A Learning Classifier Systems Model - Design and Analysis of Learning Classifier Systems - page 36

where p N ( H ) stands for the estimated probability of head after N experiments.
This batch learning approach can be easily turned into an incremental approach
by

N− 1

p N ( H )= 1

1
N

y n = p N− 1 ( H )+ 1

N y N + N ( y N −

p N− 1 ( H )) , (3.6)

n =1

starting with p 1 ( H )= y 1 . Hence, to update the model p N− 1 ( H ) with the new
observation y N , one only needs to maintain the number N of experiments so far.
Comparing (3.5) and (3.6) it is apparent that, whilst the incremental approach
yields the same results as the batch approach, it is far less transparent in what
it is actually calculating.
Let us now assume that the coin changes its properties slowly over time, and
we therefore trust recent observations more. This is achieved by modifying the
incremental update to

p N ( H )= p N− 1 ( H )+ γ ( y N − p N− 1 ( H )) , (3.7)

where 0 <γ 1 is the recency factor that determines the influence of past

observations to the current estimate. Recursive substitution of p n ( H )resultsin
the batch learning equation

≤

N

γ ) N p 0 ( H )+ γ ) N−n y n .

p N ( H )=(1 − γ (1 − (3.8)

n =1

Inspecting this equation reveals that observations n experiments back in time
are weighted by γ (1

γ ) n . Additionally, it can be seen that an initial bias
p 0 ( H ) is introduced that decays exponentially with the number of available
observations. Again, the batch learning formulation has led to greater insight
and transparency.

−

Are LCS Batch Learners or Incremental Learners?

LCS are often considered to be incremental learners. While they are usually
implemented as such, there is no reason not to design them as batch learners
when applying them to regression or classifications tasks, given that all data is
available at once. Indeed, Pittsburgh-style LCS usually require an individual
representing a set of classifiers to be trained on the full data, and hence can
be interpreted as incrementally implemented batch learners when applied to
regression and classification tasks.
Even Michigan-style LCS can acquire batch learning when the classifiers are
trained independently: each classifier can be trained on the full data at once and
is later only queried for its fitness evaluation and its prediction.
As the aim is to understand what LCS are learning, we - for now - will prefer
transparency over performance. Hence, the LCS model is predominantly descri-
bed from a batch learning perspective, although, throughout Chaps. 5, 6 and 7,