An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations

The stochastic approximation algorithm (SAA), starting from the pioneer work by Robbins and Monro in 1950s, has been successfully applied in systems and control, statistics, machine learning, and so forth. In this paper, we will review the development of SAA in China, to be specific, the stochastic...

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Vydané v:	Algorithms Ročník 14; číslo 6; s. 174
Hlavný autor:	Zhao, Wenxiao
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Basel MDPI AG 01.06.2021
Predmet:	Algorithms Approximation centralized and distributed algorithm Differential equations expanding truncation technique Machine learning Mathematical analysis Noise Principal components analysis Probabilistic methods stochastic approximation algorithm
ISSN:	1999-4893, 1999-4893
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Abstract	The stochastic approximation algorithm (SAA), starting from the pioneer work by Robbins and Monro in 1950s, has been successfully applied in systems and control, statistics, machine learning, and so forth. In this paper, we will review the development of SAA in China, to be specific, the stochastic approximation algorithm with expanding truncations (SAAWET) developed by Han-Fu Chen and his colleagues during the past 35 years. We first review the historical development for the centralized algorithm including the probabilistic method (PM) and the ordinary differential equation (ODE) method for SAA and the trajectory-subsequence method for SAAWET. Then, we will give an application example of SAAWET to the recursive principal component analysis. We will also introduce the recent progress on SAAWET in a networked and distributed setting, named the distributed SAAWET (DSAAWET).
AbstractList	The stochastic approximation algorithm (SAA), starting from the pioneer work by Robbins and Monro in 1950s, has been successfully applied in systems and control, statistics, machine learning, and so forth. In this paper, we will review the development of SAA in China, to be specific, the stochastic approximation algorithm with expanding truncations (SAAWET) developed by Han-Fu Chen and his colleagues during the past 35 years. We first review the historical development for the centralized algorithm including the probabilistic method (PM) and the ordinary differential equation (ODE) method for SAA and the trajectory-subsequence method for SAAWET. Then, we will give an application example of SAAWET to the recursive principal component analysis. We will also introduce the recent progress on SAAWET in a networked and distributed setting, named the distributed SAAWET (DSAAWET).
Author	Zhao, Wenxiao
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Cites_doi	10.1214/aos/1176342825 10.1049/cps2.12007 10.1016/0304-4149(87)90039-1 10.1214/aoms/1177728659 10.1214/aos/1176344259 10.1109/TSP.2008.917383 10.1214/aoms/1177729586 10.1109/TAC.2013.2264553 10.1109/TAC.2010.2041997 10.1109/TAC.2004.834113 10.1007/978-3-0348-8609-3 10.1016/S0167-6911(98)00077-2 10.1109/TAC.2007.894536 10.1109/ACSSC.2014.7094854 10.1109/TAC.2012.2188353 10.1109/ACSSC.2012.6489272 10.1137/16M1086133 10.1109/TAC.2005.846556 10.4310/CIS.2015.v15.n4.a1 10.1007/s11424-011-1015-8 10.1007/978-1-4684-9352-8 10.1137/17M1162603 10.1137/1110031 10.1137/S0363012993253534 10.1016/0378-4754(88)90073-0 10.1007/s11768-017-7086-x 10.1016/j.sysconle.2012.08.008 10.1137/S0363012995281730 10.1007/BF02917010 10.1109/TAC.1977.1101552 10.1007/s11432-012-4582-y 10.1137/S0363012995282784 10.1214/aoms/1177699797 10.1109/TAC.2010.2041686 10.1109/9.847721 10.1109/TAC.2019.2912713 10.1109/TAC.2014.2359311 10.1109/TIT.2013.2275131 10.1109/ICNN.1993.298642 10.1007/978-1-4899-2696-8 10.1109/TAC.2008.2009515 10.1016/j.automatica.2016.08.007
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SubjectTerms	Algorithms Approximation centralized and distributed algorithm Differential equations expanding truncation technique Machine learning Mathematical analysis Noise Principal components analysis Probabilistic methods stochastic approximation algorithm
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Title	An Introduction to Development of Centralized and Distributed Stochastic Approximation Algorithm with Expanding Truncations
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