The document provides an overview of the classifier systems XCS and UCS. It describes the key components and functioning of each system. The main differences between XCS and UCS are in their explore regimes, how they update classifier parameters, and how fitness is computed. The document outlines various test problems used to experiment with XCS and UCS, including parity, decoder, imbalanced multiplexer, and position problems. It presents results on these problems to compare the performance of XCS, UCS without fitness sharing, and UCS with a proposed new fitness sharing scheme.
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IWLCS'2006: A Further Look at UCS Classifier System
1. A Further Look at UCS
Classifier System
Cl ifi S t
Albert Orriols-Puig
Ester Bernadó-Mansilla
Research Group in Intelligent Systems
Enginyeria i Arquitectura La Salle
Ramon Llull University
Barcelona, Spain
,p
2. Aim
Provide a deep insight into UCS
p g
Introduce a fitness sharing scheme in UCS
Highlight the differences between XCS and UCS
Enginyeria i Arquitectura la Salle Slide 2
GRSI
3. Outline
1. Description of XCS
2. Description of UCS
3. Differences b t
3 Diff between XCS and UCS
d
4.
4 Test-bed
5. Experimentation
6. Conclusions
Enginyeria i Arquitectura la Salle Slide 3
GRSI
4. 1. Description of XCS
2. Description of UCS
1. Description of XCS
p 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
In single-step tasks:
g p
Environment
Match Set [M]
Problem
instance
1C A PεF num as ts exp
Selected
3C A PεF num as ts exp
action
5C A PεF num as ts exp
Population [P] 6C A PεF num as ts exp
Match set
REWARD
…
generation
1C A PεF num as ts exp
Prediction Array
2C A PεF num as ts exp
3C A PεF num as ts exp
…
c1 c2 cn
4C A PεF num as ts exp
5C A PεF num as ts exp
6C A PεF num as ts exp Random Action
…
Action S t
A ti Set [A]
1C A PεF num as ts exp
Deletion
Classifier
3C A PεF num as ts exp
Selection, Reproduction,
Parameters
mutation
5C A PεF num as ts exp
Update
6C A PεF num as ts exp
…
Genetic Algorithm
Enginyeria i Arquitectura la Salle Slide 4
GRSI
5. 1. Description of XCS
2. Description of UCS
2. Description of UCS
p 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
Only for single-step tasks
y g p
Environment
Match Set [M]
M t hS t
Problem instance
P bl it
+
output class 1C A acc F num cs ts exp
3C A acc F num cs ts exp
Population [P] 5C A acc F num cs ts exp
6C A acc F num cs ts exp
…
1C A acc F num cs ts exp
2C A acc F num cs ts exp
3C A acc F num cs ts exp
4C A acc F num cs ts exp correct set Classifier
5C A acc F num cs ts exp generation
Parameters
6C A acc F num cs ts exp Match set
Update
… generation
Correct S t [C]
C t Set
3 C A acc F num cs ts exp # Correct
Deletion Selection, Reproduction,
acc =
6 C A acc F num cs ts exp
mutation
Experience
p
…
Fitness = accν
Genetic Algorithm
Enginyeria i Arquitectura la Salle Slide 5
GRSI
6. 1. Description of XCS
2. Description of UCS
3. Differences between XCS and UCS 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
Three main differences:
– Explore regime
– Parameter updates
– Fitness computation
Enginyeria i Arquitectura la Salle Slide 6
GRSI
7. 1. Description of XCS
2. Description of UCS
3. Differences between XCS and UCS 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
Explore Regime
Populations
XCS evolved
Prediction Maximal general classifiers predicting the correct class
…
c1 c2 cn
Array
Maximal general classifiers predicting the incorrect class
Random action So,
So XCS also explores low rewarded niches
[A] 1. 000 0#######:0 1000 0 …
Complete 2. 000 1#######:0 0 0…
