Adaptive filter theory
Neurocomputing: foundations of research
Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Technical Note: \cal Q-Learning
Machine Learning
Linear least-squares algorithms for temporal difference learning
Machine Learning - Special issue on reinforcement learning
Numerical Recipes in C++: the art of scientific computing
Numerical Recipes in C++: the art of scientific computing
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Introduction to Reinforcement Learning
Introduction to Reinforcement Learning
Classifiers that approximate functions
Natural Computing: an international journal
Least-Squares Temporal Difference Learning
ICML '99 Proceedings of the Sixteenth International Conference on Machine Learning
A Preliminary Investigation of Modified XCS as a Generic Data Mining Tool
IWLCS '01 Revised Papers from the 4th International Workshop on Advances in Learning Classifier Systems
Extending XCSF beyond linear approximation
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
XCS with computed prediction in multistep environments
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Classifier fitness based on accuracy
Evolutionary Computation
IEEE Transactions on Evolutionary Computation
Recursive least squares and quadratic prediction in continuous multistep problems
Proceedings of the 10th annual conference companion on Genetic and evolutionary computation
Hierarchical evolution of linear regressors
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Analysis and Improvements of the Classifier Error Estimate in XCSF
Learning Classifier Systems
Evolving Classifiers Ensembles with Heterogeneous Predictors
Learning Classifier Systems
Learning sensorimotor control structures with XCSF: redundancy exploitation and dynamic control
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Modularization of xcsf for multiple output dimensions
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Resource management and scalability of the XCSF learning classifier system
Theoretical Computer Science
Filtering sensory information with XCSF: improving learning robustness and control performance
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Self organizing classifiers and niched fitness
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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We analyze generalization in XCSF and introduce three improvements. We begin by showing that the types of generalizations evolved by XCSF can be influenced by the input range. To explain these results we present a theoretical analysis of the convergence of classifier weights in XCSF which highlights a broader issue. In XCSF, because of the mathematical properties of the Widrow-Hoff update, the convergence of classifier weights in a given subspace can be slow when the spread of the eigenvalues of the autocorrelation matrix associated with each classifier is large. As a major consequence, the system's accuracy pressure may act before classifier weights are adequately updated, so that XCSF may evolve piecewise constant approximations, instead of the intended, and more efficient, piecewise linear ones. We propose three different ways to update classifier weights in XCSF so as to increase the generalization capabilities of XCSF: one based on a condition-based normalization of the inputs, one based on linear least squares, and one based on the recursive version of linear least squares. Through a series of experiments we show that while all three approaches significantly improve XCSF, least squares approaches appear to be best performing and most robust. Finally we show how XCSF can be extended to include polynomial approximations.