Stochastic approximation with discontinuous dynamics, differential inclusions, and applications
Stochastic approximation with discontinuous dynamics, differential inclusions, and applications
复制标题
DOI：
10.1214/22-aap1829
复制
发表时间：
2021-08
期刊：
影响因子：
--
通讯作者：
N. Nguyen;G. Yin
中科院分区：
文献类型：
--
作者：
N. Nguyen;G. Yin
这项工作发展了新的结果随机逼近算法。重点讨论了带间断的算法和极限的处理。主要内容包括微分包含，集值分析，非光滑分析和随机微分包含的使用。在广泛的条件下，它示出了一个适当的缩放序列的迭代有一个微分包含极限。此外，它是第一次显示，一个中心和缩放序列的迭代弱收敛到一个随机微分包含极限。然后将结果用于处理几个应用实例，包括马尔可夫决策过程，Lasso算法，Pegasos算法，支持向量机分类和学习。文中还提供了一些数值例子。
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and non-smooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled sequence of the iterates has a differential inclusion limit. In addition, it is shown for the first time that a centered and scaled sequence of the iterates converges weakly to a stochastic differential inclusion limit. The results are then used to treat several application examples including Markov decision process, Lasso algorithms, Pegasos algorithms, support vector machine classification, and learning. Some numerical demonstrations are also provided.