Stochastic Bigger Subspace Algorithms for Nonconvex Stochastic Optimization

It is well known that the stochastic optimization problem can be regarded as one of the most hard problems since, in most of the cases, the values of f and its gradient are often not easily to be solved, or the F(∙, ξ) is normally not given clearly and (or) the distribution function P is equivocal....

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Vydané v:	IEEE access Ročník 9; s. 1
Hlavní autori:	Yuan, Gonglin, Zhou, Yingjie, Wang, Liping, Yang, Qingyuan
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Piscataway IEEE 01.01.2021 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Algorithms Approximation algorithms Complexity Complexity analysis Complexity theory Convergence Convergence property Distribution functions Machine learning Machine learning algorithms Nonconvex function Optimization Quasi Newton methods Random variables Stochastic processes Stochastic subspace algorithm
ISSN:	2169-3536, 2169-3536
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Abstract	It is well known that the stochastic optimization problem can be regarded as one of the most hard problems since, in most of the cases, the values of f and its gradient are often not easily to be solved, or the F(∙, ξ) is normally not given clearly and (or) the distribution function P is equivocal. Then an effective optimization algorithm is successfully designed and used to solve this problem that is an interesting work. This paper designs stochastic bigger subspace algorithms for solving nonconvex stochastic optimization problems. A general framework for such algorithm is presented for convergence analysis, where the so-called the sufficient descent property, the trust region feature, and the global convergence of the stationary points are proved under the suitable conditions. In the worst-case, we will turn out that the complexity is competitive under a given accuracy parameter. We will proved that the SFO-calls complexity of the presented algorithm with diminishing steplength is O(ϵ-1/1-β) and the SFO-calls complexity of the given algorithm with random constant steplength is O(ϵ-2) respectively, where β ∈ (0.5,1) and ϵ is accuracy and the needed conditions are weaker than the quasi-Newton methods and the normal conjugate gradient algorithms. The detail algorithm framework with variance reduction is also proposed for experiments and the nonconvex binary classification problem is done to demonstrate the performance of the given algorithm.
AbstractList	It is well known that the stochastic optimization problem can be regarded as one of the most hard problems since, in most of the cases, the values of <tex-math notation="LaTeX">$f$ </tex-math> and its gradient are often not easily to be solved, or the <tex-math notation="LaTeX">$F(\cdot, \xi)$ </tex-math> is normally not given clearly and (or) the distribution function <tex-math notation="LaTeX">$P$ </tex-math> is equivocal. Then an effective optimization algorithm is successfully designed and used to solve this problem that is an interesting work. This paper designs stochastic bigger subspace algorithms for solving nonconvex stochastic optimization problems. A general framework for such algorithm is presented for convergence analysis, where the so-called the sufficient descent property, the trust region feature, and the global convergence of the stationary points are proved under the suitable conditions. In the worst-case, we will turn out that the complexity is competitive under a given accuracy parameter. We will proved that the <tex-math notation="LaTeX">$SFO$ </tex-math>-calls complexity of the presented algorithm with diminishing steplength is <tex-math notation="LaTeX">$O\left({\epsilon ^{-{\frac {1}{1-\beta }}}\right)$ </tex-math> and the <tex-math notation="LaTeX">$SFO$ </tex-math>-calls complexity of the given algorithm with random constant steplength is <tex-math notation="LaTeX">$O(\epsilon ^{-2})$ </tex-math> respectively, where <tex-math notation="LaTeX">$\beta \in (0.5,1)$ </tex-math> and <tex-math notation="LaTeX">$\epsilon $ </tex-math> is accuracy and the needed conditions are weaker than