Efficient GNN-Based Client Selection for Optimizing Resource Allocation in Hierarchical Federated Learning

Hierarchical Federated Learning (HFL) effectively reduces communication overhead by deploying edge servers as an intermediary tier. Meanwhile, this architecture introduces a critical and NP-hard client selection problem: it necessitates coordinated selection of massive and heterogeneous clients in each aggregation round to minimize system-wide latency and energy consumption. To tackle this challenge, we formulate the client selection and bandwidth allocation as a joint optimization problem, and propose a novel framework that decouples the problem into two manageable subproblems. We introduce a hybrid algorithm that models the HFL system as a graph and leverages a Graph Neural Network (GNN) to capture the multi-dimensional node features and the underlying network topology. The GNN generates a selection score for each potential client-edge pair, which directly informs a greedy selection algorithm that constructs the final aggregation subset. This approach strategically decouples the intractable selection task from bandwidth allocation, reducing the latter to a convex subproblem that can be solved efficiently for optimality. Extensive simulations on the CIFAR-10 dataset, under both IID and challenging non-IID distributions, validate the superiority of our algorithm. It substantially outperforms established baselines, achieving robust model convergence while simultaneously minimizing total latency and energy consumption.