Almost all existing hierarchical federated learning (FL) models are limited to two aggregation layers, restricting scalability and flexibility in complex, large-scale networks. In this work, we propose a Multi-Layer Hierarchical Federated Learning framework (QMLHFL), which appears to be the first study that generalizes hierarchical FL to arbitrary numbers of layers and network architectures through nested aggregation, while employing a layer-specific quantization scheme to meet communication constraints. We develop a comprehensive convergence analysis for QMLHFL and derive a general convergence condition and rate that reveal the effects of key factors, including quantization parameters, hierarchical architecture, and intra-layer iteration counts. Furthermore, we determine the optimal number of intra-layer iterations to maximize the convergence rate while meeting a deadline constraint that accounts for both communication and computation times. Our results show that QMLHFL consistently achieves high learning accuracy, even under high data heterogeneity, and delivers notably improved performance when optimized, compared to using randomly selected values.

翻译：几乎所有现有的分层联邦学习模型都局限于两个聚合层，这在复杂的大规模网络中限制了可扩展性和灵活性。本文提出了一种多层分层联邦学习框架，这似乎是首个通过嵌套聚合将分层联邦学习推广至任意层数和网络架构的研究，同时采用层特定量化方案以满足通信约束。我们为QMLHFL建立了完整的收敛性分析，推导出通用的收敛条件和速率，揭示了量化参数、分层架构和层内迭代次数等关键因素的影响。此外，我们确定了层内迭代的最优次数，以在满足同时考虑通信时间和计算时间的截止期限约束下最大化收敛速率。实验结果表明，QMLHFL即使在高度数据异质性条件下也能持续实现较高的学习精度，且经过优化后相比随机选择参数值能显著提升性能。