Accuracy Exponentiation in UCS and its Effect on Voting Margins

UCS is a a Learning Classifier System (LCS) which evolves condition-action rules for supervised classification tasks. In UCS the fitness of a rule is based on its accuracy raised to a power $\nu$, and this fitness is used in both the search for good rules (via a genetic algorithm) and in a classification vote. We trace the origin of the UCS fitness function through three successive versions of the XCS accuracy function, for which we present previously unpublished details and rationales. Through numerical examples and empirical studies we demonstrate that $\nu$ tunes both selective pressure in genetic search and the voting margin in classification, and demonstrate that $\nu$ (or some alternative) is necessary for both. We appeal to margin theory to explain the effect on classification and so connect the LCS field with ensemble systems, and we suggest $\nu$ might be useful as a noise-correction parameter. We argue that the design of fitness functions has always been the central difficulty for Michigan LCSs and that better understanding can help both parameterisation of existing algorithms and development of new ones.