%0 Journal Article
%T 一种自适应选取步长的随机交替方向乘子法<br>A Stochastic Alternating Direction Multiplier Method with Adaptive Step Selection
%A 李静
%A 薛丹
%J Advances in Applied Mathematics
%P 4090-4104
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.129401
%X 本文研究了具有可分离变量的凸随机优化问题，提出了一种新的随机交替方向乘子(ADMM)算法。该算法是ADMM与自适应选取步长的随机缩减梯度算法(SVRG-BB)的结合，利用BB步长实现了SVRG-ADMM方法自适应选取步长，而无需再使用递减步长或者手动调节步长。在一般的假设条件下，证明了算法的收敛性。 最后给出相关数值实验表明了算法的有效性。<br />
This paper considers the problem of convex stochastic optimization with separable variables. We propose a stochastic alternating direction method of multipliers (AD- MM) algorithm to solve this convex stochastic optimization problem. The algorithm can be roughly regarded as a combination of ADMM and adaptive step stochastic reduced gradient algorithm (SVRG-BB). BB step size is used to realize the adaptive step size selection by SVRG-ADMM method, without decreasing step size or manu- ally adjusting step size. Under general assumptions, the convergence of the algorithm is proved. Finally, numerical experiments are given to show the effectiveness of the algorithm.
%K 随机优化，交替方向乘子法，机器学习<br>Stochastic Optimization
%K Alternating Direction Method of Multipliers
%K Machine Learning
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=72629