Multikernel Passive Stochastic Gradient Algorithms and Transfer Learning
This article develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost function are evaluated. Classical passive stochastic gradient algorithms use a kernel...
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| Veröffentlicht in: | IEEE transactions on automatic control Jg. 67; H. 4; S. 1792 - 1805 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
IEEE
01.04.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9286, 1558-2523 |
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| Abstract | This article develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost function are evaluated. Classical passive stochastic gradient algorithms use a kernel that approximates a Dirac delta to weigh the gradients based on how far they are evaluated from the desired point. In this article, we construct a multikernel passive stochastic gradient algorithm. The algorithm performs substantially better in high dimensional problems and incorporates variance reduction. We analyze the weak convergence of the multikernel algorithm and its rate of convergence. In numerical examples, we study the multikernel version of the passive least mean squares algorithm for transfer learning to compare the performance with the classical passive version. |
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| AbstractList | This article develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost function are evaluated. Classical passive stochastic gradient algorithms use a kernel that approximates a Dirac delta to weigh the gradients based on how far they are evaluated from the desired point. In this article, we construct a multikernel passive stochastic gradient algorithm. The algorithm performs substantially better in high dimensional problems and incorporates variance reduction. We analyze the weak convergence of the multikernel algorithm and its rate of convergence. In numerical examples, we study the multikernel version of the passive least mean squares algorithm for transfer learning to compare the performance with the classical passive version. |
| Author | Yin, George Krishnamurthy, Vikram |
| Author_xml | – sequence: 1 givenname: Vikram orcidid: 0000-0002-4170-6056 surname: Krishnamurthy fullname: Krishnamurthy, Vikram email: vikramk@cornell.edu organization: School of Electrical and Computer Engineering, Cornell University, Ithaca, NY, USA – sequence: 2 givenname: George orcidid: 0000-0002-2951-0704 surname: Yin fullname: Yin, George email: gyin@uconn.edu organization: Department of Mathematics, University of Connecticut, Storrs, CT, USA |
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| Cites_doi | 10.1002/0471221104 10.1109/TAP.1986.1143812 10.1080/02331887708801361 10.1109/ISIT.2018.8437871 10.1109/9.481610 10.1109/TIT.1987.1057305 10.1002/SERIES1345 10.1214/aos/1176343595 10.1007/0-387-28982-8 10.1214/12-EJS675 10.1002/9780470316658 10.1109/TKDE.2009.191 10.1109/PROC.1972.8817 10.1109/TSP.2013.2254481 |
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| References | ref13 ref15 ref14 Kushner (ref12) 1984 ref20 Ethier (ref6) 1986 ref10 ref2 ref1 Nazin (ref3) 1989; 50 ref17 ref16 ref19 ref18 ref7 ref4 A (ref9) 2000; 3 Benveniste (ref11) 1990; 22 Krishnamurthy (ref8) 2020; 22 Kushner (ref5) 2003 |
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| SubjectTerms | Algorithms Approximation algorithms Bernstein von-Mises theorem Convergence Cost function Kernel Least mean squares Least mean squares algorithm Machine learning Monte Carlo methods Noise measurement Ordinary differential equations passive least mean squares (LMS) stochastic gradient algorithm stochastic sampling Transfer learning Variance analysis variance reduction weak convergence |
| Title | Multikernel Passive Stochastic Gradient Algorithms and Transfer Learning |
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