Mixing Independently Trained Classifiers - Design and Analysis of Learning Classifier Systems - page 99

6 Mixing Independently Trained Classifiers
An essential part of the introduced model and of LCS in general that hardly
any research has been devoted to is how to combine the local models provided
by the classifiers to produce a global model. More precisely, given an input and
the output prediction of all matched classifiers, the task is to combine these pre-
dictions to form a global prediction. This task will be called the mixing problem ,
and some model that provides an approach to this task a mixing model .
Whilst some early LCS (for example, SCS [95]) aimed at choosing a single
“best” classifier to provide the global prediction, in modern Michigan-style LCS,
predictions of matching classifiers have been mixed to give the “system predic-
tion”, that is, what will be called the global prediction. In XCS, for example,
Wilson [237] defined the mixing model as follows:
“There are several reasonable ways to determine [the global prediction]
P ( a i ). We have experimented primarily with a fitness-weighted average
of the prediction of classifiers advocating a i . Presumably, one wants a
method that yields the system's “best guess” as to the payoff [ ... ]tobe
received if a i is chosen”,
and maintains this model for all XCS derivatives without any further discussion.
As will be discussed in Sect. 6.2.5, the fitness he is referring to is a complex
heuristic measure of the quality of a classifier. While the aim is not to redefine
the fitness of a classifier in XCS, it is questioned if it is really the best measure
to use when mixing the local classifier predictions. The mixing model has been
changed in YCS [33], a simplified version of XCS and accuracy-based LCS in
general, such that the classifier update equations can be formulated by difference
equations, and by Wada et al. [223] to linearise the underlying model for the
purpose of correcting XCS for use with reinforcement learning (see Sects. 4.5
and 9.3.6). In either case the motivation for changing the mixing model differs
from the motivation in this chapter, which is to improve the performance of the
model itself, rather than to simplify it or to modify its formulation for the use
in reinforcement learning.
A formal treatment of the mixing problem requires a formal statement of the
aim that is to be reached. In a previous, related study [83] this aim was defined