To address the deviation issues caused by intermittent client unavailability due to resource constraints or uncertainty in federated learning, researchers proposed the FedSWE algorithm. This algorithm achieves provable robustness towards heterogeneous and non-stationary random client availability through a hybrid local update mechanism that combines missing computation compensation, stable global updates, and implicit gossiping. Compared with the standard FedAvg, FedSWE introduces only minor memory and computational overhead, enabling linear acceleration in specific situations and converging to the stationary point of non-convex objective functions. The research team verified the analytical results and performance advantages of this algorithm through numerical experiments simulating diverse client unavailability dynamics on real datasets.