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.

翻译：本文提出了一种新颖的多集合分层联邦学习算法，该算法融合了用于通信高效的量化技术，并展现出对统计异质性的鲁棒性。与传统的分层联邦学习算法不同，我们的方法在集合内迭代中结合梯度聚合，在集合间迭代中则采用模型聚合。我们建立了一个全面的分析框架来评估其最优性差距和收敛速度，并与传统算法的相应方面进行比较。此外，我们推导出一种问题公式，以得到最优系统参数的闭式解。研究结果表明，我们的算法在多种参数设置下均能稳定实现高学习精度，并在异质数据分布场景中显著优于其他分层算法。