It has been shown many times that the evolutionary online learning XCS classifier system is a robustly generalizing reinforcement learning system, which also yields highly competitive results in data mining applications. The XCSF version of the system is a real-valued function approximation system, which learns piecewise overlapping local linear models to approximate an iteratively sampled function. While the theory on the binary domain side goes as far as showing that XCS can PAC learn a slightly restricted set of k-DNF problems, theory for XCSF is still rather sparse. This paper takes the theory from the XCS side and projects it onto the real-valued XCSF domain. For a set of functions, in which fitness guidance is given, we even show that XCSF scales optimally with respect to the population size, requiring only a constant overhead to ensure that the evolutionary process can locally optimize the evolving structures. Thus, we provide foundations concerning scalability and resource management for XCSF. Furthermore, we reveal dimensions of problem difficulty for XCSF and local linear learners in general showing how structural alignment, that is, alignment of XCSF's solution representation to the problem structure, can reduce the complexity of challenging problems by orders of magnitude. © 2010 Elsevier B.V. All rights reserved.
Stalph, P. O., Llorà, X., Goldberg, D. E., & Butz, M. V. (2012). Resource management and scalability of the XCSF learning classifier system. Theoretical Computer Science, 425, 126–141. https://doi.org/10.1016/j.tcs.2010.07.007