action map …
UCS
Maximal general classifiers predicting the correct class
Environment
Always exploring the class of the input instance
Example + class
1. 000 0#######:0 1000 0 …
[C] Best 2. 000 1#######:1 0 0…
action map …
Enginyeria i Arquitectura la Salle Slide 7
GRSI
8. 1. Description of XCS
2. Description of UCS
3. Differences between XCS and UCS 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
Parameter Updates
rd
XCS
Influence of the rewar
pt +1 = pt + β (R − pt )
β=0.2
ε t +1 = ε t + β ( R − pt − ε t )
e t+2
t+1 t+3 t+4 t+5 t+6 t+7 t+8
UCS time
Influence of the reward
d
number correct
acc =
experience
time
Enginyeria i Arquitectura la Salle Slide 8
GRSI
9. 1. Description of XCS
2. Description of UCS
3. Differences between XCS and UCS 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
Fitness Sharing: XCS shares fitness but UCS does not
The advantages of fitness sharing are empirically
demonstrated (Bull & Hurst, 2002)
Scheme of fitness sharing in UCS:
if acc > acc0
⎧1
=⎨
kcl∈[C ]
α (acc / acc0 )ν otherwise
⎩ We share the accuracy
with all the classifiers
in [M]
kcl ·numcl
k 'cl =
∑ kcli ·numcli
cli ∈[ M ]
[M
F = F + β ·( k '− F )
(
Enginyeria i Arquitectura la Salle Slide 9
GRSI
10. 1. Description of XCS
2. Description of UCS
4. Test-bed 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
Problems
– Parity: two-class problem
Condition
length (l)
Number of 1 mod 2
01001010 :1
Complexity: It does not permit any generalization
– Decoder: multi-class problem
Condition
length (l)
Integer value of the input
000110 :5
Complexity: the number of classes increases with the condition length
Enginyeria i Arquitectura la Salle Slide 10
GRSI
11. 1. Description of XCS
2. Description of UCS
4. Test-bed 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
Problems
– Imbalanced Multiplexer: Imbalanced two-class problem
Condition
length (l)
Value of the position bit
000 10000100 :1 indicated by the selection bits
The class labeled as 1 is under-sampled
ir = proportion between majority
Complexity: For high imbalances there is a p
p y g poor and minority class examples
sampling of minority class examples i = log2ir
– Position: imbalanced multi-class problem
Condition
length (l)
Position of the left-most
000110 :2 one-valued
one valued bit
Complexity: the number of classes and the imbalance level
increase with the condition length
g
Enginyeria i Arquitectura la Salle Slide 11
GRSI
12. 1. Description of XCS
2. Description of UCS
4. Test-bed 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
Problems
– Multiplexer with Alternating noise
Value of the position bit
0000 1000010011100101 :1 indicated by the selection bits
The output is flipped with probability Px
Complexity: The system receives noisy instances
Enginyeria i Arquitectura la Salle Slide 12
GRSI
13. 1. Description of XCS
2. Description of UCS
5. Experimentation
p 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
We used the five binary-input problems to test:
– XCS
– UCS without fitness sharing: UCSns
– UCS with fitness sharing: UCSs
To permit comparison between XCS and UCS, we measured the
percentage of the best action map achieved
We configured XCS with the following parameters:
N=25 |[O]|, α=0.1, ν=5, Rmax = 1000, ε0=1, θGA=25, β=0.2,
χ=0.8, μ=0.4, θdel=20, δ=0.1, θsub=20, P#=0.6
selection=tournament, mutation=niched,
selection=tournament mutation=niched
GAsub=true, [A]sub=false
And for UCS, we added: acc0 = 0.999, ν=5
,
Enginyeria i Arquitectura la Salle Slide 13
GRSI
14. 1. Description of XCS
5. Experimentation 2. Description of UCS
3. Differences b. XCS and UCS
