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On performance evaluation in online approximation for control.

¹College of Engineering, University of California, Riverside, CA 92521-0425, USA.

IEEE Transactions on Neural Networks

|February 8, 2008

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Evaluating function approximation accuracy online requires more than just tracking errors. This study introduces two new methods to better assess on-line performance, crucial for adaptive control and machine learning.

Area of Science:

Machine Learning
Adaptive Control
Statistical Learning Theory

Background:

On-line function approximation is vital for adaptive systems.
Commonly, training or tracking errors are used to evaluate approximation accuracy.
However, these error metrics alone are insufficient to guarantee proper function approximation.

Purpose of the Study:

To highlight the inadequacy of solely relying on training/tracking errors for evaluating on-line approximation accuracy.
To introduce and present two novel methods for a more robust evaluation of on-line performance.
To connect function approximation evaluation with concepts from Probably Approximately Correct (PAC) learning and persistence of excitation.

Main Methods:

Analysis of the limitations of traditional training/tracking error evaluation.

Related Experiment Videos

Development and presentation of two alternative methodologies for on-line performance assessment.

Discussion of theoretical underpinnings from statistical learning and adaptive control.

Main Results:

Demonstration that analysis of training or tracking error is not sufficient for proper function approximation evaluation.
Introduction of two alternative methods offering a more comprehensive assessment of on-line performance.
Highlighting the relevance of Probably Approximately Correct (PAC) learning and persistence of excitation concepts.

Conclusions:

Standard error analysis methods are inadequate for validating on-line function approximation.
The proposed alternative methods provide a more rigorous evaluation of on-line performance.
A deeper understanding of on-line approximation accuracy is essential for reliable adaptive systems.