How Fitness Estimates Interact with Reproduction Rates: Towards Variable Offspring Set Sizes in XCSF

Abstract

Despite many successful applications of the XCS classifier system, a rather crucial aspect of XCS’ learning mechanism has hardly ever been modified: exactly two classifiers are reproduced when XCSF’s iterative evolutionary algorithm is applied in a sampled problem niche. In this paper, we investigate the effect of modifying the number of reproduced classifiers. In the investigated problems, increasing the number of reproduced classifiers increases the initial learning speed. In less challenging approximation problems, also the final approximation accuracy is not affected. In harder problems, however, learning may stall, yielding worse final accuracies. In this case, over-reproductions of inaccurate, ill-estimated, over-general classifiers occur. Since the quality of the fitness signal decreases if there is less time for evaluation, a higher reproduction rate can deteriorate the fitness signal, thus—dependent on the difficulty of the approximation problem—preventing further learning improvements. In order to speed-up learning where possible while still assuring learning success, we propose an adaptive offspring set size that may depend on the current reliability of classifier parameter estimates. Initial experiments with a simple offspring set size adaptation show promising results.