# Federated Minimax Optimization: Improved Convergence Analyses and Algorithms Source: [Federated Minimax Optimization: Improved Convergence Analyses and Algorithms]() Collection index: [llms.txt]() Data updated: 2025-10-28T13:56:00.410Z Authors: Pranay Sharma, Rohan Panda, Gauri Joshi, Pramod K. Varshney Published: 2022-03-09T16:21:31.000Z ## Abstract In this paper, we consider nonconvex minimax optimization, which is gaining prominence in many modern machine learning applications such as GANs. Large-scale edge-based collection of training data in these applications calls for communication-efficient distributed optimization algorithms, such as those used in federated learning, to process the data. In this paper, we analyze Local stochastic gradient descent ascent (SGDA), the local-update version of the SGDA algorithm. SGDA is the core algorithm used in minimax optimization, but it is not well-understood in a distributed setting. We prove that Local SGDA has \\textit{order-optimal} sample complexity for several classes of nonconvex-concave and nonconvex-nonconcave minimax problems, and also enjoys \\textit{linear speedup} with respect to the number of clients. We provide a novel and tighter analysis, which improves the convergence and communication guarantees in the existing literature. For nonconvex-PL and nonconvex-one-point-concave functions, we improve the existing complexity results for centralized minimax problems. Furthermore, we propose a momentum-based local-update algorithm, which has the same convergence guarantees, but outperforms Local SGDA as demonstrated in our experiments. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on CIFAR10 (test) (AUC)](): Image Classification; CIFAR10 (test); AUC: 89.3. - [Image Classification on CATvsDOG (test)](): Image Classification; CATvsDOG (test); AUC: 89.9. - [Image Classification on Melanoma (test)](): Image Classification; Melanoma (test); AUC: 0.73. - [Image Classification on FashionMNIST (test)](): Image Classification; FashionMNIST (test); Accuracy: not recorded. ## Original sources and implementation [Original paper]() [PDF]()