%0 Journal Article
%T 基于Polyak步长的动量方法<br>Polyak Step-Size for Momentum Method
%A 张欣悦
%A 张欣彤
%J Advances in Applied Mathematics
%P 117-122
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.143097
%X 近年来&#65292;动量方法广泛地应用在机器学习训练中。本文基于Polyak步长和移动平均动量(MAG)方法提出了一个新的动量方法(LAGP)&#65292;并将其与随机梯度结合&#65292;提出SLAGP方法。建立了LAGP方法在半强凸条件下的线性收敛性&#65292;以及SLAGP算法在半强凸条件下的线性收敛性。数值实验表明LAGP和SLAGP与其他流行算法相比有明显优势。<br>Recently, momentum methods have been widely adopted in training machine learning. In this paper, based on the Polyak step-size and the Moving Average Gradient (MAG) method, a new momentum method (LAGP) is proposed. By combining it with the stochastic gradient, the SLAGP method is developed. The linear convergence of the LAGP method under the semi-strongly convex condition, and the linear convergence of the SLAGP algorithm under the semi-strongly convex condition are established. Numerical experiments show that LAGP and SLAGP have significant advantages compared with other popular algorithms.
%K 机器学习&#65292
%K 动量方法&#65292
%K 自适应步长<br>Machine Learning
%K Momentum Method
%K Adaptive Step-Size
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=109062