# Generalized ADMM in Distributed Learning via Variational Inequality

arXiv: https://arxiv.org/abs/2104.12608 · HTML: https://mlsanity.com/paper/2104.12608/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 26 Apr 2021.

## Builds on (most cited first, 10 of 10)

- [COLA: Decentralized Linear Learning](https://mlsanity.com/paper/1808.04883/) (2018)
- [GADMM: Fast and Communication Efficient Framework for Distributed Machine Learning](https://mlsanity.com/paper/1909.00047/) (2019)
- [A General Analysis of the Convergence of ADMM](https://mlsanity.com/paper/1502.02009/) (2015)
- [Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems](https://mlsanity.com/paper/1306.2454/) (2013)
- [Q-GADMM: Quantized Group ADMM for Communication Efficient Decentralized Machine Learning](https://mlsanity.com/paper/1910.10453/) (2019)
- [L-FGADMM: Layer-Wise Federated Group ADMM for Communication Efficient Decentralized Deep Learning](https://mlsanity.com/paper/1911.03654/) (2019)
- [An Explicit Rate Bound for the Over-Relaxed ADMM](https://mlsanity.com/paper/1512.02063/) (2015)
- [Nonconvex Generalization of Alternating Direction Method of Multipliers for Nonlinear Equality Constrained Problems](https://mlsanity.com/paper/1705.03412/) (2017)
- [Distributed Inexact Successive Convex Approximation ADMM: Analysis-Part I](https://mlsanity.com/paper/1907.08969/) (2019)
- [Representation of Federated Learning via Worst-Case Robust Optimization Theory](https://mlsanity.com/paper/1912.05571/) (2019)

## Abstract (arXiv)

Due to the explosion in size and complexity of modern data sets and privacy concerns of data holders, it is increasingly important to be able to solve machine learning problems in distributed manners. The Alternating Direction Method of Multipliers (ADMM) through the concept of consensus variables is a practical algorithm in this context where its diverse variations and its performance have been studied in different application areas. In this paper, we study the effect of the local data sets of users in the distributed learning of ADMM. Our aim is to deploy variational inequality (VI) to attain an unified view of ADMM variations. Through the simulation results, we demonstrate how more general definitions of consensus parameters and introducing the uncertain parameters in distribute approach can help to get the better results in learning processes.