一种非凸随机优化框架下的度量学习算法研究  

Research on a Metric Learning Algorithm under the Non-convex Stochastic Optimization Framework

作　　者：徐忠城 胡恩良[1,2] XU Zhongcheng;HU Enliang(School of Mathematics,Yunnan Normal University,Kunming 650500,China;Yunnan Key Laboratory of Modern Analytical Mathematics and Applications,Kunming 650500,China)

机构地区：[1]云南师范大学数学学院,云南昆明650500 [2]云南省现代分析数学及其应用重点实验室,云南昆明650500

出　　处：《现代信息科技》2025年第5期99-104,共6页Modern Information Technology

基　　金：云南省现代分析数学及其应用重点实验室(202302AN360007);国家自然科学项目(62266055)。

摘　　要：文章针对度量学习原凸问题的非凸重新表述,提出了一种带方差缩减策略的非凸随机优化算法(ML_NSVR),用于更高效地求解非凸度量学习问题。在适当的初始选择下,该算法在有限制的强凸条件下能够收敛,其收敛性得到了理论证明。数值实验验证了算法的有效性,为解决非凸度量学习问题提供了一种新的思路。同时,文章将所提算法与传统的随机梯度下降算法(SGD)和随机方差缩减梯度算法(SVRG)进行了优化效果对比。实验结果表明,ML_NSVR算法的效率更高。Aiming at the non-convex re-representation of the original convex problem in metric learning,ML_NSVR is proposed as a non-convex stochastic optimization algorithm with variance reduction strategy to solve non-convex metric learning problems more efficiently.Under appropriate initial selection,the algorithm can converge under restricted strongly convex conditions,and its convergence is proved theoretically.The effectiveness of the algorithm is verified by numerical experiments,which provides a new idea for solving non-convex metric learning problems.At the same time,this paper compares the optimization effect of the proposed algorithm with the traditional Stochastic Gradient Descent(SGD)algorithm and the Stochastic Variance Reduction Gradient(SVRG)algorithm.

关 键 词：随机优化 度量学习 方差缩减 非凸优化 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]