We propose a new Bayesian approach to generalize the federated Alternating Direction Method of Multipliers (ADMM). We show that the solutions of variational-Bayesian (VB) objectives are associated with a duality structure that not only resembles the structure of ADMM's fixed-points but also generalizes it. For example, ADMM-like updates are recovered when the VB objective is optimized over the isotropic-Gaussian family, and new non-trivial extensions are obtained for other exponential-family distributions. These extensions include a Newton-like variant that converges in one step on quadratic objectives and an Adam-like variant that yields up to 7% accuracy boosts for deep heterogeneous cases. Our work opens a new Bayesian way to generalize ADMM and other primal-dual methods.

翻译：本文提出了一种新的贝叶斯方法来推广联邦交替方向乘子法（ADMM）。我们证明了变分贝叶斯（VB）目标函数的解具有一种对偶结构，该结构不仅类似于ADMM不动点的结构，而且对其进行了推广。例如，当在各项同性高斯族上优化VB目标函数时，可以恢复出类似ADMM的更新规则；而对于其他指数族分布，则可得到新的非平凡扩展。这些扩展包括一个在二次目标函数上一步收敛的类牛顿变体，以及一个在深度异构场景下能带来高达7%精度提升的类Adam变体。我们的工作为推广ADMM及其他原始-对偶方法开辟了一条新的贝叶斯路径。