Spatial Convergence of Federated Learning in Large-Scale Cellular Networks

The deployment of federated learning in a wireless network, called federated edge learning (FEEL), exploits low-latency access to distributed mobile data to efficiently train an AI model while preserving data privacy. In this work, we study the spatial (i.e., spatially averaged) learning performance of FEEL deployed in a large-scale cellular network with spatially random distributed devices. The derived spatial convergence rate is found to be constrained by a limited number of active devices regardless of device density and converges to the ground-true rate exponentially fast as the number grows. The population of active devices depends on network parameters such as processing gain and signal-to-interference threshold for decoding. Combing the derived results, intuitive guidelines are given for large-scale FEEL network provisioning and planning to reduce the model training latency without violating the learning accuracy.