GECCO-2014 Learning Classifier Systems: A Gentle Introduction

Pier Luca Lanzi - GECCO-2014, July 12-16, 2014 Vancouver BC
Learning Classifier Systems
A Gentle Introduction

Outline
• Introduction
 Why? When?
 What areas? What Applications?
• Learning Classifier Systems
 What Learning?
 Classifiers?
 How do they work?
 What decisions?
 General principles
 Better classifiers
 Theory?
• Survey of applications
2

4
a real system
with an unknown
underlying
dynamics
Why? What was the goal?
if C1 :buy 30
if C2 :sell -2
…
evolved rules provide
a plausible, human
readable, model of
the unknown system
apply a classifier system online
to generate a behavior
matched the real system

To state, in concrete technical form, a model of
a complete mind and its several aspects
5
• A cognitive system interacting
with an environment
• Binary detectors and effectors
• Knowledge = set of classifiers
• Condition-action rules that
recognize a situation and
propose an action
• Payoff reservoir for
the system’s needs
• Payoff distributed through
an epochal algorithm
• Internal memory as
message list
• Genetic search of classifiers
Holland’s Vision, Cognitive System One

6Holland’s Learning Classifier Systems
• Explicit representation of the incoming reward
• Good classifiers are the
ones that predict
high rewards
• Credit Assignment using
Bucket Brigade
• Rule Discovery through
a genetic algorithm
applied to the entire
rule base (on the whole
solution)
• Description was vast
It did not work right off!
Very limited success
• David E. Goldberg: Computer-aided gas pipeline operation using genetic
algorithms and rule learning, PhD thesis. University of Michigan. Ann Arbor,
MI.
Rule Discovery Component
Perceptions
Detectors
Reward Action
Effectors
Match Set
Classifiers
matching
the current
sensory inputs
Population
Classifiers
representing
the current
knowledge
Evaluation of
the actions in
the match set
Credit Assignment
Component
1 2
3

7Learning System LS-1 &
Pittsburgh Classifier Systems
Holland models learning as ongoing adaptation process
De Jong instead views learning as optimization
Genetic algorithms applied to a population of rule sets
1. t := 0
2. Initialize the population P(t)
3. Evaluate the rules sets in P(t)
4. While the termination condition is not satisfied
5. Begin
6. Select the rule sets in P(t) and generate Ps(t)
7. Recombine and mutate the rule sets in Ps(t)
8. P(t+1) := Ps(t)
9. t := t+1
10. Evaluate the rules sets in P(t)
11. End No apportionment of credit
Offline evaluation of rule sets
Pittsburgh
Classifier
System

1970s
1980s
1990s
2000s
XCS is born, first results on classification
& robotics applications, but interest fades wa
Genetic algorithms and CS-1
Research flourishes, success is limited
Evolving rules as optimization
Research follows Holland’s vision
Success is still limited
Classifier systems finally work
Focus on classification (UCS)
Large development of models
Facetwise theory and applications
Genomic and epidemiological applications
Reinforcement
Learning
&
Machine
Learning

10Stewart W. Wilson &
The XCS Classifier System
1.Simplify the model
2.Go for accurate predictions
not high payoffs
3.Apply the genetic algorithm
to subproblems not to
the whole problem
4.Focus on classifier systems as
reinforcement learning
with rule-based generalization
5.Use reinforcement learning (Q-learning) to distribute reward
• Wilson, S.W.: Classifier Fitness Based on Accuracy. Evolutionary
Computation 3(2), 149-175 (1995).
Most developed and studied model so far

Classification
(label prediction)
Regression
(numerical
prediction)
Sequential
Decision
Making

13
Computational
Models of Cognition
Complex
Adaptive
Systems
Classification
& Data mining
Autonomous
Robotics
Others
Traffic controllers
Target recognition
Fighter maneuvering
…

