# Decentralized Distributed Optimization for Saddle Point Problems

arXiv: https://arxiv.org/abs/2102.07758 · HTML: https://mlsanity.com/paper/2102.07758/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2021.

## Built on by (most cited first, 10 of 10)

- [Federated Minimax Optimization: Improved Convergence Analyses and Algorithms](https://mlsanity.com/paper/2203.04850/) (2022)
- [Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Survey](https://mlsanity.com/paper/2208.13592/) (2022)
- [Distributed Saddle-Point Problems Under Similarity](https://mlsanity.com/paper/2107.10706/) (2021)
- [Federated Minimax Optimization with Client Heterogeneity](https://mlsanity.com/paper/2302.04249/) (2023)
- [Robust Decentralized Learning with Local Updates and Gradient Tracking](https://mlsanity.com/paper/2405.00965/) (2024)
- [Adaptive Federated Minimax Optimization with Lower Complexities](https://mlsanity.com/paper/2211.07303/) (2022)
- [CDMA: A Practical Cross-Device Federated Learning Algorithm for General Minimax Problems](https://mlsanity.com/paper/2105.14216/) (2021)
- [Stochastic Gradient Methods with Compressed Communication for Decentralized Saddle Point Problems](https://mlsanity.com/paper/2205.14452/) (2022)
- [Switch and Conquer: Efficient Algorithms By Switching Stochastic Gradient Oracles For Decentralized Saddle Point Problems](https://mlsanity.com/paper/2309.00997/) (2023)
- [Fast Decentralized Gradient Tracking for Federated Minimax Optimization with Local Updates](https://mlsanity.com/paper/2405.04566/) (2024)

## Abstract (arXiv)

We consider distributed convex-concave saddle point problems over arbitrary connected undirected networks and propose a decentralized distributed algorithm for their solution. The local functions distributed across the nodes are assumed to have global and local groups of variables. For the proposed algorithm we prove non-asymptotic convergence rate estimates with explicit dependence on the network characteristics. To supplement the convergence rate analysis, we propose lower bounds for strongly-convex-strongly-concave and convex-concave saddle-point problems over arbitrary connected undirected networks. We illustrate the considered problem setting by a particular application to distributed calculation of non-regularized Wasserstein barycenters.