Introduction - Design and Analysis of Learning Classifier Systems - page 8

Fortunately, taking the model-centred view to finding such a definition sim-
plifies its approach significantly: a set of classifiers can be interpreted as a model
for the data. With such a perspective, the aim of finding the best set of classifiers
becomes that of finding the model that explains the data best. This is the core
problem of the field of model selection , and many methods have been develo-
ped to handle it, such as structural risk minimisation (SRM) [218], minimum
description length (MDL) [101], or Bayesian model selection [159].
The advantage of taking the model-centred approach is not only to be able
to provide a formal definition for the optimal classifier set. It also reveals the
assumptions made about the data, and hence gives us hints about the cases
in which the method might excel the performance of other related methods.
Also, the model is independent of the method to train it, and therefore we can
choose amongst several to perform this task and also acquire their performance
guarantees. Furthermore, it makes LCS directly comparable to other machine
learning methods that explicitly identify their underlying model.
The probabilistic formulation of the model underlying a set of classifiers was
inspired by the related Mixtures-of-Experts model [120, 121], which was exten-
ded such that it can describe such a set. This process was simplified by having
already analysed the function approximation and reinforcement learning compo-
nent which allowed the integration of related LCS concepts into the description
of the model. In fact, the resulting model allows for expressing both function
approximation and reinforcement learning, which makes the model-centred ap-
proach for LCS holistic — it integrates function approximation, reinforcement
learning and classifier replacement.

1.3.3 Summarising the Approach

In summary, the taken approach is the following: firstly, the relevant problem
types are described formally, followed by a probabilistic formulation of a set of
classifiers, and how such a model can be trained by methods from adaptive filter
theory [105] and statistical machine learning [19, 165], given some data.
The definition of the optimal set of classifiers that is to be sought for is based
on Bayesian model selection [19, 119], which requires a Bayesian LCS model.
Adding priors to the probabilistic LCS model results in such a Bayesian model.
It can be trained by variational Bayesian inference, and two methods of searching
the space of classifier sets are introduced. These are then used to demonstrate
that defining the best set of classifiers as the one that describes the data best
leads to viable results, as preliminary studies have already shown [82].
As handling sequential decision tasks requires the merger of the introduced
LCS model with methods from reinforcement learning, it is shown how such a
combination can be derived from first principles. One of the major issues of such
combinations is their algorithmic stability, and so we discuss how this can be
analysed. In addition, some further issues, such as learning tasks that require
long action sequences, and the exploration/exploitation dilemma, are discussed
in the light of the model.