Adaptive ADMM with Spectral Penalty Parameter Selection
Abstract
The alternating direction method of multipliers (ADMM) is a versatile tool for solving a wide range of constrained optimization problems, with differentiable or non-differentiable objective functions. Unfortunately, its performance is highly sensitive to a penalty parameter, which makes ADMM often unreliable and hard to automate for a non-expert user. We tackle this weakness of ADMM by proposing a method to adaptively tune the penalty parameters to achieve fast convergence. The resulting adaptive ADMM (AADMM) algorithm, inspired by the successful Barzilai-Borwein spectral method for gradient descent, yields fast convergence and relative insensitivity to the initial stepsize and problem scaling.
Cite
Text
Xu et al. "Adaptive ADMM with Spectral Penalty Parameter Selection." International Conference on Artificial Intelligence and Statistics, 2017.Markdown
[Xu et al. "Adaptive ADMM with Spectral Penalty Parameter Selection." International Conference on Artificial Intelligence and Statistics, 2017.](https://mlanthology.org/aistats/2017/xu2017aistats-adaptive/)BibTeX
@inproceedings{xu2017aistats-adaptive,
title = {{Adaptive ADMM with Spectral Penalty Parameter Selection}},
author = {Xu, Zheng and Figueiredo, Mário A. T. and Goldstein, Tom},
booktitle = {International Conference on Artificial Intelligence and Statistics},
year = {2017},
pages = {718-727},
url = {https://mlanthology.org/aistats/2017/xu2017aistats-adaptive/}
}