1. Support Vector Machines for
Computing Action Mappings in
Learning Classifier Systems
Daniele Loiacono, Andrea Marelli, Pier Luca Lanzi
Politecnico di Milano, Italy
Illinois Genetic Algorithms Laboratory,
University of Illinois at Urbana Champaign, USA
CEC 2007, Singapore, September 26, 2007

2. One Minute Intro to Classifier Systems
Solution
Condition-action rules
Representation
Problem
Online RL Genetic
Evaluate Search
Algorithm

3. One Minute Intro to Classifier Systems
If condition C holds in state S, then action A will produce
a payoff p, with an error ε and an accuracy F

4. Many actions = many decisions
The more the actions,
the more difficult the learning
Too many actions?
Compute actions,
don’t represent them!

5. (our way to) Computed Actions
If condition C holds in state S, then action Af(st,w)
a will produce
st,
is payoff p, by an error ε, ε and an as accurate as F
a affected with an error i.e., it is accuracy F
Classifiers are made of
The condition
The parameter vector w to compute the action
The error ε
The fitness F
There is no action! There is no reward.
The action is computed using the
action function af(st,w)

6. Testing
Classifiers matching st are put in [M]
All the actions are computed
For each action a in [M], the classification accuracy
C(st,a) is computed as,
The action with the highest accuracy is selected

7. Learning
The target action at is used to update w
Classifier error is updated according to
a is the action computed by the classifier
εf (xt,at,a) is the error function
Several error functions, we used the simplest one:
0 if action is correct (a = at), 1000 otherwise
The others parameters are updated as usual

8. Computing Actions with SVMs
Previously, arrays of perceptrons and neural
networks proved successfull in computing the
classifier action
Why Support Vector Machines?
Good generalization capabilities
Fast convergence rate
Effective with highly non linear problems

9. Support Vector Machines
When new points are
red or blue?
SVM finds the best
separating hyperplane
The hyperplane is
defined by the nearest
points
Such points are called
Support Vectors

10. Non-linearly separable problems
Φ: x → φ(x)
INPUT SPACE FEATURES SPACE

11. Training incrementally SVM
We used a modified chunking algorithm
On the arrival of a new sample:
i. Build a training set with the most recent ΘSV Support
Vectors and the new sample
ii. Train from scratch the SVM on such training set
iii. Update the set of Support Vectors (add new ones and
remove the ones discarded in the last training process)
Computational complexity (worst case)
Update: O(2nΘSV )
n is the size of
Output: O( n (ΘSV)2 )
inputs
Memory: O(ΘSV (n + ΘSV) )

12. Experiments
Compute actions using
SVM, NN and array of perceptron
Several binary functions
Boolean Multiplexer
Binary Shift
Binary Sum
Measure the performance as
Classification accuracy
Number of classifiers

13. Boolean Multiplexer (20 bits)
Even in simple problems SVM learn faster
than perceptron and NN

14. Binary Shift
8 bits string as input, 8 bits string as output
Each bit in the output string is independent
(it depends by a single input bit)

15. Binary Sum
Input: 8 bits string (two 4 bits operand)
Output: a 5 bits string (result of a binary sum)
Each bits in the output depends by several
input bits

16. Binary Sum
SVM learns faster but NN evolves a more
compact solution

17. Conclusions
Learning actions with SVM is faster than with
than NN and perceptron
In some problems NN and perceptrons may
offer a more compact representation
SVM is not suitable when the actions can be
decomposed in independent component
(e.g. binary shift)
SVM is particularly suited for solving sparse
problems (see more later)