Quantized Hierarchical Federated Learning: A Robust Approach to Statistical Heterogeneity

This paper presents a novel hierarchical federated learning algorithm within multiple sets that incorporates quantization for communication-efficiency and demonstrates resilience to statistical heterogeneity. Unlike conventional hierarchical federated learning algorithms, our approach combines gradient aggregation in intra-set iterations with model aggregation in inter-set iterations. We offer a comprehensive analytical framework to evaluate its optimality gap and convergence rate, comparing these aspects with those of conventional algorithms. Additionally, we develop a problem formulation to derive optimal system parameters in a closed-form solution. Our findings reveal that our algorithm consistently achieves high learning accuracy over a range of parameters and significantly outperforms other hierarchical algorithms, particularly in scenarios with heterogeneous data distributions.