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.

翻译：本文提出了多重贪婪拟牛顿法（MGSR1-SP），一种用于求解强凸-强凹（SCSC）鞍点问题的新方法。该方法通过迭代贪婪更新，显著改进了此类问题中固有的平方不定Hessian矩阵的近似，从而大幅提升了算法的稳定性和效率。我们对MGSR1-SP进行了详尽的理论分析，证明了其具有线性-二次收敛速率。在AUC最大化与对抗去偏问题上的数值实验表明，与现有先进算法相比，该方法展现出更优的收敛速率。这些结果证实了MGSR1-SP在广泛的机器学习应用中的潜力，特别是在需要高效且精确的Hessian矩阵近似的场景下，能够有效提升性能。