15

16
• The goal is to maximize the amount of reward received
• How much future reward when at is performed in st?
• What is the expected payoff for st and at?
• Need to compute a value function, Q(st,at) payoff
Learning Classifier Systems as
Reinforcement Learning Methods
Environment
Agent
st atrt+1
st+1

How does reinforcement
learning work?
Define the inputs, the actions,
and how the reward is determined
Define the expected payoff
Compute a value function Q(st,at) mapping
state-action pairs into expected payoffs

18
• At the beginning, is initialized with random values
• At time t,
• Parameters,
 Discount factor 
 The learning rate 
 The action selection strategy
How does reinforcement learning work?
Then, Q-learning is an option.
incoming rewardnew estimate
previous value
new estimate

How does reinforcement
learning work?
Reinforcement learning assumes
that Q(st,at) is represented as a table
But the real world is complex,
the number of possible inputs can be huge!
We cannot afford an exact Q(st,at)

20The Mountain Car Example
GOAL
Task: drive an underpowered
car up a steep mountain road
st = position,
velocity
rt = 0 when goal is
reached, -1 otherwise
Value Function
Q(st,at)

21What are the issues?
•Exact representation infeasible
•Approximation mandatory
•The function is unknown,
it is learnt online from experience
Learning an unknown payoff function
while also trying to approximate it
Approximator works on intermediate estimates
While also providing information for the learning
Convergence is not guaranteed

Whats does this have to do with
Learning Classifier Systems?
They solve reinforcement learning problems
Represent the payoff function Q(st, at) as
a population of rules, the classifiers
Classifiers are evolved while
Q(st, at) is learned online

24
payoff
surface for A
What is a classifier?
IF condition C is true for input s
THEN the payoff of action A is p
s
payoff
l u
p
Condition
C(s)=l≤s≤u
General conditions covering
large portions of the problem
space
Accurate approximations

25What types of solutions?

• Two key components
• A genetic algorithm works on problem space
decomposition (condition-action)
• Supervised or reinforcement learning is used
for learning local prediction models
Problem Space

28How do learning classifier systems work?
The main performance cycle
statest
Environment
Agent

statest
Environment
Agent
Population[P]
Rulesdescribing
thecurrent solution

statest
Matching
Environment
Agent
Rulesdescribing
thecurrent solution
Population[P]
Ruleswhose
conditionmatchst
MatchSet [M]

statest
Matching
Environment
Agent
Rulesdescribing
thecurrent solution
Population[P]
Ruleswhose
conditionmatchst
MatchSet [M]
Action
Evaluation
PredictionArray
Thevalueof each
actionin[M]

How do learning classifier systems work?
32
statest
Matching
Environment
Agent
Rulesdescribing
thecurrent solution
Population[P]
Ruleswhose
conditionmatchst
MatchSet [M]
Action
Evaluation
PredictionArray
Thevalueof each
actionin[M]
Action
Selection
ActionSet [A]
Rulesin[M] withthe
selectedaction.

statest
Matching
Rulesdescribing
thecurrent solution
Population[P]
Ruleswhose
conditionmatchst
MatchSet [M]
Action
Evaluation
PredictionArray
Thevalueof each
actionin[M]
Action
Selection
ActionSet [A]
Rulesin[M] withthe
selectedaction.
actionat
Environment
Agent

statest
Matching
Environment
Agent
Rulesdescribing
thecurrent solution
Population[P]
Ruleswhose
conditionmatchst
MatchSet [M]
Action
Evaluation
PredictionArray
Thevalueof each
actionin[M]
Action
Selection
ActionSet [A]
Rulesin[M] withthe
selectedaction.
actionat
The classifiers predict an expected payoff
The incoming reward is used to update
the rules which helped in getting the reward
Any reinforcement learning algorithm can
be used to estimate the classifier prediction

statest
Matching
Rulesdescribing
thecurrent solution
Population[P]
Ruleswhose
conditionmatchst
MatchSet [M]
Action
Evaluation
PredictionArray
Thevalueof each
actionin[M]
Action
Selection
ActionSet [A]
Rulesin[M] withthe
selectedaction.
actionatrewardrt
ActionSet at t-1[A]-1
Rulesin[M] withthe
selectedaction.
Reinforcement
Learning

