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）交互结构与局部设备到设备（D2D）通信相结合。我们在具有多个D2D集群的实际边缘网络中研究该架构，这些集群被建模为时变有向通信图。我们的研究提出了一种算法，用于控制以下两项之间的基本权衡：（a）模型训练过程向全局优化器收敛的速度，以及（b）全局聚合所需的D2S传输次数。具体而言，在半去中心化方法中，我们基于列随机权重矩阵将D2D共识更新注入联邦平均框架，这些矩阵封装了集群内的连接性。为推导该算法，我们展示了当前全局模型的期望最优性差距如何依赖于D2D集群加权邻接矩阵的最大两个奇异值（进而依赖于其密度）。随后，我们根据D2D集群的节点度数导出这些奇异值的紧界，并利用所得表达式设计一个阈值，该阈值控制任何给定全局聚合轮次中所需参与客户端的数量，以确保期望的收敛速率。在真实世界数据集上的仿真表明，与依赖连接结构及学习任务的基线方法相比，我们的连接感知算法能够显著降低达到目标精度所需的总通信成本。