This paper introduces the Multiple Greedy Quasi-Newton (MGSR1-SP) method, a novel approach to solving strongly-convex-strongly-concave (SCSC) saddle point problems. Our method enhances the approximation of the squared indefinite Hessian matrix inherent in these problems, significantly improving both stability and efficiency through iterative greedy updates. We provide a thorough theoretical analysis of MGSR1-SP, demonstrating its linear-quadratic convergence rate. Numerical experiments conducted on AUC maximization and adversarial debiasing problems, compared with state-of-the-art algorithms, underscore our method's enhanced convergence rate. These results affirm the potential of MGSR1-SP to improve performance across a broad spectrum of machine learning applications where efficient and accurate Hessian approximations are crucial.

本研究针对强凸-强凹鞍点问题提出了一种新颖的方法——多重贪婪准牛顿（MGSR1-SP）法，旨在提高本类问题中平方无定 Hessian 矩阵的近似效果，从而显著提升算法的稳定性和效率。通过对 MGSR1-SP 的理论分析，证明其线性-二次收敛率，并通过数值实验展示其在 AUC 最大化和对抗去偏问题中的优越收敛能力，表明该方法在机器学习中的广泛应用潜力。

多重贪婪准牛顿法解决鞍点问题