Convergence Analysis of Nonconvex Distributed Stochastic Zeroth-order Coordinate Method [article]

Shengjun Zhang, Yunlong Dong, Dong Xie, Lisha Yao, Colleen P. Bailey, Shengli Fu
2021 arXiv   pre-print
This paper investigates the stochastic distributed nonconvex optimization problem of minimizing a global cost function formed by the summation of n local cost functions. We solve such a problem by involving zeroth-order (ZO) information exchange. In this paper, we propose a ZO distributed primal-dual coordinate method (ZODIAC) to solve the stochastic optimization problem. Agents approximate their own local stochastic ZO oracle along with coordinates with an adaptive smoothing parameter. We show
more » ... that the proposed algorithm achieves the convergence rate of 𝒪(√(p)/√(T)) for general nonconvex cost functions. We demonstrate the efficiency of proposed algorithms through a numerical example in comparison with the existing state-of-the-art centralized and distributed ZO algorithms.
arXiv:2103.12954v4 fatcat:a63gdmvicjddfhwzt3hmus2nh4