Lyapunov-based optimization of edge resources for energy-efficient adaptive federated learning

The aim of this paper is to propose a novel dynamic resource allocation strategy for energy-efficient adaptive federated learning at the wireless network edge, with latency and learning performance guarantees. We consider a set of devices collecting local data and uploading processed information to an edge server, which runs stochastic gradient-based algorithms to perform continuous learning and adaptation. Hinging on Lyapunov stochastic optimization tools, we dynamically optimize radio parameters (e.g., set of transmitting devices, transmit powers, bits, and rates) and computation resources (e.g., CPU cycles at devices and at server) in order to strike the best trade-off between power, latency, and performance of the federated learning task. The framework admits both a model-based implementation, where the learning performance metrics are available in closed-form, and a data-driven approach, which works with online estimates of the learning performance of interest. The method is then customized to the case of federated least mean squares (LMS) estimation, and federated training of deep convolutional neural networks. Numerical results illustrate the effectiveness of our strategy to perform energy-efficient, low-latency, adaptive federated learning at the wireless network edge.