一类解决极大极小值问题的学习步长算法  

A learned step-size algorithm for minimax optimization problem

作　　者：王淇淇 WANG Qi-qi(School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]北京邮电大学理学院,北京100876

出　　处：《哈尔滨商业大学学报（自然科学版）》2022年第6期742-747,共6页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金(11971073)。

摘　　要：为了解决极大极小值问题,在现有的解决此类问题的几种算法下,提出了一类改进算法,即学习步长算法.新算法将原有算法的更新格式中当前梯度项和上一步梯度项的系数,即算法的步长自动地学习出来,并可以根据当前的目标函数动态地调整步长,而不需要手动选择步长.将新算法与现有的算法在函数集上做数值实验对比,新算法的性能表现比其他算法更好.实验结果表明,针对极大极小值问题,该学习步长算法是一种有效的改进算法.In order to solve the minimax optimization problem,a new algorithm was proposed inspired by the existing algorithms for the problems,called the learned step-size algorithm.The algorithm automatically learned the coefficients of the current gradient term and the previous gradient term in the format,such that the step-size could be dynamically and automatically adjusted according to the current objective function,instead of manually choosing the step-size.Numerical experiments had been conducted to compare the learned step-size algorithm with the existing algorithms,indicating the new algorithm performed better than other algorithms.The results showed that the learned step-size algorithm was an effective algorithm.

关 键 词：极大极小值问题 鞍点 学习步长 梯度下降 优化问题 机器学习 

分 类 号：O224[理学—运筹学与控制论]