The saddle-point optimization problems have a lot of practical applications. This paper focuses on such non-smooth problems in decentralized case. This work contains generalization of recently proposed sliding for centralized problem. Through specific penalization method and this sliding we obtain algorithm for non-smooth decentralized saddle-point problems. Note, the proposed method approaches lower bounds both for number of communication rounds and calls of (sub-)gradient per node.
@article{arxiv.2210.06086,
title = {The Mirror-Prox Sliding Method for Non-smooth decentralized saddle-point problems},
author = {Ilya Kuruzov and Alexander Rogozin and Demyan Yarmoshik and Alexander Gasnikov},
journal= {arXiv preprint arXiv:2210.06086},
year = {2024}
}