Federated learning (FL) is a novel approach to machine learning that allows multiple edge devices to collaboratively train a model without disclosing their raw data. However, several challenges hinder the practical implementation of this approach, especially when devices and the server communicate over wireless channels, as it suffers from communication and computation bottlenecks in this case. By utilizing a communication-efficient framework, we propose a novel zero-order (ZO) method with a one-point gradient estimator that harnesses the nature of the wireless communication channel without requiring the knowledge of the channel state coefficient. It is the first method that includes the wireless channel in the learning algorithm itself instead of wasting resources to analyze it and remove its impact. The two main difficulties of this work are that in FL, the objective function is usually not convex, which makes the extension of FL to ZO methods challenging, and that including the impact of wireless channels requires extra attention. However, we overcome these difficulties and comprehensively analyze the proposed zero-order federated learning (ZOFL) framework. We establish its convergence theoretically, and we prove a convergence rate of $O(\frac{1}{\sqrt[3]{K}})$ in the nonconvex setting. We further demonstrate the potential of our algorithm with experimental results, taking into account independent and identically distributed (IID) and non-IID device data distributions.

利用通信高效的框架，我们提出了一种新颖的、基于零阶方法的联邦学习（ZOFL）框架，通过利用无线通信信道的特性，在学习算法本身中包含无线信道，而无需分析并消除其影响。

渲染有用的无线环境：一种零阶随机联邦学习方法