ESR-MHFL: Edge Server Reallocation for Multi- Hierarchical Federated Learning

Federated Learning (FL) enables efficient and privacy-preserving Edge Intelligence (EI) in Mobile Edge Computing (MEC). However, implementing FL-enabled EI services faces critical challenges, including data and device heterogeneity, limited network resources, uneven distribution of network infrastructure, etc., which may intensify with increasing system scale. These challenges are particularly acute in multi-provider environments where edge servers are suboptimally allocated across federations, leading to degraded convergence and increased training costs. In this paper, we present a novel Multiple Hierarchical Federated Learning (MHFL) architecture for large-scale FL and design an Edge Server Reallocation scheme (ESR-MHFL) to enhance training efficiency by optimally redistributing edge servers among federations based on their contribution to model convergence. We first develop a closed-form analysis model for MHFL to quantify training time, computation, and communication costs. To improve training efficiency, we analyze the impacts of edge server allocation on convergence and formulate server reallocation as a multi-item auction problem with theoretical guarantees. We then propose ESR-MHFL, which leverages Coalition Structure Generation (CSG) and greedy matching methods to simplify the reallocation problem and enhance efficiency. Extensive numerical simulations demonstrate that ESR-MHFL not only improves model accuracy while reducing training cost but also exhibits strong compatibility with existing client selection methods, achieving improved training efficiency. The total economic expenditure combining all components