This paper explores the challenges of implementing Federated Learning (FL) in practical scenarios featuring isolated nodes with data heterogeneity, which can only be connected to the server through wireless links in an infrastructure-less environment. To overcome these challenges, we propose a novel mobilizing personalized FL approach, which aims to facilitate mobility and resilience. Specifically, we develop a novel optimization algorithm called Random Walk Stochastic Alternating Direction Method of Multipliers (RWSADMM). RWSADMM capitalizes on the server's random movement toward clients and formulates local proximity among their adjacent clients based on hard inequality constraints rather than requiring consensus updates or introducing bias via regularization methods. To mitigate the computational burden on the clients, an efficient stochastic solver of the approximated optimization problem is designed in RWSADMM, which provably converges to the stationary point almost surely in expectation. Our theoretical and empirical results demonstrate the provable fast convergence and substantial accuracy improvements achieved by RWSADMM compared to baseline methods, along with its benefits of reduced communication costs and enhanced scalability.

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.

FL approach, which aims to facilitate mobility and resilience.

This paper explores the challenges of implementing Federated Learning (FL) in practical scenarios featuring isolated nodes with data heterogeneity, which can only be connected to the server through wireless links in an infrastructure-less environment. To overcome these challenges, we propose a novel mobilizing personalized FL approach, which aims to facilitate mobility and resilience. Specifically, we develop a novel optimization algorithm called Random Walk Stochastic Alternating Direction Method of Multipliers (RWSADMM). RWSADMM capitalizes on the server's random movement toward clients and formulates local proximity among their adjacent clients based on hard inequality constraints rather than requiring consensus updates or introducing bias via regularization methods. To mitigate the computational burden on the clients, an efficient stochastic solver of the approximated optimization problem is designed in RWSADMM, which provably converges to the stationary point almost surely in expectation.