Semi-decentralized federated learning blends the conventional device to-server (D2S) interaction structure of federated model training with localized device-to-device (D2D) communications. We study this architecture over practical edge networks with multiple D2D clusters modeled as time-varying and directed communication graphs. Our investigation results in an algorithm that controls the fundamental trade-off between (a) the rate of convergence of the model training process towards the global optimizer, and (b) the number of D2S transmissions required for global aggregation. Specifically, in our semi-decentralized methodology, D2D consensus updates are injected into the federated averaging framework based on column-stochastic weight matrices that encapsulate the connectivity within the clusters. To arrive at our algorithm, we show how the expected optimality gap in the current global model depends on the greatest two singular values of the weighted adjacency matrices (and hence on the densities) of the D2D clusters. We then derive tight bounds on these singular values in terms of the node degrees of the D2D clusters, and we use the resulting expressions to design a threshold on the number of clients required to participate in any given global aggregation round so as to ensure a desired convergence rate. Simulations performed on real-world datasets reveal that our connectivity-aware algorithm reduces the total communication cost required to reach a target accuracy significantly compared with baselines depending on the connectivity structure and the learning task.

翻译：半去中心化联邦学习将传统联邦模型训练中的设备到服务器（D2S）交互结构与本地设备间（D2D）通信相结合。我们针对具有多个D2D簇的实际边缘网络研究该架构，并将其建模为时变有向通信图。通过研究，我们提出一种算法，用于控制以下两个基本目标之间的权衡：（a）模型训练过程向全局优化器的收敛速度，以及（b）全局聚合所需的D2S传输次数。具体而言，在我们的半去中心化方法中，基于列随机权重矩阵（该矩阵封装了簇内连接性）将D2D共识更新注入联邦平均框架。为推导该算法，我们展示了当前全局模型的预期最优性差距如何取决于D2D簇加权邻接矩阵的最大两个奇异值（从而取决于其密度）。随后，我们基于D2D簇的节点度数推导出这些奇异值的紧界，并利用所得表达式设计阈值，以确定在任何给定全局聚合轮次中所需参与的客户端数量，从而确保期望的收敛速度。基于真实数据集的仿真表明，与依赖连接结构和学习任务的基线方法相比，我们的感知连接性算法在达到目标精度时显著降低了总通信成本。