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

• URL: http://arxiv.org/abs/2310.03613v1
• Date: Thu, 5 Oct 2023 15:48:41 GMT
• Title: Solving a Class of Non-Convex Minimax Optimization in Federated Learning
• Authors: Xidong Wu, Jianhui Sun, Zhengmian Hu, Aidong Zhang, Heng Huang
• Abstract summary: The minimax problems arise throughout machine learning applications, ranging from machine learning training to large-scale learning. We propose a class of algorithms for non minimax problems (emphi) that reduce complexity to $varepsilon-6)$. We prove that FedSGDA-M has the best sample complexity of $O(kappa2-3)$ and the best-known communication of $O(kappa2-3)$.
• Score: 84.98927714326908
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 (\emph{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 $O(\kappa^{3} N^{-1}\varepsilon^{-3})$ and the best-known communication complexity of $O(\kappa^{2}\varepsilon^{-2})$. 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.

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