A formal framework and extensions for function approximation in learning classifier systems

@article{citeulike:2516703, abstract = {Abstract\ \  Learning Classifier Systems (LCS) consist of the three components: function approximation, reinforcement learning, and classifier replacement. In this paper we formalize the function approximation part, by providing a clear problem definition, a formalization of the LCS function approximation architecture, and a definition of the function approximation aim. Additionally, we provide definitions of optimality and what conditions need to be fulfilled for a classifier to be optimal. As a demonstration of the usefulness of the framework, we derive commonly used algorithmic approaches that aim at reaching optimality from first principles, and introduce a new Kalman filter-based method that outperforms all currently implemented methods, in addition to providing further insight into the probabilistic basis of the localized model that a classifier provides. A global function approximation in LCS is achieved by combining the classifier’s localized model, for which we provide a simplified approach when compared to current LCS, based on the Maximum Likelihood of a combination of all classifiers. The formalizations in this paper act as the foundation of a currently actively developed formal framework that includes all three LCS components, promising a better formal understanding of current LCS and the development of better LCS algorithms.}, author = {Drugowitsch, Jan and Barry, Alwyn }, citeulike-article-id = {2516703}, doi = {10.1007/s10994-007-5024-8}, journal = {Machine Learning}, keywords = {learning}, month = {January}, number = {1}, pages = {45--88}, posted-at = {2008-03-11 21:27:10}, priority = {2}, title = {A formal framework and extensions for function approximation in learning classifier systems}, url = {http://dx.doi.org/10.1007/s10994-007-5024-8}, volume = {70}, year = {2008} }

TY - JOUR ID - citeulike:2516703 L3 - citeulike-article-id:2516703 TI - A formal framework and extensions for function approximation in learning classifier systems JF - Machine Learning VL - 70 IS - 1 SP - 45 EP - 88 N2 - Abstract   Learning Classifier Systems (LCS) consist of the three components: function approximation, reinforcement learning, and classifier replacement. In this paper we formalize the function approximation part, by providing a clear problem definition, a formalization of the LCS function approximation architecture, and a definition of the function approximation aim. Additionally, we provide definitions of optimality and what conditions need to be fulfilled for a classifier to be optimal. As a demonstration of the usefulness of the framework, we derive commonly used algorithmic approaches that aim at reaching optimality from first principles, and introduce a new Kalman filter-based method that outperforms all currently implemented methods, in addition to providing further insight into the probabilistic basis of the localized model that a classifier provides. A global function approximation in LCS is achieved by combining the classifier’s localized model, for which we provide a simplified approach when compared to current LCS, based on the Maximum Likelihood of a combination of all classifiers. The formalizations in this paper act as the foundation of a currently actively developed formal framework that includes all three LCS components, promising a better formal understanding of current LCS and the development of better LCS algorithms. KW - learning AU - Drugowitsch, Jan AU - Barry, Alwyn PY - 2008/01/07/ UR - http://dx.doi.org/10.1007/s10994-007-5024-8 ER -