Sparse kernel recursive least squares using L1 regularization and a fixed-point sub-iteration

2014 ◽  
Author(s):  
Badong Chen ◽  
Nanning Zheng ◽  
Jose C. Principe
Keyword(s):  
Fixed Point ◽  
Least Squares ◽  
Recursive Least Squares ◽  
Sparse Kernel

scholarly journals Kernel Recursive Least-Squares Temporal Difference Algorithms with Sparsification and Regularization

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Chunyuan Zhang ◽  
Qingxin Zhu ◽  
Xinzheng Niu
Keyword(s):  
Online Learning ◽  
Least Squares ◽  
Computational Cost ◽  
Recursive Least Squares ◽  
Learning Problems ◽  
Temporal Difference ◽  
Sparse Kernel Methods ◽  
Feature Dictionary ◽  
Window Approach ◽  
Sparse Kernel

By combining with sparse kernel methods, least-squares temporal difference (LSTD) algorithms can construct the feature dictionary automatically and obtain a better generalization ability. However, the previous kernel-based LSTD algorithms do not consider regularization and their sparsification processes are batch or offline, which hinder their widespread applications in online learning problems. In this paper, we combine the following five techniques and propose two novel kernel recursive LSTD algorithms: (i) online sparsification, which can cope with unknown state regions and be used for online learning, (ii)L2andL1regularization, which can avoid overfitting and eliminate the influence of noise, (iii) recursive least squares, which can eliminate matrix-inversion operations and reduce computational complexity, (iv) a sliding-window approach, which can avoid caching all history samples and reduce the computational cost, and (v) the fixed-point subiteration and online pruning, which can makeL1regularization easy to implement. Finally, simulation results on two 50-state chain problems demonstrate the effectiveness of our algorithms.

scholarly journals Identification by Recursive Least Squares with Kalman Filter (RLS-KF) Applied to a Robotic Manipulator

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Darielson A. Souza ◽  
Josias G. Batista ◽  
Felipe J. S. Vasconcelos ◽  
Laurinda L. N. Dos Reis ◽  
Gabriel F. Machado ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Least Squares ◽  
Robotic Manipulator ◽  
Recursive Least Squares
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