Theoretical XCS parameter settings of learning accurate classifiers

XCS is the most popular type of Learning Classifier System, but setting optimum parameter values is more of an art than a science. Early theoretical work required the impractical assumption that classifier parameters had fully converged with infinite update times. The aim of this work is to derive a theoretical condition to mathematically guarantee that XCS identifies maximally accurate classifiers, such that subsequent deletion methods can be used optimally, in as few updates as possible. Consequently, our theory provides a universally usable setup guide for three important parameter settings; the learning rate, the accuracy update and the threshold for subsumption deletion. XCS with our best parameter settings solves the 70-bit multiplexer problem with only 21% of instances that the standard XCS setup needs. On a highly class-imbalanced multiplexer problem with inaccurate classifiers having more than 99.99% classification accuracy, our theory enables XCS to identify only 100% accurate classifiers as accurate and thus obtain the optimal performance.