# Jointly Improving the Sample and Communication Complexities in Decentralized Stochastic Minimax Optimization

arXiv: https://arxiv.org/abs/2307.09421 · HTML: https://mlsanity.com/paper/2307.09421/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2023.

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

- [Robust Decentralized Learning with Local Updates and Gradient Tracking](https://mlsanity.com/paper/2405.00965/) (2024)
- [Achieving Near-Optimal Convergence for Distributed Minimax Optimization with Adaptive Stepsizes](https://mlsanity.com/paper/2406.02939/) (2024)
- [Nonconvex Decentralized Stochastic Bilevel Optimization under Heavy-Tailed Noise](https://mlsanity.com/paper/2509.15543/) (2025)
- [On the Communication Complexity of Decentralized Stochastic Bilevel Optimization](https://mlsanity.com/paper/2311.11342/) (2023)

## Abstract (arXiv)

We propose a novel single-loop decentralized algorithm called DGDA-VR for solving the stochastic nonconvex strongly-concave minimax problem over a connected network of M agents. By using stochastic first-order oracles to estimate the local gradients, we prove that our algorithm finds an ε-accurate solution with O(ε-3) sample complexity and O(ε-2) communication complexity, both of which are optimal and match the lower bounds for this class of problems. Unlike competitors, our algorithm does not require multiple communications for the convergence results to hold, making it applicable to a broader computational environment setting. To the best of our knowledge, this is the first such algorithm to jointly optimize the sample and communication complexities for the problem considered here.