4. Test-bed
5 2 The Parity Problem
5.2. 5. Experimentation
6. Conclusions
Parity with l=3 to l 9
l 3 l=9
Complete Action Map Par3
000:0 100:1 000:1 100:0
001:1 101:0 001:0 101:1
010:1 110:0 010:0 110:1
011:0 111:1 p 011:1 111:0
When an optimal classifier is
- Correct optimalthe fitness of
discovered, classifiers
the other classifiers in the
- Incorrect optimal classifiers
population is not affected
Difficulty: Lack of fitness guidance
XCS: 00#001#:0 P = 500, ε=500
500
UCS: 00#001#:0 acc = 0.5
Enginyeria i Arquitectura la Salle Slide 14
GRSI
15. 1. Description of XCS
5. Experimentation 2. Description of UCS
3. Differences b. XCS and UCS
4. Test-bed
5 3 The Decoder Problem
5.3. 5. Experimentation
6. Conclusions
Decoder with l=3 to l 6
l 3 l=6
Complete Action Map Dec3
000:0 1##:0 #1#:0 ##1:0
XCS cannot solve Dec6 in 100,000
100 000
001:1 1##:1 #1#:1 ##0:1
learning iterations:
010:2 1##:2 #0#:2 ##1:2
UCSs slightly improves UCSns
011:3 1##:3 #0#:3 ##0:3
100:4 0##:4 #1#:4 ##1:4
101:5 0##:5 #1#:5 ##0:5
110:6 0##:6 #0#:6 ##1:6
111:7 0##:7 #0#:7 ##0:7
- Correct optimal classifiers
- Incorrect optimal classifiers
Difficulty: Multiple classes
Enginyeria i Arquitectura la Salle Slide 15
GRSI
16. 1. Description of XCS
5. Experimentation 2. Description of UCS
3. Differences b. XCS and UCS
4. Test-bed
5 3 The Decoder Problem
5.3. 5. Experimentation
6. Conclusions
Fitness Dilemma i XCS (B t et al 2003)
Fit Dil in (Butz t l
Condition Class Correct P Error
Ratio
R ti
Error increases
###1# 2 0.125 125 218.75
until P=500
##01# 2 0.250 250 375
#001# 2 0.500 500 500
0001# 2 1 1000 0
Enginyeria i Arquitectura la Salle Slide 16
GRSI
17. 1. Description of XCS
5. Experimentation 2. Description of UCS
3. Differences b. XCS and UCS
4. Test-bed
5 4 The Imbalanced Multiplexer Problem
5.4. 5. Experimentation
6. Conclusions
Imbalanced 11-Mux for i=0 to i=9
11 Mux
Example: for i=6
Complete Action Map for the Multiplexer Problem
000 0#######:0
0####### 0 000 1#######:1
1####### 1 000 0#######:1
0####### 1 000 1#######:0
1####### 0
Classifier acc F
001 #0######:0 001 #1######:1 001 #0######:1 001 #1######:0
### ########:0 0.9928 0.9302
010 ##0#####:0 010 ##1#####:1 010 ##0#####:1 010 ##1#####:0
UCSs can solve the multiplexer
000 0#######:0 1.00 1.00
011 ###0####:0 011 ###1####:1
up t 011 ###0####:1 011 ###1####:0
to i 9 and XCS up to i=8
i=9 d t i8
100 ####0###:0 100 ####1###:1 100 ####0###:1 100 ####1###:0
• Similar values of fitness
101 #####0##:0 101 #####1##:1 101 #####0##:1 101 #####1##:0
• The overgeneral has more genetic opportunities
110 ######0#:0 110 ######1#:1 110 ######0#:1 110 ######1#:0
111 #######0:0 111 #######1:1 111 #######0:1 111 #######1:0
- Correct optimal classifiers
- Incorrect optimal classifiers
The system were configured following the
guidelines in (Orriols and Bernadó, 2006)
Difficulty: As the imbalance level increases, the
sampling rate of minority class examples decreases.
That is, low search rate for promising rules
predicting the minority class
Enginyeria i Arquitectura la Salle Slide 17
GRSI
18. 1. Description of XCS
5. Experimentation 2. Description of UCS
3. Differences b. XCS and UCS
4. Test-bed
5 5 The Position Problem
5.5. 5. Experimentation
6. Conclusions
Position with l 3 to l 9
l=3 l=9
Complete Action Map for the Pos3
000:0 1##:0 #1#:0 ##1:0
XCS h to explore all the correct
has t l ll th t
001:1 1##:1 #1#:1 ##0:0
action map
01#:2 1##:2 #0#:2
UCS only0##:3
y explores the best action
p
1##:3
map - Correct optimal classifiers
- Incorrect optimal classifiers
Difficulty: Class imbalance and multiple classes.
