Age-Aware Partial Gradient Update Strategy for Federated Learning Over the Air

We propose an age-aware strategy to update gradients in an over-the-air federated learning system. The system comprises an edge server and multiple clients, collaborating to minimize a global loss function. In each communication round, clients perform local training, modulate their gradient updates onto a set of shared orthogonal waveforms, and simultaneously transmit the analog signals to the edge server. The edge server then extracts a noisy aggregated gradient from the received radio signal, updates the global model, and broadcasts it to the clients for the next round of local computing. Despite enabling all clients to upload information in every communication round, the system is constrained by the limited number of available waveform carriers, allowing only a subset of gradient parameters to be transmitted. To address this issue, our method maintains an age vector on the edge server, tracking the time elapsed since each coordinate of the global model was last updated. The server leverages this information to prioritize gradient entries for transmission, ensuring that outdated yet significant parameters are updated more frequently. We derive the convergence rate of the proposed algorithm to quantify its effectiveness. Furthermore, experimental evaluations on the MNIST and CIFAR-10 datasets demonstrate that our approach achieves higher accuracy and more stable convergence performance compared to baseline methods, highlighting its potential for improving communication efficiency in over-the-air federated learning systems.