The reinforcement component
• For each classifier C in [A]-1 the prediction p is updated as follows:
P  r +  maxaA PredictionArray(a)
p  p + (P- p)
• Compare this with Q-learning
A rule “corresponds” to Q-table
p “corresponds” to the value Q(s,a)
P “corresponds” to “r+maxaQ(st,a)”

Where do classifiers come from?
In principle, any search method may be used
Evolutionary computation is nice because
it is representation “independent”
A genetic algorithm select, recombines,
mutate existing classifiers to search for better ones

What are the good classifiers?
What is the classifier fitness?
The goal is to approximate a target value function
with as few classifiers as possible
We wish to have an accurate approximation
One possible approach is to define fitness
as a function of the classifier prediction accuracy

What about generalization?
The genetic algorithm can take care of this
General classifiers apply more often,
thus they are reproduced more
But since fitness is based on classifiers accuracy
only accurate classifiers are likely to be reproduced
The genetic algorithm evolves
maximally general maximally accurate classifiers

41How to apply learning classifier systems
• Determine the inputs, the actions,
and how reward is distributed
• Determine what is the expected payoff
that must be maximized
• Decide an action selection strategy
• Set up the parameter 
Environment
Learning Classifier System
st rt at
• Select a representation for conditions,
the recombination and the mutation operators
• Select a reinforcement learning algorithm
• Setup the parameters, mainly the population size,
the parameters for the genetic algorithm, etc.
• Parameter 

42Things can be extremely simple!
For instance in supervised classification
Environment
example class
1 if the class is correct
0 if the class is not correct
• Select a representation for conditions and
the recombination and mutation operators
• Setup the parameters, mainly the population size,
the parameters for the genetic algorithm, etc.

An Example… 44
A1 A2 A3 A4 A5 A6 CLASS
1 1 1 1 3 1 1
1 1 1 1 3 2 1
1 1 1 3 2 1 1
1 1 1 3 3 2 1
1 1 2 3 1 2 1
1 2 1 1 1 2 1
1 2 1 1 2 1 0
1 2 1 1 3 1 0
1 2 1 1 4 2 0
1 2 1 2 1 1 1
1 2 1 2 3 1 0
… … … … … … …
Six Attributes
Severalcases
A hidden
concept…
What is the concept?

Traditional Approach?
• Classification  Trees  C4.5? ID3? CHAID? …
• Classification  Rules  CN2? C4.5rules? …
• Prediction  Trees  CART? …
45
Task
Representation
Algorithm

I Need to Classify, I Want Trees, What
Algorithm? ID3? C4.5? CHAID?
46

I Need to Classify, I Want Rules!
What Algorithm?
• OneRule
if A5 = 3 then 0 (11/19)
if A5 = 2 then 0 (11/20)
if A5 = 4 then 0 (11/23)
if A5 = 1 then 1 (29/0)
correct: 91 out of 124 training
examples.
• Rule Learner
if A5 = 4 and A1 = 1 then 0 (1/13)
if A5 = 1 then 1 (29/0)
if A4 = 2 and A5 = 2 then 0 (1/6)
if A1 = 1 and A2 = 2 then 0 (0/10)
else 0 (27/29)
correct: 87 out of 116 training examples.
47
 FOIL
is_0(A1,A2,A3,A4,A5,A6) :- a1  a2 and a5  1
Different task, different solution representation?
Completely different algorithm!

