Semi-Asynchronous Over-the-Air Federated Learning Over Heterogeneous Edge Devices

As a distributed machine learning framework where many edge devices collaboratively train a model without data sharing, federated edge learning (FEEL) has been investigated extensively under wireless transmission scenarios. However, the traditional synchronous FEEL mechanism suffers from limited resources, leading to bottleneck nodes when the FEEL tasks are conducted in a wireless network. In this paper, we present a novel semi-asynchronous FEEL algorithm designed for application over wireless multi-access channels, particularly in scenarios involving data and devices with inherent heterogeneity. In this context, we embrace the concept of over-the-air computation (AirComp) to facilitate simultaneous processes of local model uploading and global model aggregation. We analyze the theoretical convergence performance of the proposed algorithm called PAOTA and formulate the upper bound of the expected optimal gap between the expected and optimal global loss values. Considering the staleness and divergence of local updates from edge devices, we minimize the convergence upper bound of the FEEL global model by optimizing the uplink transmit power of edge devices at each aggregation period. The simulation results demonstrate the robust performance of PAOTA using synthetic and real data in wireless networks. Furthermore, with the same target accuracy, the training time required for PAOTA is less than that of synchronous-based FEEL algorithms.