Mobility-Aware Device Sampling for Statistical Heterogeneity in Hierarchical Federated Learning

Hierarchical Federated Learning (HFL) is a practical implementation of federated learning in mobile edge computing, employing edge servers as intermediaries between mobile devices and the cloud server for device coordination and cloud communication. However, the devices are usually mobile users with unpredictable mobile trajectories and statistical heterogeneity, leading to the edge models optimized along dynamic edge data distribution directions and further resulting in instability and slow convergence of the global model. In this work, we propose a Mobility-Aware deviCe sampling algorithm in HFL, namely MACH, which can dynamically maintain the device sampling strategy at each edge to accelerate the convergence of the global model. First, we analyze the convergence bound of HFL with mobile devices under arbitrary device sampling probabilities. Based on this convergence bound, we formalize the sampling optimization problem for mobility-aware device sampling, aiming to minimize the convergence error under time-averaged cost constraints, while taking the limited device-edge wireless channel capacity into account. Next, we introduce the MACH algorithm, consisting of two underlying components: experience updating and edge sampling. Experience updating utilizes an upper confidence bound method to estimate device statistical information online, and edge sampling customizes a sampling strategy on each edge based on the estimated device statistical information. Finally, extensive experimental results through real-world mobile device trajectories validate that MACH can reduce the time required to achieve a target accuracy by 25.00% - 56.86%.