Federated ADMM from Bayesian Duality

We propose a new Bayesian approach to derive and extend the federated Alternating Direction Method of Multipliers (ADMM). We show that the solutions of variational-Bayesian objectives are associated with a duality structure that not only resembles ADMM but also extends it. For example, ADMM-like updates are recovered when the objective is optimized over the isotropic-Gaussian family, and new non-trivial extensions are obtained for other more flexible exponential families. Examples include a Newton-like variant that converges in one step on quadratics and an Adam-like variant called IVON-ADMM that has the same cost as Adam but yields up to 7\% accuracy boosts in heterogeneous deep learning. Our work opens a new direction to use Bayes to extend ADMM and other primal-dual methods.