Background - Design and Analysis of Learning Classifier Systems - page 21

to the use of neural networks to compute the prediction [35, 175, 176, 156], and
even Support Vector Machines (SVMs) [157].
What became clear was that each classifier approximates the function that is
formed by a mapping from the value of the states to their associated payoffs,
over the states that it matches [241]. In other words, each classifier provides
a localised model of that function, where the localisation is determined by the
condition and action of the classifier — even in the initial XCS, where the model
is provided by a simple averaging over the payoff of all matched states [78]. This
concept is illustrated in Fig. 2.4.

2.3.2 Localisation and Representation

Similar progress was made in how the condition of a classifier can be represented:
while XCS initially used ternary strings for that task [237, 238], the represen-
tational repertoire was soon increased to real-numbered interval representations
to handle real-valued states [239], as a prerequisite to function approximation
with computed predictions [240, 241]. Amongst other representations used with
XCS(F) to determine the matching of a classifier are now hyper-ellipsoids [41, 41],
neural networks [38], S-expressions [144], and convex hulls [147]. Fuzzy classifier
representations [60] additionally introduce matching by degree which — despite
a different approach to their design - makes them very similar to the model that
is presented here.
The possibility of using arbitrary representations in XCS(F) to determine
matching of a classifier was highlighted in [241]. In fact, classifiers that model
the payoff for a particular set of states and a single action can conceptually
be seen as perform matching in the space of states and actions, as they only
model the payoff if their condition matches the state, and their action is the one
that is performed. Similarly, classifiers without actions, such as the ones used
for function approximation [240, 241], perform matching in the space of states
alone.

2.3.3 Classifiers as Localised Maps from Input to Output

To summarise, classifiers in XCS are localised models of the function that maps
the value of the states to their associated payoffs. The localisation is determined
by the condition/action pair that specifies which states and which actions of the
environment are matched.
When LCS are applied to regression tasks, the standard machine learning
terminology is to call the state/action pair the input and the associated payoff
the output . Thus, the localised model of a classifier provides a mapping from
the input to the output, and its localisation is determined by the input alone,
asshowninFig.2.4.
Sequential decision tasks can be mapped onto the same concept by specifying
an input by the state/action pair, and its associated output by the payoff. Simi-
larly, in classification tasks the input is given by the attributes, and the output
is the class label, as used in UCS [161], which is a variant of XCS specialised