Dynamic Grouping and Aggregation Weight Optimization for Hierarchical Federated Learning with Quantization

Zihao Peng, Nan Zou, Jiandian Zeng, Boyuan Li, Shengbo Chen, Tian Wang, Weijia Jia

Abstract: Hierarchical Federated Learning (HFL) alleviates communication bottlenecks by organizing the system into multiple layers: client, intermediate aggregator, and server. Clients and aggregation layers form groups based on connection patterns, and the methods used for grouping and aggregation directly affect convergence performance. Currently, some studies have proposed grouping algorithms to address the non-independent and identically distributed (non-IID) characteristics of client data to improve performance. However, these methods do not account for network heterogeneity, such as clients using different quantization levels or adaptive quantization strategies to minimize communication overhead. Moreover, most methods rely on heuristics that blindly explore the combinatorial grouping space, incurring substantial computational overhead. In this paper, we conduct a rigorous convergence analysis and frame the dual challenges of heterogeneous data and quantization heterogeneity in HFL as the joint optimization of aggregation weights and grouping strategy. Specifically, we derive the optimal closed-form solution for the aggregation weights and propose an Alternating Optimization Hierarchical Optimal Weights (AO-HOW) algorithm to compute these weights. Building on this result, we propose DyGHFL—Dynamic Exclusion–Reallocation Grouping for Hierarchical Federated Learning, a structu-reaware and efficient greedy algorithm that reorganizes groups by maximizing structured gain and updating weight coefficients according to current system conditions. Experiments on multiple datasets show that DyGHFL consistently outperforms existing baselines, demonstrating its effectiveness in HFL.

External IDs:doi:10.1109/ton.2026.3668185