Federated ADMM from Bayesian Duality
Abstract
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.
Cite
Text
Möllenhoff et al. "Federated ADMM from Bayesian Duality." International Conference on Learning Representations, 2026.Markdown
[Möllenhoff et al. "Federated ADMM from Bayesian Duality." International Conference on Learning Representations, 2026.](https://mlanthology.org/iclr/2026/mollenhoff2026iclr-federated/)BibTeX
@inproceedings{mollenhoff2026iclr-federated,
title = {{Federated ADMM from Bayesian Duality}},
author = {Möllenhoff, Thomas and Swaroop, Siddharth and Doshi-Velez, Finale and Khan, Mohammad Emtiyaz},
booktitle = {International Conference on Learning Representations},
year = {2026},
url = {https://mlanthology.org/iclr/2026/mollenhoff2026iclr-federated/}
}