Thou shalt have no other model

Genetics-Based
Generalization
Accurate Estimates
About Classifiers
(Powerful RL)
Classifier
Representation

50Learning Classifier Systems:
One Principle Many Representations
Genetic
Search
Estimates
RL & MLKnowledge
Representation
Conditions &
Prediction
Ternary Conditions
0, 1, #
Symbolic
Conditions
Attribute-Value
Conditions
Ternary rules
0, 1, #
if a5<2 or
a1=a2, class=1
if A1=1and A2=11
if A1=2 andA2=21
Ternary Conditions
0, 1, #
Attribute-Value
Conditions
Symbolic
Conditions
Same framework!
Just plug-in your favorite representation

52
payoff
landscape of A
What is computed prediction?
Replace the prediction p by
a parametrized function p(s,w)
s
payoff
l u
p(s,w)=w0+sw1
Condition
C(s)=l≤s≤u
Which Representation?
Which type of
approximation?
Stewart W. Wilson: Classifiers that approximate functions. Natural Computing
1(2-3): 211-234 (2002)

53Same example with computed prediction
No need to change the framework
Just plug-in your favorite estimator
Linear, Polynomial, NNs, SVMs, tile-coding
Lanzi, PL, Extending XCSF beyond linear approximation. GECCO, 2005
Loiacono D. and Lanzi P.L.. Evolving neural networks for classiﬁer prediction with XSCF. ECAI, 2006
Lanzi and Loiacono XCSF with neural prediction. IEEE CEC, 2006.
Loiacono, D., Marelli A., and Lanzi PL. Support vector regression for classiﬁer prediction. GECCO, 2007.

What do we want?
Fast learning
Learn something as soon as possible!
Accurate solutions
As the learning proceeds
the solution accuracy should improve

Is there another approach?
payoff
landscape
s
payoff
l u
p(s,w)=w0
p(s,w)=w1s+w0p(s,w)=NN(s,w)
Initially, constant
prediction may be good
As learn proceeds,
the solution should improve…
… as much as possible.
55

Ensemble Classifiers 56
None of prediction models is the “best”
Let evolution search for the “most suited”
NN
Almost as fast as using best model
Model is adapted effectively in each subspace

Learning Classifier Systems
Representation, Reinforcement Learning,
& Genetics-based Search
Unified theory is impractical
Develop facetwise models

59Facetwise Models for a Theory of Evolution
and Learning
• Prof. David E. Goldberg
University of Illinois at Urbana Champaign
• Facetwise approach for the analysis
and the design of genetic algorithms
• In learning classifier systems
 Separate learning from evolution
 Simplify the problem by focusing
only on relevant aspect
 Derive facetwise models
• Applied to model several aspects of evolution

S([A]) = S([P])/(2-S([P]))
Since the genetic algorithm is applied to the action set,
there is a generalization pressure regulated by this equation.
N>-log(1-θ)/p
Given the probability θ to maintain all the subsolutions
with occurrence probability p, then the population size N …
O(L 2o+a)
Time to converge for a problem of L bits order o
and with a problem classes
Martin V. Butz, Tim Kovacs, Pier Luca Lanzi, Stewart W. Wilson: Toward a theory of generalization and
learning in XCS. IEEE Trans. Evolutionary Computation 8(1): 28-46 (2004)
Martin V. Butz, Kumara Sastry, David E. Goldberg: Strong, Stable, and Reliable Fitness Pressure in XCS
due to Tournament Selection. Genetic Programming and Evolvable Machines 6(1): 53-77 (2005)
Martin V. Butz, David E. Goldberg, Pier Luca Lanzi: Bounding Learning Time in XCS. GECCO (2) 2004:
739-750

What the Advanced Topics?
• Models Tailored for Applications
Anticipatory Behavior (ACS)
Data Mining, classification and prediction (e.g., UCS)
Epidemiology (e.g., EpiCS, EpiXCS)
ExSTraCS (Bioinformatics)
• Improved representations of conditions (GP, GEP, …)
• Improved representations of actions (GP, Code
Fragments)
• Improved genetic search (EDAs, ECGA, BOA, ….)
• Improved estimators
• Scalability
Matching
Distributed models
62

