With the rapid growth of edge intelligence, the deployment of federated learning (FL) over wireless networks has garnered increasing attention, which is called Federated Edge Learning (FEEL). In FEEL, both mobile devices transmitting model parameters over noisy channels and collecting data in diverse environments pose challenges to the generalization of trained models. Moreover, devices can engage in decentralized FL via Device-to-Device communication while the communication topology of connected devices also impacts the generalization of models. Most recent theoretical studies overlook the incorporation of all these effects into FEEL when developing generalization analyses. In contrast, our work presents an information-theoretic generalization analysis for topology-aware FEEL in the presence of data heterogeneity and noisy channels. Additionally, we propose a novel regularization method called Federated Global Mutual Information Reduction (FedGMIR) to enhance the performance of models based on our analysis. Numerical results validate our theoretical findings and provide evidence for the effectiveness of the proposed method.

翻译：随着边缘智能技术的快速发展，无线网络中的联邦学习（FL）部署日益受到关注，此类应用被称作联邦边缘学习（FEEL）。在FEEL中，移动设备需通过噪声信道传输模型参数，并在异构环境中采集数据，这些因素对训练模型的泛化性能构成挑战。此外，设备可通过设备间通信（D2D）参与去中心化联邦学习，而连接设备的通信拓扑结构同样影响模型的泛化能力。近期理论研究大多未将上述所有因素纳入FEEL的泛化分析中。相比之下，本研究针对数据异构与噪声信道环境下的拓扑感知FEEL，提出了一种基于信息论的泛化分析方法。进一步地，基于理论分析，我们提出了一种名为联邦全局互信息缩减（FedGMIR）的新型正则化方法以提升模型性能。数值实验结果验证了理论发现，并证明了所提方法的有效性。