the quasi-Newton methods and the normal conjugate gradient algorithms. The detail algorithm framework with variance reduction is also proposed for experiments and the nonconvex binary classification problem is done to demonstrate the performance of the given algorithm. It is well known that the stochastic optimization problem can be regarded as one of the most hard problems since, in most of the cases, the values of f and its gradient are often not easily to be solved, or the F(∙, ξ) is normally not given clearly and (or) the distribution function P is equivocal. Then an effective optimization algorithm is successfully designed and used to solve this problem that is an interesting work. This paper designs stochastic bigger subspace algorithms for solving nonconvex stochastic optimization problems. A general framework for such algorithm is presented for convergence analysis, where the so-called the sufficient descent property, the trust region feature, and the global convergence of the stationary points are proved under the suitable conditions. In the worst-case, we will turn out that the complexity is competitive under a given accuracy parameter. We will proved that the SFO-calls complexity of the presented algorithm with diminishing steplength is O(ϵ-1/1-β) and the SFO-calls complexity of the given algorithm with random constant steplength is O(ϵ-2) respectively, where β ∈ (0.5,1) and ϵ is accuracy and the needed conditions are weaker than the quasi-Newton methods and the normal conjugate gradient algorithms. The detail algorithm framework with variance reduction is also proposed for experiments and the nonconvex binary classification problem is done to demonstrate the performance of the given algorithm. It is well known that the stochastic optimization problem can be regarded as one of the most hard problems since, in most of the cases, the values of [Formula Omitted] and its gradient are often not easily to be solved, or the [Formula Omitted] is normally not given clearly and (or) the distribution function [Formula Omitted] is equivocal. Then an effective optimization algorithm is successfully designed and used to solve this problem that is an interesting work. This paper designs stochastic bigger subspace algorithms for solving nonconvex stochastic optimization problems. A general framework for such algorithm is presented for convergence analysis, where the so-called the sufficient descent property, the trust region feature, and the global convergence of the stationary points are proved under the suitable conditions. In the worst-case, we will turn out that the complexity is competitive under a given accuracy parameter. We will proved that the [Formula Omitted]-calls complexity of the presented algorithm with diminishing steplength is [Formula Omitted] and the [Formula Omitted]-calls complexity of the given algorithm with random constant steplength is [Formula Omitted] respectively, where [Formula Omitted] and [Formula Omitted] is accuracy and the needed conditions are weaker than the quasi-Newton methods and the normal conjugate gradient algorithms. The detail algorithm framework with variance reduction is also proposed for experiments and the nonconvex binary classification problem is done to demonstrate the performance of the given algorithm.
Author	Zhou, Yingjie Yang, Qingyuan Wang, Liping Yuan, Gonglin
Author_xml	– sequence: 1 givenname: Gonglin surname: Yuan fullname: Yuan, Gonglin organization: College of Mathematics and Information Science, Center for Applied Mathematics of Guangxi, Guangxi University, Nanning, Guangxi,P.R. China, 530004 – sequence: 2 givenname: Yingjie surname: Zhou fullname: Zhou, Yingjie organization: College of Mathematics and Information Science, Center for Applied Mathematics of Guangxi, Guangxi University, Nanning, Guangxi,P.R. China, 530004 – sequence: 3 givenname: Liping surname: Wang fullname: Wang, Liping organization: College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, P.R. China, 210016 – sequence: 4 givenname: Qingyuan surname: Yang fullname: Yang, Qingyuan organization: Nanning College For Vocational Technology, Nanning, Guangxi, P.R. China, 530004. (e-mail: qyyang08@163.com)