64
Computational
Models of Cognition
Complex
Adaptive
Systems
Classification
& Data mining
Autonomous
Robotics
Others
Traffic controllers
Target recognition
Fighter maneuvering
…

66What Applications?
Computational Models of Cognition
• Learning classifier system model
certain aspects of cognition
 Human language learning
 Perceptual category learning
 Affect theory
 Anticipatory and latent learning
• Learning classifier systems provide good
models for animals in experiments
in which the subjects must learn internal
models to perform as well as they do
• Martin V. Butz, University of Würzburg,
Department of Cognitive Psychology III
Cognitive Bodyspaces:
Learning and Behavior (COBOSLAB)
• Wolfgang Stolzmann, Daimler Chrysler
• Rick R. Riolo, University of Michigan,
Center for the Study of Complex Systems

67References
• Butz, M.V.: Anticipatory Learning Classifier Systems, Genetic
Algorithms and Evolutionary Computation, vol. 4.
Springer-Verlag (2000)
• Riolo, R.L.: Lookahead Planning and
Latent Learning in a Classifier System.
In: J.A. Meyer, S.W. Wilson (eds.)
From Animals to Animats 1.
Proceedings of the First International
Conferenceon Simulation of Adaptive
Behavior (SAB90), pp. 316{326.
A Bradford Book. MIT Press (1990)
• Stolzmann, W. and Butz, M.V. and Hoffman, J. and Goldberg, D.E.:
First Cognitive Capabilities in the Anticipatory Classifier System. In:
From Animals to Animats: Proceedings of the Sixth International
Conference on Simulation of Adaptive Behavior. MIT Press (2000)

Computational Economics
• To models one single agent acting in
the market (BW Arthur, JH Holland, B LeBaron)
• To model many interactive agents each one
controlled by its own classifier system.
• Modeling the behavior of agents trading
risk free bonds and risky assets
• Different trader types modeled by supplying
different input information sets
to a group of homogenous agents
• Later extended to a multi-LCS architecture
applied to portfolio optimization
• Technology startup company
founded in March 2005

70References
• Sor Ying (Byron) Wong, Sonia Schulenburg: Portfolio allocation using
XCS experts in technical analysis, market conditions and options
market. GECCO (Companion) 2007: 2965-2972
• Sonia Schulenburg, Peter Ross: An Adaptive Agent Based Economic
Model. Learning Classifier Systems 1999: 263-282
• BW Arthur, J.H. Holland, B. LeBaron, R. Palmer, and P. Tayler: "Asset
Pricing Under Endogenous Expectations in an Artificial Stock Market,“
in The Economy as an Evolving Complex System II. Edited (with S.
Durlauf and D. Lane), Addison-Wesley, 1997.
• BW Arthur, R. Palmer, J. Holland, B. LeBaron, and P. Taylor:
"Artificial Economic Life: a Simple Model of a Stockmarket,“ Physica
D, 75, 264-274, 1994

Classification and Data Mining
• Bull, L. (ed) Applications of Learning
Classifier Systems. Springer. (2004)
• Bull, L., Bernado Mansilla, E. & Holmes, J.
(eds) Learning Classifier Systems in
Data Mining. Springer. (2008)
• Nowadays, by far the most important
application domain for LCSs
• Many models GA-Miner, REGAL, GALE GAssist
• Performance comparable to state of the art machine learning
Human Competitive Results 2007
X Llorà, R Reddy, B Matesic, R Bhargava: Towards Better than
Human Capability in Diagnosing Prostate Cancer Using Infrared
Spectroscopic Imaging

Hyper-Heuristics
• Ross P., Marin-Blazquez J., Schulenburg S.,
and Hart E., Learning a Procedure that can
Solve Hard Bin-packing Problems: A New
GA-Based Approach to Hyper-Heuristics.
In Proceedings of GECCO 2003
• Bin-packing and timetabling problems
• Pick a set of non-evolutionary heuristics
• Use classifier system to learn a solution process
not a solution
• The classifier system learns a sequence of heuristics which should be
applied to gradually transform the problem from its initial state to its
final solved state.

