Efficient Gradient Updating Strategies with Adaptive Power Allocation for Federated Learning over Wireless Backhaul

In this paper, efficient gradient updating strategies are developed for the federated learning when distributed clients are connected to the server via a wireless backhaul link. Specifically, a common convolutional neural network (CNN) module is shared for all the distributed clients and it is trained through the federated learning over wireless backhaul connected to the main server. However, during the training phase, local gradients need to be transferred from multiple clients to the server over wireless backhaul link and can be distorted due to wireless channel fading. To overcome it, an efficient gradient updating method is proposed, in which the gradients are combined such that the effective SNR is maximized at the server. In addition, when the backhaul links for all clients have small channel gain simultaneously, the server may have severely distorted gradient vectors. Accordingly, we also propose a binary gradient updating strategy based on thresholding in which the round associated with all channels having small channel gains is excluded from federated learning. Because each client has limited transmission power, it is effective to allocate more power on the channel slots carrying specific important information, rather than allocating power equally to all channel resources (equivalently, slots). Accordingly, we also propose an adaptive power allocation method, in which each client allocates its transmit power proportionally to the magnitude of the gradient information. This is because, when training a deep learning model, the gradient elements with large values imply the large change of weight to decrease the loss function.