Bucket brigade performance: I. Long sequences of classifiers
Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application
Bucket brigade performance: II. Default hierarchies
Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application
Learning and bucket brigade dynamics in classifier systems
CNLS '89 Proceedings of the ninth annual international conference of the Center for Nonlinear Studies on Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks on Emergent computation
Emergent behavior in classifier systems
CNLS '89 Proceedings of the ninth annual international conference of the Center for Nonlinear Studies on Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks on Emergent computation
Adaptive filter theory (2nd ed.)
Adaptive filter theory (2nd ed.)
Neural Computation
Introduction to Reinforcement Learning
Introduction to Reinforcement Learning
Neuro-Dynamic Programming
Classifiers that approximate functions
Natural Computing: an international journal
Least Squares Policy Evaluation Algorithms with Linear Function Approximation
Discrete Event Dynamic Systems
Properties of the Bucket Brigade
Proceedings of the 1st International Conference on Genetic Algorithms
A Randomized ANOVA Procedure for Comparing Performance Curves
ICML '98 Proceedings of the Fifteenth 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
Policy Iteration for Factored MDPs
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
An Introduction to the Kalman Filter
An Introduction to the Kalman Filter
Applications of Learning Classifier Systems
Applications of Learning Classifier Systems
Extending XCSF beyond linear approximation
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Kernel-based, ellipsoidal conditions in the real-valued XCS classifier system
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
Rule-based evolutionary online learning systems: learning bounds, classification, and prediction
Rule-based evolutionary online learning systems: learning bounds, classification, and prediction
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Neural Networks: A Comprehensive Foundation (3rd Edition)
Neural Networks: A Comprehensive Foundation (3rd Edition)
Mixing independent classifiers
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Classifier fitness based on accuracy
Evolutionary Computation
Limits in long path learning with XCS
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
Toward a theory of generalization and learning in XCS
IEEE Transactions on Evolutionary Computation
Mixing independent classifiers
Proceedings of the 9th annual conference on Genetic and evolutionary computation
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
Learning Classifier Systems: Looking Back and Glimpsing Ahead
Learning Classifier Systems
Analysis and Improvements of the Classifier Error Estimate in XCSF
Learning Classifier Systems
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Fleet estimation for defence logistics using a multi-objective learning classifier system
Proceedings of the 13th 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
Online, GA based mixture of experts: a probabilistic model of ucs
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Proceedings of the 13th annual conference companion 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
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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.