate \underline{M}ethod~(ZOOM) to solve the stochastic optimization problem over a decentralized network with only zeroth-order~(ZO) oracle feedback available. Moreover, we equip a simple mechanism "powerball" to ZOOM and propose ZOOM-PB to accelerate the convergence of ZOOM. Compared with the existing methods, we verify the proposed algorithms through two benchmark examples in the literature, namely the black-box binary classification and the generating adversarial examples from black-box DNNs in order to compare with the existing state-of-the-art centralized and distributed ZO algorithms. The numerical results demonstrate a faster convergence rate of the proposed algorithms.