Abstract. A classifier system, XCSF, is introduced in which the prediction estimation mech-
anism is used to learn approximations to functions. The addition of weight vectors to the
classifiers allows piecewise-linear approximation, where the classifier’s prediction is calcu-
lated instead of being a fixed scalar. The weight vector and the classifier’s condition co-adapt.
Results on functions of up to six dimensions show high accuracy. The idea of calculating
the prediction leads to the concept of a generalized classifier in which the payoff prediction
approximates the environmental payoff function over a subspace defined by the classifier
condition and an action restriction specified in the classifier, permitting continuous-valued
actions.