Distributed Kernel-Based Gradient Descent Algorithms
We study the generalization ability of distributed learning equipped with a divide-and-conquer approach and gradient descent algorithm in a reproducing kernel Hilbert space (RKHS). Using special spectral features of the gradient descent algorithms and a novel integral operator approach, we provide o...
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| Published in | Constructive approximation Vol. 47; no. 2; pp. 249 - 276 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.04.2018
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0176-4276 1432-0940 |
| DOI | 10.1007/s00365-017-9379-1 |
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| Abstract | We study the generalization ability of distributed learning equipped with a divide-and-conquer approach and gradient descent algorithm in a reproducing kernel Hilbert space (RKHS). Using special spectral features of the gradient descent algorithms and a novel integral operator approach, we provide optimal learning rates of
distributed gradient descent algorithms
in probability and partly conquer the saturation phenomenon in the literature in the sense that the maximum number of local machines to guarantee the optimal learning rates does not vary if the regularity of the regression function goes beyond a certain quantity. We also find that additional unlabeled data can help relax the restriction on the number of local machines in distributed learning. |
|---|---|
| AbstractList | We study the generalization ability of distributed learning equipped with a divide-and-conquer approach and gradient descent algorithm in a reproducing kernel Hilbert space (RKHS). Using special spectral features of the gradient descent algorithms and a novel integral operator approach, we provide optimal learning rates of
distributed gradient descent algorithms
in probability and partly conquer the saturation phenomenon in the literature in the sense that the maximum number of local machines to guarantee the optimal learning rates does not vary if the regularity of the regression function goes beyond a certain quantity. We also find that additional unlabeled data can help relax the restriction on the number of local machines in distributed learning. We study the generalization ability of distributed learning equipped with a divide-and-conquer approach and gradient descent algorithm in a reproducing kernel Hilbert space (RKHS). Using special spectral features of the gradient descent algorithms and a novel integral operator approach, we provide optimal learning rates of distributed gradient descent algorithms in probability and partly conquer the saturation phenomenon in the literature in the sense that the maximum number of local machines to guarantee the optimal learning rates does not vary if the regularity of the regression function goes beyond a certain quantity. We also find that additional unlabeled data can help relax the restriction on the number of local machines in distributed learning. |
| Author | Zhou, Ding-Xuan Lin, Shao-Bo |
| Author_xml | – sequence: 1 givenname: Shao-Bo surname: Lin fullname: Lin, Shao-Bo email: sblin1983@gmail.com organization: College of Mathematics and Information Science, Wenzhou University – sequence: 2 givenname: Ding-Xuan surname: Zhou fullname: Zhou, Ding-Xuan organization: Department of Mathematics, City University of Hong Kong |
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| Cites_doi | 10.1145/1327452.1327492 10.1007/978-94-009-1740-8 10.1214/17-EJS1258 10.1109/MCI.2014.2350953 10.1016/j.jco.2006.07.001 10.1007/s00365-006-0663-2 10.1109/ALLERTON.2014.7028543 10.1016/j.camwa.2008.09.014 10.1142/S0219530514500110 10.1109/TIT.2003.813564 10.1007/s10208-006-0196-8 10.1088/1361-6420/aa72b2 10.1007/s00365-006-0659-y 10.1142/S0219530510001564 10.1162/neco.2008.05-07-517 10.1109/TKDE.2013.109 10.1007/978-1-4757-2545-2 |
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| Keywords | Integral operator 41A35 Distributed learning 68T05 Gradient descent algorithm Learning theory 94A20 |
