控制理论与应用2024，Vol.41Issue(7)：1187-1196,10.DOI:10.7641/CTA.2024.30534
基于鲁棒控制的自适应分数阶梯度优化算法设计
The novel adaptive fractional order gradient decent algorithms design via robust control
摘要
Abstract
The vanilla fractional order gradient descent may converge to a region around the global minimum instead of converging to the exact minimum point,or even diverge,in the case where the objective function is strongly convex.To address this problem,a novel adaptive fractional order gradient descent(AFOGD)method and a novel adaptive fractional order accelerated gradient descent(AFOAGD)method are proposed in this paper.Inspired by the quadratic constraints and Lyapunov stability analysis from robust control theory,we establish a linear matrix inequality to analyse the convergence of our proposed algorithms.We prove that our proposed algorithms can achieve R-l inear convergence when the objective function is L-smooth and m-strongly-convex.Several numerical simulations are demonstrated to verify the effectiveness and superiority of our proposed algorithms.关键词
梯度下降法/自适应算法/鲁棒控制/分数阶微积分/加速算法Key words
gradient descent/adaptive algorithm/robust control/fractional order calculus/accelerated algorithm引用本文复制引用
刘佳旭,陈嵩,蔡声泽,许超,褚健..基于鲁棒控制的自适应分数阶梯度优化算法设计[J].控制理论与应用,2024,41(7):1187-1196,10.基金项目
Supported by the Science and Technology Innovation 2030 New Generation Artificial Intelligence Major Project(2018AAA0100902),the National Key Research and Development Program of China(2019YFB1705800)and the National Natural Science Foundation of China(61973270). （2018AAA0100902）
