XCS Classifier System Reliably Evolves Accurate, Complete, and Minimal Representations for Boolean Functions

Abstract

Wilson’s recent XCS classifier system forms complete mappings of the payoff environment in the reinforcement learning tradition thanks to its accuracy based fitness. According to Wilson’s Generalization Hypothesis, XCS has a tendency towards generalization. With the XCS Optimality Hypothesis, I suggest that XCS systems can evolve optimal populations (representations); populations which accurately map all input/action pairs to payoff predictions using the smallest possible set of non-overlapping classifiers. The ability of XCS to evolve optimal populations for boolean multiplexer problems is demonstrated using condensation, a technique in which evolutionary search is suspended by setting the crossover and mutation rates to zero. Condensation is automatically triggered by self-monitoring of performance statistics, and the entire learning process is terminated by autotermination. Combined, these techniques allow a classifier system to evolve optimal representations of boolean functions without any form of supervision. A more complex but more robust and efficient technique for obtaining optimal populations called subset extraction is also presented and compared to condensation.