针对边缘设备通信频繁与不稳定的难题，提出局部更新与部分参与的扩散学习新方法。

Diffusion learning is a framework that endows edge devices with advanced intelligence. By processing and analyzing data locally and allowing each agent to communicate with its immediate neighbors, diffusion effectively protects the privacy of edge devices, enables real-time response, and reduces reliance on central servers. However, traditional diffusion learning relies on communication at every iteration, leading to communication overhead, especially with large learning models. Furthermore, the inherent volatility of edge devices, stemming from power outages or signal loss, poses challenges to reliable communication between neighboring agents. To mitigate these issues, this paper investigates an enhanced diffusion learning approach incorporating local updates and partial agent participation. Local updates will curtail communication frequency, while partial agent participation will allow for the inclusion of agents based on their availability. We prove that the resulting algorithm is stable in the mean-square error sense and provide a tight analysis of its Mean-Square-Deviation (MSD) performance. Various numerical experiments are conducted to illustrate our theoretical findings.