# Federated ADMM from Bayesian Duality

Source: [Federated ADMM from Bayesian Duality](<https://www.sota2.com/research/paper/68fa5da71e209131ce9dbecb>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-03-06T05:00:05.533Z

Authors: Thomas M\\"ollenhoff, Siddharth Swaroop, Finale Doshi-Velez, Mohammad Emtiyaz Khan

Published: 2025-06-16T07:02:33.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on MNIST 100 clients, highly heterog. (test)](<https://www.sota2.com/research/sota/image-classification-on-mnist-100-clients-highly-heterog-test.md>): Image Classification; MNIST 100 clients, highly heterog. (test); Test Accuracy: 96.

- [Image Classification on CIFAR-100 10 clients, heterog. (test)](<https://www.sota2.com/research/sota/image-classification-on-cifar-100-10-clients-heterog-test.md>): Image Classification; CIFAR-100 10 clients, heterog. (test); Test Accuracy: 46.6.

- [Image Classification on Fashion-MNIST homogeneous (test)](<https://www.sota2.com/research/sota/image-classification-on-fashion-mnist-homogeneous-test.md>): Image Classification; Fashion-MNIST homogeneous (test); Test Accuracy: 84.1.

- [Image Classification on CIFAR-10 heterogeneous (test)](<https://www.sota2.com/research/sota/image-classification-on-cifar-10-heterogeneous-test.md>): Image Classification; CIFAR-10 heterogeneous (test); Test Accuracy: 80.3.

- [Image Classification on Fashion-MNIST heterogeneous (test)](<https://www.sota2.com/research/sota/image-classification-on-fashion-mnist-heterogeneous-test.md>): Image Classification; Fashion-MNIST heterogeneous (test); Test Accuracy: 83.

- [Image Classification on FashionMNIST (test)](<https://www.sota2.com/research/sota/image-classification-on-fashionmnist-test.md>): Image Classification; FashionMNIST (test); Accuracy: not recorded.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2506.13150>)

[PDF](<https://arxiv.org/pdf/2506.13150.pdf>)