Multiple Greedy Quasi-Newton Methods for Saddle Point Problems

TL;DR

This paper presents MGSR1-SP, a new quasi-Newton method for saddle point problems that improves convergence and stability by better approximating the Hessian, with strong theoretical guarantees and promising experimental results.

Contribution

Introduces MGSR1-SP, a novel greedy quasi-Newton method that enhances Hessian approximation for saddle point problems, with proven linear-quadratic convergence.

Findings

Demonstrates improved convergence rate over existing methods.

Provides theoretical analysis confirming linear-quadratic convergence.

Shows effectiveness on AUC maximization and adversarial debiasing tasks.

Abstract

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.