Convergence Analysis of Nonconvex Distributed Stochastic Zeroth-order Coordinate Method
This addresses optimization in distributed settings where only function values are available, but it is incremental as it builds on existing zeroth-order methods.
The paper tackles the stochastic distributed nonconvex optimization problem by proposing ZODIAC, a zeroth-order distributed primal-dual coordinate method, achieving a convergence rate of O(√p/√T) for general nonconvex functions.
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 that the proposed algorithm achieves the convergence rate of $\mathcal{O}(\sqrt{p}/\sqrt{T})$ 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.