On the scalability of XCS(F)

Many successful applications have proven the potential of Learning Classifier Systems and the XCS classifier system in particular in datamining, reinforcement learning, and function approximation tasks. Recent research has shown that XCS is a highly flexible system, which can be adapted to the task at hand by adjusting its condition structures, learning operators, and prediction mechanisms. However, fundamental theory concerning the scalability of XCS dependent on these enhancements and problem difficulty is still rather sparse and mainly restricted to boolean function problems. In this article we developed a learning scalability theory for XCSF---the XCS system applied to real-valued function approximation problems. We determine crucial dependencies on functional properties and on the developed solution representation and derive a theoretical scalability model out of these constraints. The theoretical model is verified with empirical evidence. That is, we show that given a particular problem difficulty and particular representational constraints XCSF scales optimally. In consequence, we discuss the importance of appropriate prediction and condition structures regarding a given problem and show that scalability properties can be improved by polynomial orders, given an appropriate, problem-suitable representation.

[1]  Larry Bull,et al.  A Neural Learning Classifier System with Self-Adaptive Constructivism for Mobile Robot Control , 2006, Artificial Life.

[2]  Martin V. Butz,et al.  Function Approximation With XCS: Hyperellipsoidal Conditions, Recursive Least Squares, and Compaction , 2008, IEEE Transactions on Evolutionary Computation.

[3]  Daniele Loiacono,et al.  Prediction update algorithms for XCSF: RLS, Kalman filter, and gain adaptation , 2006, GECCO '06.

[4]  Martin V. Butz,et al.  Gradient descent methods in learning classifier systems: improving XCS performance in multistep problems , 2005, IEEE Transactions on Evolutionary Computation.

[5]  Jan Drugowitsch,et al.  A formal framework and extensions for function approximation in learning classifier systems , 2007, Machine Learning.

[6]  Martin V. Butz.  Kernel-based, ellipsoidal conditions in the real-valued XCS classifier system , 2005, GECCO '05.

[7]  Christopher Stone,et al.  An analysis of continuous-valued representations for learning classifier systems , 2005 .

[8]  Martin V. Butz,et al.  Rule-Based Evolutionary Online Learning Systems - A Principled Approach to LCS Analysis and Design , 2006, Studies in Fuzziness and Soft Computing.

[9]  Daniele Loiacono,et al.  Generalization in the XCSF Classifier System: Analysis, Improvement, and Extension , 2007, Evolutionary Computation.

[10]  Stewart W. Wilson.  Classifiers that approximate functions , 2002, Natural Computing.

[11]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[12]  Ester Bernadó-Mansilla,et al.  Accuracy-Based Learning Classifier Systems: Models, Analysis and Applications to Classification Tasks , 2003, Evolutionary Computation.

[13]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[14]  Pier Luca Lanzi,et al.  An Analysis of Generalization in the XCS Classifier System , 1999, Evolutionary Computation.

[15]  John H. Holland,et al.  Cognitive systems based on adaptive algorithms , 1977, SGAR.

[16]  Martin V. Butz.  Combining Gradient-Based With Evolutionary Online Learning: An Introduction to Learning Classifier Systems , 2007, 7th International Conference on Hybrid Intelligent Systems (HIS 2007).

[17]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[18]  Martin V. Butz,et al.  Empirical analysis of generalization and learning in XCS with gradient descent , 2007, GECCO '07.

[19]  Stewart W. Wilson.  Generalization in the XCS Classifier System , 1998 .

[20]  Martin V. Butz,et al.  Toward a theory of generalization and learning in XCS , 2004, IEEE Transactions on Evolutionary Computation.

[21]  Larry Bull,et al.  A neural learning classifier system with self-adaptive constructivism , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[22]  Stewart W. Wilson.  Classifier Fitness Based on Accuracy , 1995, Evolutionary Computation.

[23]  Stewart W. Wilson.  Classifier Conditions Using Gene Expression Programming , 2008, IWLCS.

[24]  Ester Bernadó-Mansilla,et al.  Bounding XCS's parameters for unbalanced datasets , 2006, GECCO '06.

[25]  Martin V. Butz,et al.  Computational Complexity of the XCS Classifier System , 2005 .

[26]  D.E. Goldberg,et al.  Classifier Systems and Genetic Algorithms , 1989, Artif. Intell..