TY - JOUR
T1 - Online Kernel Learning with Adaptive Bandwidth by Optimal Control Approach
AU - Zhang, Jiaming
AU - Ning, Hanwen
AU - Jing, Xingjian
AU - Tian, Tianhai
N1 - Funding Information:
Manuscript received September 18, 2018; revised March 24, 2019, October 3, 2019, and February 26, 2020; accepted May 14, 2020. Date of publication June 4, 2020; date of current version May 3, 2021. This work was supported in part by the National Social Science Foundation of China under Project 19BTJ025, in part by the Fundamental Research Funds for the Central Universities under Project 2722020PY038, in part by the National Natural Science Foundation of China under Project 11301544, Project 61773401, and Project 11571368, in part by the China Scholarship Council under Project 201707085011, in part by the Research Grants Council, University Grants Committee, Hong Kong, through the General Research Fund under Project 15206717, and in part by the Internal Research Grants through The Hong Kong Polytechnic University. (Corresponding author: Hanwen Ning.) Jiaming Zhang and Hanwen Ning are with the School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China (e-mail: [email protected]; [email protected]).
Publisher Copyright:
© 2012 IEEE.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/5/3
Y1 - 2021/5/3
N2 - Online learning methods are designed to establish timely predictive models for machine learning problems. The methods for online learning of nonlinear systems are usually developed in the reproducing kernel Hilbert space (RKHS) associated with Gaussian kernel in which the kernel bandwidth is manually selected and remains steady during the entire modeling process in most cases. This setting may make the learning model rigid and inappropriate for complex data streams. Since the bandwidth appears in a nonlinear term of the kernel model, it raises substantial challenges in the development of learning methods with an adaptive bandwidth. In this article, we propose a novel approach to address this important open issue. By a carefully casted linearization scheme, the nonlinear learning problem is reasonably transformed into a state feedback control problem for a series of controllable systems. Then, by employing optimal control techniques, an effective algorithm is developed, and the parameters in the learning model including kernel bandwidth can be efficiently updated in a real-time manner. By taking advantage of the particular structure of the Gaussian kernel model, a theoretical analysis on the convergence and rationality of the proposed method is also provided. Compared with the kernel algorithms with a fixed bandwidth, our novel learning framework can not only achieve adaptive learning results with a better prediction accuracy but also show performance that is more robust with a faster convergence speed. Encouraging numerical results are provided to demonstrate the advantages of our new method.
AB - Online learning methods are designed to establish timely predictive models for machine learning problems. The methods for online learning of nonlinear systems are usually developed in the reproducing kernel Hilbert space (RKHS) associated with Gaussian kernel in which the kernel bandwidth is manually selected and remains steady during the entire modeling process in most cases. This setting may make the learning model rigid and inappropriate for complex data streams. Since the bandwidth appears in a nonlinear term of the kernel model, it raises substantial challenges in the development of learning methods with an adaptive bandwidth. In this article, we propose a novel approach to address this important open issue. By a carefully casted linearization scheme, the nonlinear learning problem is reasonably transformed into a state feedback control problem for a series of controllable systems. Then, by employing optimal control techniques, an effective algorithm is developed, and the parameters in the learning model including kernel bandwidth can be efficiently updated in a real-time manner. By taking advantage of the particular structure of the Gaussian kernel model, a theoretical analysis on the convergence and rationality of the proposed method is also provided. Compared with the kernel algorithms with a fixed bandwidth, our novel learning framework can not only achieve adaptive learning results with a better prediction accuracy but also show performance that is more robust with a faster convergence speed. Encouraging numerical results are provided to demonstrate the advantages of our new method.
KW - Adaptive kernel bandwidth
KW - online learning
KW - optimal control approach
KW - robust learning
UR - http://www.scopus.com/inward/record.url?scp=85105575387&partnerID=8YFLogxK
U2 - 10.1109/TNNLS.2020.2995482
DO - 10.1109/TNNLS.2020.2995482
M3 - Article
AN - SCOPUS:85105575387
SN - 2162-237X
VL - 32
SP - 1920
EP - 1934
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
IS - 5
M1 - 9108601
ER -