A Fast Federated Method for Minimax Problems with Sequential Convergence Guarantees

Peiran Yu, Wenhan Xian, Heng Huang

Keywords: federated learning, minimax optimization

Abstract: Federated learning (FL) has recently been actively studied to collaboratively train machine learning models across clients without directly sharing data and to address data-hungry issues. Many FL works have been focusing on minimizing a loss function but many important machine learning tasks such as adversarial training, GANs, fairness learning, and AUROC maximization are formulated as minimax problems. In this paper, we propose a new federated learning method for minimax problems. Our method allows client drift and addresses the data heterogeneity issue. In theoretical analysis, we prove that our method can improve sample complexity and has convergence guarantees for the updates of the model parameters, i.e., the sequences generated by the method. Given the Kurdyka-Łojasiewicz (KL) exponent of a novel potential function related to the objective function, we demonstrate that the sequences generated by our method converge finitely, linearly, or sublinearly. Our assumptions on the KL property are weaker than previous work on the sequential convergence of centralized minimax methods. Additionally, we further weaken the KL assumption by deducing the KL exponent of the potential function from that of the original objective function. We validate our federated learning method on AUC maximization tasks. The experimental results demonstrate that our method outperforms state-of-the-art federated learning methods when the distributions of local training data are non-IID.

Primary Area: optimization

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Submission Number: 8120