A Algorithm

The RWSADMM scheme is as presented in Algorithm 1. Client Note that we only use one client in each derivation iteration. Our proof of convergence for the proposed stochastic ADMM-based federated learning algorithm is non-trivial and non-straightforward. This is a significant novelty and challenge in the proof, as it is the first method introduced in federated learning that considers this type of server movement. The proof sketch is summarized as follows. Under Assumption 4.2, the sequence created by the RWSADMM, i.e., The proof details are provided in the following.