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

Code

• github.com/xidongwu/federated-minimax-and-conditional-stochastic-optimization
  OfficialIn paperpytorch★ 2

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 (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(^-6). Under nonconvex-strongly-concave and nonconvex-PL minimax settings, we prove that FedSGDA-M has the best-known sample complexity of O(^3 N^-1^-3) and the best-known communication complexity of O(^2^-2). FedSGDA-M is the first algorithm to match the best sample complexity O(^-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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