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.

翻译：联邦学习（FL）是一种新颖的机器学习方法，允许多个边缘设备在不披露原始数据的情况下协作训练模型。然而，若干挑战阻碍了该方法的实际部署，特别是当设备与服务器通过无线信道通信时，其会面临通信和计算瓶颈。通过利用一个通信高效框架，我们提出了一种新颖的零阶（ZO）方法，该方法采用单点梯度估计器，能够利用无线通信信道的固有特性，而无需掌握信道状态系数。这是首个将无线信道本身纳入学习算法的方法，而非耗费资源对其进行分析并消除其影响。本工作的两大难点在于：在联邦学习中，目标函数通常非凸，这导致将FL扩展至ZO方法颇具挑战；同时，纳入无线信道的影响需要额外关注。然而，我们克服了这些难点，并对所提出的零阶联邦学习（ZOFL）框架进行了全面分析。我们从理论上证明了其收敛性，并论证了在非凸设定下收敛速率达到\(O(\frac{1}{\sqrt[3]{K}})\)。我们进一步通过实验结果展示了该算法的潜力，考虑了独立同分布（IID）和非独立同分布（non-IID）的设备数据分布。