Maximum imbalance ratio between classes:
irmax = 2l-1
Enginyeria i Arquitectura la Salle Slide 18
GRSI
19. 1. Description of XCS
5. Experimentation 2. Description of UCS
3. Differences b. XCS and UCS
4. Test-bed
5 6 The Multiplexer with Alternating Noise
5.6. 5. Experimentation
6. Conclusions
20-bit Multiplexer with alternating noise
g
Complete Action Map for the Multiplexer Problem
0000 0###############:0 0000 1###############:1 0000 0###############:1 0000 1###############:0
p
In all cases, optimal classifiers0001 #0##############:1
are
0001 #0##############:0 0001 #1##############:1 0001 #1##############:0
continuously created and removed ##0#############:1
0010 ##0#############:0 0010 ##1#############:1 0010 0010 ##1#############:0
Windowed0011 ###1############:1 0011 ###0############:1
averages make oscillate the
0011 ###0############:0 0011 ###1############:0
parameters of XCS’s classifiers 0100 ####0###########:1
0100 ####0###########:0 0100 ####1###########:1 0100 ####1###########:0
Optimal classifiers are considered #####0########## 1
as
0101 #####0########## 0
#####0##########:0 0101 #####1########## 1
#####1##########:1 0101 #####0##########:1 0101 #####1########## 0
#####1##########:0
inaccurate 0110 ######1#########:1 0110 ######0#########:1
0110 ######0#########:0 0110 ######1#########:0
A non-fitness sharing scheme presents
0111 #######0########:0 0111 #######1########:1 0111 #######0########:1 0111 #######1########:0
slightly better results
1000 ########0#######:0 0000 ########1#######:1 0000 ########0#######:1 0000 ########1#######:0
1001 #########0######:0 0001 #########1######:1 0001 #########0######:1 0001 #########1######:0
- Correct optimal classifiers
1010 ##########0#####:0 0010 ##########1#####:1 0010 ##########0#####:1 0010 ##########1#####:0
- Incorrect optimal classifiers
1011 ###########0####:0 0011 ###########1####:1 0011 ###########0####:1 0011 ###########1####:0
1100 ############0###:0 0100 ############1###:1 0100 ############0###:1 0100 ############1###:0
1101 #############0##:0 0101 #############1##:1 0101 #############0##:1 0101 #############1##:0
1110 ##############0#:0 0110 ##############1#:1 0110 ##############0#:1 0110 ##############1#:0
1111 ###############0:0 0111 ###############1:1 0111 ###############0:1 0111 ###############1:0
Difficulty: The system receive examples labeled wrongly
XCS: Optimal incorrect classifiers will receive Px positive rewards
UCS: The system will need to create classifiers
covering noisy examples. Lots of coverings.
Enginyeria i Arquitectura la Salle Slide 19
GRSI
20. 1. Description of XCS
2. Description of UCS
6. Conclusions 3. Differences b. XCS and UCS
4. Test-bed
5. Experimentation
6. Conclusions
We introduced UCS, and specialization of XCS
We improved UCS by introducing fitness sharing
– Fitness sharing is necessary in imbalanced datasets, avoiding
overgeneral classifiers when the optimal classifiers are discovered
g p
UCS presents some advantages in the tested domains:
– It does not suffer from fitness dilemma
– It only explores the correct class, decreasing the convergence time in
p
problems with large complete action maps
g p p
XCS is more general, and it can be applied to multi-step
problems
As further work, we want to analyze the differences of UCSs
and XCS with bilateral accuracy
Enginyeria i Arquitectura la Salle Slide 20
GRSI
21. A Further Look at UCS
Classifier System
Cl ifi S t
Albert Orriols-Puig
Ester Bernadó-Mansilla
Research Group in Intelligent Systems
Enginyeria i Arquitectura La Salle
Ramon Llull University
Barcelona, Spain
,p