Bounding the Population Size in XCS to Ensure Reproductive Opportunities

Despite several recent successful comparisons and applications of the accuracy-based learning classifier system XCS, it is hardly understood how crucial parameters should be set in XCS nor how XCS can be expect to scale up in larger problems. Previous research identified a covering challenge in XCS that needs to be obeyed to ensure that the genetic learning process takes place. Furthermore, a schema challenge was identified that, once obeyed, ensures the existence of accurate classifiers. This paper departs from these challenges deriving a reproductive opportunity bound. The bound assures that more accurate classifiers get a chance for reproduction. The relation to the previous bounds as well as to the specificity pressure in XCS are discussed as well. The derived bound shows that XCS scales in a machine learning competitive way.