Federated Edge Learning (FEEL) is a distributed machine learning technique where each device contributes to training a global inference model by independently performing local computations with their data. More recently, FEEL has been merged with over-the-air computation (OAC), where the global model is calculated over the air by leveraging the superposition of analog signals. However, when implementing FEEL with OAC, there is the challenge on how to precode the analog signals to overcome any time misalignment at the receiver. In this work, we propose a novel synchronization-free method to recover the parameters of the global model over the air without requiring any prior information about the time misalignments. For that, we construct a convex optimization based on the norm minimization problem to directly recover the global model by solving a convex semi-definite program. The performance of the proposed method is evaluated in terms of accuracy and convergence via numerical experiments. We show that our proposed algorithm is close to the ideal synchronized scenario by $10\%$, and performs $4\times$ better than the simple case where no recovering method is used.

翻译：联邦边缘学习(FEEL)是一种分布式的机器学习技术,其中每个装置都通过独立进行本地数据计算来帮助培训一个全球推论模型。 最近,感觉已经与超空计算(OAC)相结合,即全球模型通过利用模拟信号的叠加作用对空气进行计算。然而,在应用OAC时,在如何预先编码模拟信号以克服接收器任何时间的不匹配方面存在挑战。在这项工作中,我们提出一种新的无同步性方法,以恢复全球模型在空气中的参数,而无需事先提供关于时间错配的任何信息。为此,我们根据标准的最小化问题构建一个平面优化,以便通过解决一个配置的半确定型程序直接恢复全球模型。拟议方法的性能通过数字实验从准确性和趋同性的角度进行评估。我们表明,我们提议的算法接近理想的同步情景10美元,比没有使用恢复方法的简单案例要好4美元。