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Cites_doi	10.1016/j.irfa.2021.101676 10.1016/j.ins.2015.03.073 10.1137/S1052623497318992 10.1007/s12559-018-9583-8 10.1137/030601880 10.1145/1132973.1132979 10.1007/s10479-008-0420-4 10.1093/comjnl/7.2.149 10.1007/s10107-010-0434-y 10.1214/07-AOS546 10.1007/s11122-006-0005-2 10.1007/BFb0121128 10.1093/imanum/drl016 10.1007/s10957-015-0781-1 10.1007/s10107-014-0846-1 10.1017/CBO9781107298019 10.1090/mcom/3178 10.1137/0802003 10.1016/j.cam.2013.04.032 10.1007/s11590-008-0086-5 10.1016/j.neucom.2014.08.067 10.1016/j.najef.2021.101510 10.1137/15M1053141 10.1109/TNNLS.2018.2868835 10.1109/TNNLS.2014.2371492 10.1016/j.patcog.2010.01.013 10.1016/j.amc.2005.11.150 10.1016/S0191-2615(99)00031-4 10.1017/CBO9780511779398 10.1016/0041-5553(69)90035-4 10.1007/s10107-011-0442-6 10.1109/TSP.2014.2357775 10.1007/BF00940464 10.1214/aoms/1177728716 10.1007/BF01589116 10.1137/140961791 10.1137/120880811 10.6028/jres.049.044 10.1214/aoms/1177729586 10.1007/s10107-015-0871-8 10.1016/j.ins.2018.04.033 10.1016/j.cam.2009.08.001 10.1007/s10107-006-0708-6 10.1023/A:1022558715350 10.1137/110848864 10.1016/j.cam.2015.03.014 10.1137/130936361 10.1137/140954362 10.1137/070704277 10.1137/0330046 10.1080/17442508308833246 10.1145/1553374.1553463 10.1214/aoms/1177706619
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References	ref56 ref12 ref15 ref58 ref52 ref55 ref11 ref54 ref10 bach (ref1) 2014; 15 mokhtari (ref47) 2015; 16 mason (ref45) 1999 ref16 ref18 gaivoronski (ref19) 1978; 14 ref51 defazio (ref13) 2014 fletcher (ref17) 1997; 1 ref46 dai (ref9) 2015; 270 ref42 ref41 gower (ref25) 2016 ref44 ref49 ref8 ref7 ref3 ref6 ref5 le roux (ref40) 2012 bach (ref2) 2013 ref34 ref37 ref36 ref31 johnson (ref35) 2013; 26 ref30 polak (ref53) 1969; 3 ref33 ref32 ref39 ref38 moritz (ref48) 2016 shamir (ref59) 2013 ref71 bottou (ref4) 1998 ref70 schraudolph (ref57) 2007 ref73 ref72 tan (ref61) 2016 ref68 ref24 ref67 ref23 ref26 ref69 ref64 ref20 ref63 ref66 ref22 duchi (ref14) 2011; 12 ref65 ref21 ref28 ref27 ref29 nesterov (ref50) 2003 ref60 ref62 lucchi (ref43) 2015
References_xml	– ident: ref10 doi: 10.1016/j.irfa.2021.101676 – ident: ref60 doi: 10.1016/j.ins.2015.03.073 – ident: ref11 doi: 10.1137/S1052623497318992 – start-page: 71 year: 2013 ident: ref59 article-title: Stochastic gradient descent for non-smooth optimization: Convergence results and optimal averaging schemes publication-title: Proc Int Conf Mach Learn – ident: ref33 doi: 10.1007/s12559-018-9583-8 – ident: ref26 doi: 10.1137/030601880 – year: 2015 ident: ref43 article-title: A variance reduced stochastic Newton method publication-title: arXiv 1503 08316 – ident: ref27 doi: 10.1145/1132973.1132979 – ident: ref67 doi: 10.1007/s10479-008-0420-4 – ident: ref18 doi: 10.1093/comjnl/7.2.149 – year: 1998 ident: ref4 article-title: Online algorithms and stochastic approximations publication-title: Online Learning and Neural Networks – ident: ref38 doi: 10.1007/s10107-010-0434-y – ident: ref37 doi: 10.1214/07-AOS546 – ident: ref36 doi: 10.1007/s11122-006-0005-2 – ident: ref55 doi: 10.1007/BFb0121128 – ident: ref73 doi: 10.1093/imanum/drl016 – ident: ref69 doi: 10.1007/s10957-015-0781-1 – ident: ref23 doi: 10.1007/s10107-014-0846-1 – ident: ref58 doi: 10.1017/CBO9781107298019 – year: 2016 ident: ref61 article-title: Barzilai-Borwein step size for stochastic gradient descent publication-title: arXiv 1605 04131 – ident: ref63 doi: 10.1090/mcom/3178 – start-page: 2663 year: 2012 ident: ref40 article-title: A stochastic gradient method with an exponential convergence rate for strongly-convex optimization with finite training sets publication-title: Proc Adv Neural Inf Process Syst – ident: ref24 doi: 10.1137/0802003 – volume: 1 year: 1997 ident: ref17 publication-title: Practical Methods of Optimization Unconstrained Optimization – ident: ref70 doi: 10.1016/j.cam.2013.04.032 – ident: ref66 doi: 10.1007/s11590-008-0086-5 – start-page: 436 year: 2007 ident: ref57 article-title: A stochastic quasi-Newton method for online convex optimization publication-title: Proc Artif Intell Statist – ident: ref30 doi: 10.1016/j.neucom.2014.08.067 – ident: ref8 doi: 10.1016/j.najef.2021.101510 – ident: ref62 doi: 10.1137/15M1053141 – ident: ref34 doi: 10.1109/TNNLS.2018.2868835 – ident: ref72 doi: 10.1109/TNNLS.2014.2371492 – ident: ref32 doi: 10.1016/j.patcog.2010.01.013 – year: 2013 ident: ref2 article-title: Non-strongly-convex smooth stochastic approximation with convergence rate $O(1/n)$ publication-title: arXiv 1306 2119 – ident: ref64 doi: 10.1016/j.amc.2005.11.150 – year: 2003 ident: ref50 publication-title: Introductory Lectures on Convex Optimization A Basic Course – start-page: 1869 year: 2016 ident: ref25 article-title: Stochastic block BFGS: Squeezing more curvature out of data publication-title: Proc Int Conf Mach Learn – volume: 3 start-page: 35 year: 1969 ident: ref53 article-title: Note sur la convergence de directions conjugees publication-title: ESAIM Math Modelling Numer Anal -Modélisation Mathématique et Analyse Numérique – ident: ref5 doi: 10.1016/S0191-2615(99)00031-4 – ident: ref15 doi: 10.1017/CBO9780511779398 – ident: ref51 doi: 10.1016/0041-5553(69)90035-4 – ident: ref39 doi: 10.1007/s10107-011-0442-6 – volume: 26 start-page: 315 year: 2013 ident: ref35 article-title: Accelerating stochastic gradient descent using predictive variance reduction publication-title: Proc Adv Neural Inf Process Syst – ident: ref46 doi: 10.1109/TSP.2014.2357775 – ident: ref41 doi: 10.1007/BF00940464 – ident: ref7 doi: 10.1214/aoms/1177728716 – ident: ref42 doi: 10.1007/BF01589116 – ident: ref65 doi: 10.1137/140961791 – ident: ref21 doi: 10.1137/120880811 – ident: ref29 doi: 10.6028/jres.049.044 – volume: 270 start-page: 378 year: 2015 ident: ref9 article-title: A modified Perry's conjugate gradient method-based derivative-free method for solving large-scale nonlinear monotone equations publication-title: Appl Math Comput – ident: ref54 doi: 10.1214/aoms/1177729586 – start-page: 1646 year: 2014 ident: ref13 article-title: SAGA: A fast incremental gradient method with support for non-strongly convex composite objectives publication-title: Proc Adv Neural Inf Process Syst – volume: 14 start-page: 89 year: 1978 ident: ref19 article-title: Nonstationary stochastic programming problems publication-title: Cybernetics – ident: ref22 doi: 10.1007/s10107-015-0871-8 – start-page: 249 year: 2016 ident: ref48 article-title: A linearly-convergent stochasitic L-BFGS algorithm publication-title: Proc Artif Intell Statist – ident: ref31 doi: 10.1016/j.ins.2018.04.033 – ident: ref68 doi: 10.1016/j.cam.2009.08.001 – ident: ref3 doi: 10.1007/s10107-006-0708-6 – ident: ref28 doi: 10.1023/A:1022558715350 – ident: ref20 doi: 10.1137/110848864 – ident: ref71 doi: 10.1016/j.cam.2015.03.014 – volume: 16 start-page: 3151 year: 2015 ident: ref47 article-title: Global convergence of online limited memory BFGS publication-title: J Mach Learn Res – ident: ref12 doi: 10.1137/130936361 – ident: ref6 doi: 10.1137/140954362 – ident: ref49 doi: 10.1137/070704277 – ident: ref52 doi: 10.1137/0330046 – ident: ref16 doi: 10.1080/17442508308833246 – ident: ref44 doi: 10.1145/1553374.1553463 – volume: 12 start-page: 2121 year: 2011 ident: ref14 article-title: Adaptive subgradient methods for online learning and stochastic optimization publication-title: J Mach Learn Res – start-page: 512 year: 1999 ident: ref45 publication-title: Boosting algorithms as gradient descent in function space – volume: 15 start-page: 595 year: 2014 ident: ref1 article-title: Adaptivity of averaged stochastic gradient descent to local strong convexity for logistic regression publication-title: J Mach Learn Res – ident: ref56 doi: 10.1214/aoms/1177706619
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SubjectTerms	Algorithms Approximation algorithms Complexity Complexity analysis Complexity theory Convergence Convergence property Distribution functions Machine learning Machine learning algorithms Nonconvex function Optimization Quasi Newton methods Random variables Stochastic processes Stochastic subspace algorithm
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Title	Stochastic Bigger Subspace Algorithms for Nonconvex Stochastic Optimization
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