Joint Beamforming and Learning Rate Optimization for Over-the-Air Federated Learning

In this paper, we consider a joint design of beamforming vector and learning rate in MIMO over-the-air computation (AirComp) for federated learning. Since the learning performance improves with adaptive learning rates, we jointly optimize the receive beamforming vector and the learning rates. We first demonstrate the AirComp-multicasting duality between the uplink AirComp receive beamforming for federated learning systems and the downlink transmit beamforming for multicast systems. We design a low-complexity algorithm based on the projected subgradient method of the dual problem. Numerical results show that the proposed algorithm achieves nearly the same performance as the ideal federated learning system without aggregation errors.