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：随着边缘智能的快速发展，联邦学习在无线网络中的部署受到日益关注，即联邦边缘学习。在联邦边缘学习中，移动设备在噪声信道上传输模型参数并在多样化环境中收集数据，这对训练模型的泛化能力构成了挑战。此外，设备可通过设备到设备通信参与去中心化联邦学习，而连接设备的通信拓扑也会影响模型的泛化性能。近期大多数理论研究在开发泛化分析时，未能将这些影响因素全部纳入联邦边缘学习框架。相比之下，我们的工作针对存在数据异构性与噪声信道的拓扑感知联邦边缘学习，提出了一种基于信息论的泛化分析方法。同时，我们提出了一种名为联邦全局互信息缩减的新正则化方法，以基于分析结果提升模型性能。数值实验结果验证了我们的理论发现，并证明了所提方法的有效性。