Epidemiologic Surveillance
• John H. Holmes
Center for Clinical Epidemiology & Biostatistics
Department of Biostatistics & Epidemiology
University of Pennsylvania - School of Medicine
• Epidemiologic surveillance data
need adaptivity to abrupt changes
• Readable rules are attractive
• Performance similar to state
of the art machine learning
• But several important
feature-outcome relationships
missed by other methods were discovered
• Similar results were reported by
Stewart Wilson for breast cancer data

77References
• John H. Holmes, Jennifer A. Sager: Rule Discovery in Epidemiologic
Surveillance Data Using EpiXCS: An Evolutionary Computation
Approach. AIME 2005: 444-452
• John H. Holmes, Dennis R. Durbin, Flaura K. Winston: A New
Bootstrapping Method to Improve Classification Performance in
Learning Classifier Systems. PPSN 2000: 745-754
• John H. Holmes, Dennis R. Durbin, Flaura K. Winston: The learning
classifier system: an evolutionary computation approach to knowledge
discovery in epidemiologic surveillance. Artificial Intelligence in
Medicine 19(1): 53-74 (2000)

Autonomous Robotics
• In the 1990's, a major testbed
for learning classifier systems.
• Marco Dorigo and Marco Colombetti:
Robot Shaping An Experiment in Behavior
Engineering, 1997
• They introduced the concept of
robot shaping defined as the
incremental training of an autonomous agent.
• Behavior engineering methodology named BAT:
Behavior Analysis and Training.
• University of West England
applied several learning classifier system
models to several robotics problems

Modeling Artificial Ecosystems
• Jon McCormack, Monash University
• Eden: an interactive, self-generating, artificial ecosystem.
• World populated by collections of evolving virtual creatures
• Creatures move about
the environment,
 Make and listen to sounds,
 Foraging for food,
 Encountering predators,
 Mating with each other.
• Creatures evolve to
fit their landscape
• Eden has four seasons per year (15mins)
• Simple physics for rocks, biomass and sonic animals.
Jon McCormack

82Eden: An Evolutionary Sonic Ecosystem

83References
• McCormack, J. Impossible Nature The Art of Jon McCormack
Published by the Australian Centre for the Moving Image
ISBN 1 920805 08 7, ISBN 1 920805 09 5 (DVD)
• J. McCormack: New Challenges
for Evolutionary Music and Art,
ACM SIGEVOlution Newsletter,
Vol. 1(1), April 2006, pp. 5-11.
• McCormack, J. 2005, 'On the
Evolution of Sonic Ecosystems'
in Adamatzky, et al. (eds),
Artificial Life Models in Software,
Springer, Berlin.
• McCormack, J. 2003, 'Evolving Sonic Ecosystems', Kybernetes,
32(1/2), pp. 184-202.

Chemical and Neuronal Networks
• L. Bull, A. Budd, C. Stone, I. Uroukov,
B. De Lacy Costello and A. Adamatzky
University of the West of England
• Behaviour of non-linear media
controlled automatically through
evolutionary learning
• Unconventional computing
realised by such an approach.
• Learning classifier systems
 Control a light-sensitive sub-excitable
Belousov-Zhabotinski reaction
 Control the electrical stimulation of
cultured neuronal networks

Chemical and Neuronal Networks
• To control a light-sensitive sub-excitable BZ reaction, pulses of wave
fragments are injected into the checkerboard grid resulting in rich spatio-
temporal behaviour
• Learning classifier system can direct the fragments to an arbitrary position
through control of the light intensity within each cell
• Learning Classifier Systems control the electrical stimulation of cultured
neuronal networks such that they display elementary learning, respond to a
given input signal in a pre-specified way
• Results indicate that the learned stimulation protocols identify seemingly
fundamental properties of in vitro neuronal networks

