We analyze generalization in XCSF and introduce three improvements. We begin by showing that the types of generalizations evolved by XCSF can be influenced by the input range. To explain these results we present a theoretical analysis of the convergence of classifier weights in XCSF which highlights a broader issue. In XCSF, because of the mathematical properties of the Widrow-Hoff update, the convergence of classifier weights in a given subspace can be slow when the spread of the eigenvalues of the autocorrelation matrix associated with each classifier is large. As a major consequence, the system's accuracy pressure may act before classifier weights are adequately updated, so that XCSF may evolve piecewise constant approximations, instead of the intended, and more efficient, piecewise linear ones. We propose three different ways to update classifier weights in XCSF so as to increase the generalization capabilities of XCSF: one based on a condition-based normalization of the inputs, one based on linear least squares, and one based on the recursive version of linear least squares. Through a series of experiments we show that while all three approaches significantly improve XCSF, least squares approaches appear to be best performing and most robust. Finally we show how XCSF can be extended to include polynomial approximations.

Wilson's (1994) bit-register memory scheme was incorporated into the XCS classifier system and investigated in a series of non-Markov environments. Two extensions to the scheme were important in obtaining near-optimal performance in the harder environments. The first was an exploration strategy in which exploration of external actions was probabilistic as in Markov environments, but internal “actions” (register settings) were selected deterministically. The second was use of a register having more bit-positions than were strictly necessary to resolve environmental aliasing. The origins and effects of the two extensions are discussed.

In many classifier systems, the classifier strength parameter serves as a predictor of future payoff and as the classifier's fitness for the genetic algorithm. We investigate a classifier system, XCS, in which each classifier maintains a prediction of expected payoff, but the classifier's fitness is given by a measure of the prediction's accuracy. The system executes the genetic algorithm in niches defined by the match sets, instead of panmictically. These aspects of XCS result in its population tending to form a complete and accurate mapping X × A → P from inputs and actions to payoff predictions. Further, XCS tends to evolve classifiers that are maximally general, subject to an accuracy criterion. Besides introducing a new direction for classifier system research, these properties of XCS make it suitable for a wide range of reinforcement learning situations where generalization over states is desirable.

A basic classifier system, ZCS, is presented that keeps much of Holland's original framework but simplifies it to increase understandability and performance. ZCS's relation to Q-learning is brought out, and their performances compared in environments of two difficulty levels. Extensions to ZCS are proposed for temporary memory, better action selection, more efficient use of the genetic algorithm, and more general classifier representation.