提出新梯度方向，加速BFGS优化收敛速度
Quasi-Quadratic Gradient: A New Direction for Accelerating the BFGS Method in Quasi-Newton Optimization
- 用逆海森矩阵与当前梯度乘积定义新搜索方向
- 理论与实验均显示收敛速度显著优于原始BFGS
- 适合追求高效优化的机器学习研究人员
本文提出一种新型搜索方向——准二次梯度（Quasi-Quadratic Gradient, QQG），用于加速准牛顿优化中的BFGS方法。通过将逆海森矩阵近似与当前梯度相乘，显式利用局部二阶曲率信息来修正搜索路径。理论分析与实证结果表明，该方法在保持计算效率的同时，显著提升收敛速度，优于原始BFGS方法。
原文摘要 · Abstract (English)
In this paper, we introduce the Quasi-Quadratic Gradient (QQG), a novel search direction designed to accelerate the BFGS method within the quasi-Newton framework. By defining the QQG as the product of the inverse Hessian approximation and the current gradient, we explicitly leverage local second-order curvature to rectify the search path. Theoretical analysis and empirical results demonstrate that our approach significantly outperforms vanilla BFGS in convergence speed while maintaining computational efficiency.
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