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Spark User Meetup, San Francisco, California (2013) – reference: Chang, X., Lin, S.B., Zhou, D.X.: Distributed semi-supervised learning with kernel ridge regression. J. Mach. Learn. Res. (to appear) – reference: Guo, Z.-C., Lin, S.-B., Zhou, D.-X.: Learning theory of distributed spectral algorithms. Inverse Probl. (2017). doi:10.1088/1361-6420/aa72b2 – reference: DudleyRMReal Analysis and Probability, Cambridge Studies in Advanced Mathematics 742002CambridgeCambridge University Press – reference: Dicker, L.H., Foster, D.P., Hsu, D.: Kernel ridge vs. principal component regression: minimax bounds and adaptability of regularization operators, arXiv preprint arXiv:1605.08839 (2016) – reference: LinJZhouDXLearning theory of randomized Kaczmarz algorithmJ. Mach. Learn. Res.2015163341336534505411351.62133 – reference: Lin, S.B., Guo, X., Zhou, D.X.: Distributed learning with regularized least squares. J. Mach. Learn. Res. arXiv:1608.03339v2 (2016) (revision under review) – reference: HuTFanJWuQZhouDXRegularization schemes for minimum error entropy principleAnal. Appl.201513437455334067010.1142/S02195305145001101329.68216 – reference: Balcan, M., Blum, A., Fine, S., Mansour, Y.: Distributed learning, communication complexity, and privacy. In: COLT, vol. 23 (2012) – reference: ZhangYDuchiJWainwrightMCommunication-efficient algorithms for statistical optimizationJ. Mach. Learn. Res.2013143321336331444641318.62016 – reference: ZhouZHChawlaNVJinYWilliamsGJBig data opportunities and challenges: discussions from data analytics perspectivesIEEE Comput. Intell. Mag.20149627410.1109/MCI.2014.2350953 – reference: ZhangYDuchiJWainwrightMDivide and conquer kernel ridge regression: a distributed algorithm with minimax optimal ratesJ. Mach. Learn. Res.2015163299334034505401351.62142 – reference: Lo GerfoLRosascoLOdoneFDe VitoEVerriASpectral algorithms for supervised learningNeural Comput.20082018731897241710910.1162/neco.2008.05-07-5171147.68643 – reference: van der VaartAWWellnerJAWeak Convergence and Empirical Process: with Applications to Statistics1996New YorkSpringer Series in Statistics. Springer10.1007/978-1-4757-2545-20862.60002 – reference: WuQZhouDXLearning with sample dependent hypothesis spaceComput. Math. Appl.20085628962907246767810.1016/j.camwa.2008.09.0141165.68388 – reference: Blanchard, G., Mücke, N.: Parallelizing spectral algorithms for kernel learning, arXiv preprint arXiv:1610.07487 (2016) – reference: DeanJGhemawatSMapReduce: simplified data processing on large clustersCommun. ACM20085110711310.1145/1327452.1327492 – reference: BauerFPereverzevSRosascoLOn regularization algorithms in learning theoryJ. Complex.2007235272229701510.1016/j.jco.2006.07.0011109.68088 – reference: Mann, G., McDonald, R., Mohri, M., Silberman, N., Walker, D.: Efficient large-scale distributed training of conditional maximum entropy models. In: NIPS, pp. 1231–1239 (2009) – reference: RaskuttiGWainwrightMYuBEarly stopping and non-parametric regression: an optimal data-dependent stopping ruleJ. Mach. Learn. Res.20141533536631908431318.62136 – reference: SmaleSZhouDXLearning theory estimates via integral operators and their approximationsConstr. Approx.200726153172232759710.1007/s00365-006-0659-y1127.68088 – reference: Blanchard, G., Krämer, N.: Optimal learning rates for kernel conjugate gradient regression. In: NIPS, pp. 226–234 (2010) – reference: CaponnettoADeVitoEOptimal rates for the regularized least squares algorithmFound. Comput. Math.20077331368233524910.1007/s10208-006-0196-81129.68058 – reference: YaoYRosascoLCaponnettoAOn early stopping in gradient descent learningConstr. Approx.200726289315232760110.1007/s00365-006-0663-21125.62035 – reference: EnglHWHankeMNeubauerARegularization of Inverse Problems, Mathematics and Its Applications 3751996DordrechtKluwer Academic Publishers Group10.1007/978-94-009-1740-80859.65054 – volume: 51 start-page: 107 year: 2008 ident: 9379_CR9 publication-title: Commun. ACM doi: 10.1145/1327452.1327492 – volume: 15 start-page: 335 year: 2014 ident: 9379_CR20 publication-title: J. Mach. Learn. Res. – ident: 9379_CR2 – volume: 14 start-page: 3321 year: 2013 ident: 9379_CR27 publication-title: J. Mach. Learn. Res. – ident: 9379_CR4 – volume-title: Regularization of Inverse Problems, Mathematics and Its Applications 375 year: 1996 ident: 9379_CR12 doi: 10.1007/978-94-009-1740-8 – volume: 16 start-page: 3341 year: 2015 ident: 9379_CR16 publication-title: J. Mach. Learn. 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Data Eng. doi: 10.1109/TKDE.2013.109 – volume-title: Weak Convergence and Empirical Process: with Applications to Statistics year: 1996 ident: 9379_CR23 doi: 10.1007/978-1-4757-2545-2 |
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| Title | Distributed Kernel-Based Gradient Descent Algorithms |
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