Alternating Direction Method of Multipliers for Decomposable Saddle-Point Problems
Abstract
Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of multipliers to such saddle-point problems. Instead of solving the original saddle-point problem directly, this algorithm solves smaller saddle-point problems by exploiting the decomposable structure. We show the convergence of this algorithm for convex-concave saddle-point problems under a mild assumption. We also provide a sufficient condition for which the assumption holds. We demonstrate the convergence properties of the saddle-point alternating direction method of multipliers with numerical examples on a power allocation problem in communication channels and a network routing problem with adversarial costs.
Cite
@article{arxiv.2209.04536,
title = {Alternating Direction Method of Multipliers for Decomposable Saddle-Point Problems},
author = {Mustafa O. Karabag and David Fridovich-Keil and Ufuk Topcu},
journal= {arXiv preprint arXiv:2209.04536},
year = {2022}
}
Comments
Accepted to 58th Annual Allerton Conference on Communication, Control, and Computing