Solving nonsmooth decentralized optimization with affine constraints using gradient sliding

Jiawei Chen, Zhenzhen Song, Alexander Rogozin, Nhat Trung Nguyen, Irina Podlipnova, Demyan Yarmoshik, Alexander Gasnikov

Keywords: decentralized optimization, affince constraints, gradient sliding

TL;DR: we solve decentralized nonsmooth convex optimization problem with affine constraints using gradient sliding.

Abstract: This paper explores decentralized nonsmooth convex optimization with affine constraints. We extend existing research by incorporating a nonsmooth stochastic oracle, solved by the well know gradient sliding method. Our result show sliding algorithm achieves sub-optimal solution for these optimization problems under certain conditions, addressing limitations of prior methods. This work enhances the theoretical understanding of distributed optimization and offers practical solutions for applications in sensor networks and machine learning.

Submission Number: 80