# Solving a Class of Non-Convex Minimax Optimization in Federated Learning

arXiv: https://arxiv.org/abs/2310.03613 · HTML: https://mlsanity.com/paper/2310.03613/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 78 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 30 of 58)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Momentum-Based Variance Reduction in Non-Convex SGD](https://mlsanity.com/paper/1905.10018/) (2019)
- [SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path Integrated Differential Estimator](https://mlsanity.com/paper/1807.01695/) (2018)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)
- [Mime: Mimicking Centralized Stochastic Algorithms in Federated Learning](https://mlsanity.com/paper/2008.03606/) (2020)
- [Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods](https://mlsanity.com/paper/1902.08297/) (2019)
- [Distributionally Robust Federated Averaging](https://mlsanity.com/paper/2102.12660/) (2021)
- [Robust Federated Learning: The Case of Affine Distribution Shifts](https://mlsanity.com/paper/2006.08907/) (2020)
- [Stability and Generalization of Learning Algorithms that Converge to Global Optima](https://mlsanity.com/paper/1710.08402/) (2017)
- [Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization](https://mlsanity.com/paper/2011.00364/) (2020)
- [FedGAN: Federated Generative Adversarial Networks for Distributed Data](https://mlsanity.com/paper/2006.07228/) (2020)
- [Stochastic Recursive Gradient Descent Ascent for Stochastic Nonconvex-Strongly-Concave Minimax Problems](https://mlsanity.com/paper/2001.03724/) (2020)
- [Efficient Algorithms for Smooth Minimax Optimization](https://mlsanity.com/paper/1907.01543/) (2019)
- [Stochastic AUC Maximization with Deep Neural Networks](https://mlsanity.com/paper/1908.10831/) (2019)
- [FedNest: Federated Bilevel, Minimax, and Compositional Optimization](https://mlsanity.com/paper/2205.02215/) (2022)
- [Faster Single-loop Algorithms for Minimax Optimization without Strong Concavity](https://mlsanity.com/paper/2112.05604/) (2021)
- [A Decentralized Parallel Algorithm for Training Generative Adversarial Nets](https://mlsanity.com/paper/1910.12999/) (2019)
- [STEM: A Stochastic Two-Sided Momentum Algorithm Achieving Near-Optimal Sample and Communication Complexities for Federated Learning](https://mlsanity.com/paper/2106.10435/) (2021)
- [Accelerated Zeroth-Order and First-Order Momentum Methods from Mini to Minimax Optimization](https://mlsanity.com/paper/2008.08170/) (2020)
- [Local Stochastic Gradient Descent Ascent: Convergence Analysis and Communication Efficiency](https://mlsanity.com/paper/2102.13152/) (2021)
- [Federated Minimax Optimization: Improved Convergence Analyses and Algorithms](https://mlsanity.com/paper/2203.04850/) (2022)
- [Robust Multi-Agent Reinforcement Learning with State Uncertainty](https://mlsanity.com/paper/2307.16212/) (2023)
- [Faster Adaptive Federated Learning](https://mlsanity.com/paper/2212.00974/) (2022)
- [Adversarial Attack Generation Empowered by Min-Max Optimization](https://mlsanity.com/paper/1906.03563/) (2019)

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

- [Towards Unified Multi-Modal Personalization: Large Vision-Language Models for Generative Recommendation and Beyond](https://mlsanity.com/paper/2403.10667/) (2024)
- [Every Parameter Matters: Ensuring the Convergence of Federated Learning with Dynamic Heterogeneous Models Reduction](https://mlsanity.com/paper/2310.08670/) (2023)
- [Auto-Train-Once: Controller Network Guided Automatic Network Pruning from Scratch](https://mlsanity.com/paper/2403.14729/) (2024)
- [On the Role of Server Momentum in Federated Learning](https://mlsanity.com/paper/2312.12670/) (2023)
- [Stochastic Smoothed Gradient Descent Ascent for Federated Minimax Optimization](https://mlsanity.com/paper/2311.00944/) (2023)
- [Federated Stochastic Minimax Optimization under Heavy-Tailed Noises](https://mlsanity.com/paper/2511.04456/) (2025)
- [Achieving Near-Optimal Convergence for Distributed Minimax Optimization with Adaptive Stepsizes](https://mlsanity.com/paper/2406.02939/) (2024)
- [Heterogeneity-Aware Client Sampling for Optimal and Efficient Federated Learning](https://mlsanity.com/paper/2505.11304/) (2025)
- [Federated Instrumental Variable Analysis via Federated Generalized Method of Moments](https://mlsanity.com/paper/2505.21012/) (2025)
- [FedEGG: Federated Learning with Explicit Global Guidance](https://mlsanity.com/paper/2404.11888/) (2024)

## Abstract (arXiv)

The minimax problems arise throughout machine learning applications, ranging from adversarial training and policy evaluation in reinforcement learning to AUROC maximization. To address the large-scale data challenges across multiple clients with communication-efficient distributed training, federated learning (FL) is gaining popularity. Many optimization algorithms for minimax problems have been developed in the centralized setting (i.e. single-machine). Nonetheless, the algorithm for minimax problems under FL is still underexplored. In this paper, we study a class of federated nonconvex minimax optimization problems. We propose FL algorithms (FedSGDA+ and FedSGDA-M) and reduce existing complexity results for the most common minimax problems. For nonconvex-concave problems, we propose FedSGDA+ and reduce the communication complexity to O(varepsilon-6). Under nonconvex-strongly-concave and nonconvex-PL minimax settings, we prove that FedSGDA-M has the best-known sample complexity of O(kappa3 N-1varepsilon-3) and the best-known communication complexity of O(kappa2varepsilon-2). FedSGDA-M is the first algorithm to match the best sample complexity O(varepsilon-3) achieved by the single-machine method under the nonconvex-strongly-concave setting. Extensive experimental results on fair classification and AUROC maximization show the efficiency of our algorithms.