On Energy Optimization for Hierarchical Federated Learning With Delay Constraint Through Node Cooperation

In hierarchical federated learning (HFL), edge computing is introduced for partial model aggregation to reduce latency. High energy cost is an important issue to be solved in the process of parameters uploading. Our study focuses on the issue of minimizing energy cost with delay constraint through node cooperation in HFL, and the decision problem for this is NP-hard. We introduce a cost-efficient HFL (CE-HFL) framework, where nodes not only participate in model training but also transmit and aggregate model parameters for neighbors. A parameter aggregation tree is first generated, and parameter updates can be delivered to edge servers along paths in the tree while being aggregated simultaneously. Through theoretical analysis, it is proved that CE-HFL can achieve energy optimization with delay constraint. We also evaluate its performance through thorough experiments. In comparison with HierFAVG, CFL, and HFEL, it is found that CE-HFL can save energy cost up to 24.58%, 22.02%, and 6.60%, respectively.