AI 中文总结
该研究针对二次函数梯度下降无全局参数先验知识时的快速收敛问题，提出基于局部曲率估计的自适应步长算法，经仿真验证其收敛速率优于或相当近期自适应方法。
AI 中文摘要
本文针对二次函数的梯度下降在不依赖全局函数参数先验知识的前提下实现快速收敛的问题展开研究，受光滑凸函数自适应步长算法启发，提出一种基于最小与最大局部曲率运行估计的计算轻量策略；我们证明所提算法收敛至能实现最快收敛的最优常数步长，仿真结果显示，在考虑的二次情形及逻辑分类的初步测试中，所提算法达到的收敛速率与近期自适应方法相当或更优。
英文摘要
In this paper, we address the problem of achieving fast convergence in gradient descent for quadratic functions without relying on a priori knowledge of global function parameters. Inspired by adaptive stepsize algorithms for smooth convex functions, we propose a computationally lightweight strategy based on running estimates of minimal and maximal local curvatures. We prove that our proposed algorithm converges to the optimal constant stepsize which achieves the fastest convergence. Simulations show that the convergence rate achieved by our proposed algorithm is comparable or superior to recent adaptive approaches both in the quadratic case under consideration and in a preliminary test on logistic classification.
