# Decentralized Saddle-Point Problems with Different Constants of Strong Convexity and Strong Concavity

arXiv: https://arxiv.org/abs/2206.00090 · HTML: https://mlsanity.com/paper/2206.00090/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2022.

## Built on by (most cited first, 4 of 4)

- [Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Survey](https://mlsanity.com/paper/2208.13592/) (2022)
- [Federated Minimax Optimization with Client Heterogeneity](https://mlsanity.com/paper/2302.04249/) (2023)
- [Decentralized gradient descent maximization method for composite nonconvex strongly-concave minimax problems](https://mlsanity.com/paper/2304.02441/) (2023)
- [Nesterov Meets Optimism: Rate-Optimal Separable Minimax Optimization](https://mlsanity.com/paper/2210.17550/) (2022)

## Abstract (arXiv)

Large-scale saddle-point problems arise in such machine learning tasks as GANs and linear models with affine constraints. In this paper, we study distributed saddle-point problems (SPP) with strongly-convex-strongly-concave smooth objectives that have different strong convexity and strong concavity parameters of composite terms, which correspond to min and max variables, and bilinear saddle-point part. We consider two types of first-order oracles: deterministic (returns gradient) and stochastic (returns unbiased stochastic gradient). Our method works in both cases and takes several consensus steps between oracle calls.