Transmission Power Control for Over-the-Air Federated Averaging at Network Edge
Xiaowen Cao, Guangxu Zhu, Jie Xu, Shuguang Cui
Abstract
<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Over-the-air computation</i> (AirComp) has emerged as a new analog power-domain <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">non-orthogonal multiple access</i> (NOMA) technique for low-latency model/gradient-updates <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">aggregation in federated edge learning</i> (FEEL). By integrating communication and computation into a joint design, AirComp can significantly enhance the communication efficiency, but at the cost of aggregation errors caused by channel fading and noise. This paper studies a particular type of FEEL with federated averaging (FedAvg) and AirComp-based model-update aggregation, namely <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">over-the-air</i> FedAvg (Air-FedAvg). We investigate the transmission power control in Air-FedAvg to combat against the AirComp aggregation errors for enhancing the training accuracy and accelerating the training speed. Towards this end, we first analyze the convergence behavior (in terms of the optimality gap) of Air-FedAvg with aggregation errors at different outer iterations. Then, to enhance the training accuracy, we minimize the optimality gap by jointly optimizing the transmission power control at edge devices and the denoising factors at edge server, subject to a series of power constraints at individual edge devices. Furthermore, to accelerate the training speed, we also minimize the training latency of Air-FedAvg with a given targeted optimality gap, in which learning hyper-parameters including the numbers of outer iterations and local training epochs are optimized jointly with the power control. Finally, numerical results show that the proposed transmission power control policy achieves significantly faster convergence speed for Air-FedAvg, as compared with benchmark policies with fixed power transmission or per-iteration <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mean squared error</i> (MSE) minimization. It is also shown that the Air-FedAvg achieves an order-of-magnitude shorter training latency than the conventional FedAvg with digital <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">orthogonal multiple access</i> (OMA-FedAvg).