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.

翻译：本文调查了将本地成本功能加起来产生的全球成本功能最小化的非碳化物分配非碳化物优化问题。 我们通过零序(ZO)信息交流解决了这一问题。 在本文中, 我们提议了ZO分配的原始- 双协调法(ZODIAC)以解决蒸馏物优化问题。 代理人接近他们自己的本地蒸馏物分配ZO Ooracle, 加上一个适应性平滑参数的坐标。 我们显示, 提议的算法实现了一般非碳化成本功能的美元( mathcal{O} (\\ sqrt{p}/\ qrt{T}) 的趋同率。 我们通过一个数字示例, 与现有的最新集中和分布的 ZO 算法相比, 我们展示了拟议算法的效率。