Federated learning has shown its advances over the last few years but is
facing many challenges, such as how algorithms save communication resources,
how they reduce computational costs, and whether they converge. To address
these issues, this paper proposes exact and inexact ADMM-based federated
learning. They are not only communication-efficient but also converge linearly
under very mild conditions, such as convexity-free and irrelevance to data
distributions. Moreover, the inexact version has low computational complexity,
thereby alleviating the computational burdens significantly.