  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.
