When implementing hierarchical federated learning over wireless networks, scalability assurance and the ability to handle both interference and device data heterogeneity are crucial. This work introduces a new two-level learning method designed to address these challenges, along with a scalable over-the-air aggregation scheme for the uplink and a bandwidth-limited broadcast scheme for the downlink that efficiently use a single wireless resource. To provide resistance against data heterogeneity, we employ gradient aggregations. Meanwhile, the impact of uplink and downlink interference is minimized through optimized receiver normalizing factors. We present a comprehensive mathematical approach to derive the convergence bound for the proposed algorithm, applicable to a multi-cluster wireless network encompassing any count of collaborating clusters, and provide special cases and design remarks. As a key step to enable a tractable analysis, we develop a spatial model for the setup by modeling devices as a Poisson cluster process over the edge servers and rigorously quantify uplink and downlink error terms due to the interference. Finally, we show that despite the interference and data heterogeneity, the proposed algorithm not only achieves high learning accuracy for a variety of parameters but also significantly outperforms the conventional hierarchical learning algorithm.

翻译：在无线网络中实现分层联邦学习时，可扩展性保障以及处理干扰和设备数据异构性的能力至关重要。本文引入了一种新的两层学习方法以应对这些挑战，同时提出了一种用于上行链路的可扩展空中聚合方案，以及一种用于下行链路的带宽受限广播方案，二者高效地利用单一无线资源。为了抵抗数据异构性，我们采用梯度聚合方法。同时，通过优化接收端归一化因子，最小化了上下行链路干扰的影响。我们提出了一套完整的数学方法，推导了所提算法的收敛界，该方法适用于包含任意数量协作簇的多簇无线网络，并给出了特例分析与设计启示。作为实现可处理分析的关键步骤，我们通过将设备建模为边缘服务器上的泊松簇过程，建立了该设置的空间模型，并严格量化了由干扰引起的上行和下行误差项。最后，我们证明，尽管存在干扰和数据异构性，所提算法不仅能在多种参数下实现高学习精度，而且显著优于传统的分层学习算法。