87References
• Larry Bull, Adam Budd, Christopher Stone, Ivan Uroukov, Ben De
Lacy Costello and Andrew Adamatzky: Towards Unconventional
Computing through Simulated Evolution: Learning Classifier System
Control of Non-Linear Media
Artificial Life (to appear)
• Budd, A., Stone, C., Masere, J., Adamatzky, A., DeLacyCostello, B.,
Bull, L.: Towards machine learning control of chemical computers. In:
A. Adamatzky, C. Teuscher (eds.) From Utopian to Genuine
Unconventional Computers, pp. 17-36. Luniver Press
• Bull, L., Uroukov, I.S.: Initial results from the use of learning classier
systems to control n vitro neuronal networks. In: Lipson [189], pp.
369-376

89Conclusions
• Cognitive Modeling
• Complex Adaptive Systems
• Machine Learning
• Reinforcement Learning
• Metaheuristics
• …
 Many blocks to plug-in
 Several representations
 Several RL algorithms
 Several evolutionary methods
 …

Additional Information
• WWW
 http://gbml.org
 http://www.illigal.org
 UWE Learning Classifier Systems Group
http://www.cems.uwe.ac.uk/lcsg/
 A Learning Classifier Systems Bibliography
http://www.cs.bris.ac.uk/~kovacs/lcs/search.html
• Mailing lists
 lcs-and-gbml group @ Yahoo
• Proceedings of the International Workshop on Learning Classifier
Systems (Lanzi, Stolzmann, & Wilson, 2000, 2001, 2002; Kovacs,
Llorà, & Takadama, 2003-2005; Bacardit, Bernadó-Mansilla, Butz,
Kovacs, Llorà, Takadama, IWLCS2007)
• IWLCS here! (too bad if you did not come)
90

Books
• Bull, L. (Ed.). Applications of learning classifier systems. Berlin Heidelberg: Springer-
Verlag.
• Butz, M. V. (2002). Anticipatory learning classifier systems. Kluwer Academic
Publishers, Boston, MA.
• Butz, M. V. (2006). Rule-based evolutionary online learning systems: A principled
approach to LCS analysis and design. Studies in Fuzziness and Soft Computing Series,
Springer Verlag, Berlin Heidelberg, Germany.
• Bull, L. & Kovacs, T. (Eds.) (2005). Foundations of learning classifier systems. Berlin
Heidelberg: Springer-Verlag.
• Lanzi, P. L., Stolzmann, W., & Wilson, S. W. (Eds.) (2000). Learning classifier systems:
From foundations to applications (LNAI 1813). Berlin Heidelberg: Springer-Verlag.
• Drugowitsch, J., (2008) Design and Analysis of Learning Classifier Systems: A
Probabilistic Approach, Springer-Verlag
• Goldberg, D. E. (1989). Genetic algorithms in search, optimization & machine learning.
Addison-Wesley.
• Holland, J.H. (1975). Adaptation in natural and artificial systems. University of Michigan
Press.
• Kovacs, T. (2004). Strength of accuracy: Credit assignment in learning classifier
systems. Berlin Heidelberg: Springer-Verlag.
91

Software
• http://www.illigal.org
Martin Butz’s ACS & XCS in C and Java
Pier Luca Lanzi’s C++ XCSLib (XCS and XCSF)
• http://medal.cs.umsl.edu/files/XCSFJava1.1.zip
Martin Butz’s XCSF in Java
• http://www.ryanurbanowicz.com
Ryan’s Urbanowicz’s ExSTraCS
• Educational LCS (eLCS)
http://sourceforge.net/projects/educationallcs/
 Includes a basic guide for each implementation, which
progressively adds major components of a Michigan-Style LCS
algorithm.
 Code intended to be paired with the first LCS introductory textbook
written by Will Browne.
92

Thank you!
Questions?

GECCO-2014 Learning Classifier Systems: A Gentle Introduction

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GECCO-2014 Learning Classifier Systems: A Gentle Introduction