Chapter 6. Conclusions
6.2 Future Works
Future work will be addressed three issues. First, this work still roughly derives cognitive learning from Cognition Psychology. As for the entire theory of cognition, lots of faultless Psychology models even Cognition Psychology models have been flooded. The better efficiency of learning mechanism by computing simulation has the possibility to been come true. Second, although this work is the first one to the aspect, we still expect more and more AI researchers would enhance their model considering this kind of philosophy thinking. Besides, from the pass to the future, the other following models with better accuracy, and the performance might be the substitution for XCS. Third, the model considering more complex factors to finance prediction issue would be declared. Actually, the ponderable model is important to apply the right factors to the right issue to obtain the remarkable outcome.
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Appendix A. Relevant XCS Statements
In this appendix, all the following statements are reference from Wilson‘s XCS. The detailed descriptions about XCS should be looked it up in [36].
z A Classifier in XCS
XCS keeps a population of classifiers which represent its knowledge about the problem.
Each classifier is a condition-action-prediction rule having the following parts:
- The condition C∈{0, 1, #}L specifies the input states (sensory situations) in which the classifier can be applied (matches).
- The action A∈{a1,..., an,} specifies the action (possibly a classification) that the classifier proposes.
- The prediction p estimates (keeps an average of) the payoff expected if the classifier matches and its action is taken by the system.
Moreover, each classifier keeps certain additional parameters:
- The prediction error ε estimates the errors made in the predictions.
- The fitness f denotes the classifier's fitness.
- The experience exp counts the number of times since its creation that the classifier has belonged to an action set.
- The time stamp ts denotes the time-step of the last occurrence of a GA in an action set to which this classifier belonged.
- The action set size as estimates the average size of the action sets this classifier has belonged to.
- The numerosity num reflects the number of micro-classifiers (ordinary classifiers) this classifier which is technically called a macroclassifier represents.
z The Different Sets
There are four different sets that need to be considered in XCS.
- The population [P] consists of all classifiers that exist in XCS at any time t.
- The match set [M] is formed out of the current [P]. It includes all classifiers that match the current situation σ(t).
- The action set [A] is formed out of the current [M]. It includes all classifiers of [M] that propose the executed action.
- The previous action set [A]-1 is the action set that was active in the last execution cycle.
z Learning Parameters in XCS
In order to control the learning process in XCS the following parameters are used:
- N specifies the maximum size of the population (in micro-classifiers, i.e., N is the sum of the classifier numerosities).
- β is the learning rate for p, ε, f, and as.
- α, ε0, and υ are used in calculating the fitness of a classifier.
- γ is the discount factor used in multi-step problems in updating classifier predictions.
- θGA is the GA threshold. The GA is applied in a set when the average time since the last GA in the set is greater than θGA.
- χ is the probability of applying crossover in the GA.
- μ specifies the probability of mutating an allele in the offspring.
- θdel is the deletion threshold. If the experience of a classifier is greater than θdel, its fitness may be considered in its probability of deletion.
- δ specifies the fraction of the mean fitness in [P] below which the fitness of a classifier may be considered in its probability of deletion.
- θsub is the subsumption threshold. The experience of a classifier must begreater than 0,0 in order to be able to subsume another classifier.
- P# is the probability of using a # in one attribute in C when covering.
- pI, εj, and fI are used as initial values in new classifiers.
- pexplr, specifies the probability during action selection of choosing the action uniform randomly.
- θmna specifies the minimal number of actions that must be present in a match set [M], or else covering will occur.
- doGASubsumption is a Boolean parameter that specifies if offspring are to be tested for possible logical subsumption by parents.
- doActionSetSubsumption is a Boolean parameter that specifies if action sets are to be tested for subsuming classifiers.
z An Algorithmic Description of XCS
This section presents the algorithms used in XCS. When XCS is started, the modules must first of all be initialized. The parameters in the environment must be set. After the initialization, the main loop is called. RUN EXPERIMENT is the main loop. Besides, GENERATE MATCH SET, DOES MATCH, GENERATE COVERING CLASSIFIER, GENERATE PREDICTION ARRAY, SELECT ACTION, GENERATE ACTION SET, UPDATE SET, UPDATE FITNESS are the detailed sub-functions, shown as following.
RUN EXPERIMENT ( ):
1 ρ-1 Å0 2 do {
3 σ Å env: get situation
4 GENERATE MATCH SET [M] out of [P] using σ 5 GENERATE PREDICTION ARRAY PA out of [M]
6 act Å SELECT ACTION according to PA
7 GENERATE ACTION SET [A] out of [M] according to act 8 env: execute action act
17 RUN GA in [A] considering v inserting and possibly deleting in [P]
18 empty [A] -1
19 else
20 [A] -1Å [A]
21 ρ-1 Å ρ 22 σ-1 Å σ
23 } while (termination criteria are not met)
GENERATE MATCH SET ([P], σ):
1 initialize empty set [M]
2 while ([M] is empty)
3 for each classifier cl in [P]
4 if (DOES MATCH classifier cl in situation σ) 5 add classifier cl to set [M]
6 if (the number of different actions in [M] < θmna)
7 GENERATE COVERING CLASSIFIER clc, considering [M] and σ 8 add classifier clc to set [P]
9 DELETE FROM POPULATION [P]
10 empty [M]
11 return [M]
DOES MATCH (cl, σ):
1 for each attribute x in Ccl
2 if(x <> # and x <> the corresponding attribute in σ) 3 return false
4 return true
GENERATE COVERING CLASSIFIER ([M], σ):
1 initialize classifier cl
2 initialize condition Ccl with the length of σ 3 for each attribute x in Ccl
1 initialize prediction array PA to all null 2 initialize fitness sum array FSA to all 0.0 3 for each classifier cl in [M]
9 for each possible action A 10 if (FSA[A] is not zero)
11 PA[A] Å PA[A] / FSA[A]
12 return PA
SELECT ACTION (PA):
1 if (RandomNumber[0, 1) < pexplr) 2 //Do pure exploration here
3 return a randomly chosen action from those not null in PA 4 else
5 //Do pure exploitation here 6 return the best action in PA
GENERATE ACTION SET ([M], act):
1 initialize empty set [A]
2 for each classifier cl in [M] 8 //update prediction error εcl
9 if (expcl < 1 / β)
10 εcl Åεcl + (|P - pcl| - εcl) / expcl
11 else
12 εcl Åεcl +β * (|P - pcl| - εcl) 13 //update action set size estimate ascl
14 if (expcl < 1 / β)
15 ascl Å ascl + (
∑
C∈ ][ A numc - ascl) / expcl16 else
17 ascl Å ascl +β * (
∑
C∈ ][ A numc - ascl) 18 UPDATE FITNESS in set [A]19 if (doActionSctSubsumption)
20 DO ACTION SET SUBSUMPTION in [A] updating [P]
UPDATE FITNESS ([A]):
1 accuracySum Å 0
2 initialize accuracy vector k 3 for each classifier cl in [A]
4 if (εcl < ε0) 5 k(cl) Å 1 6 else
7 k(cl) Å α * (εcl / ε0)-υ
8 accuracySum Å accuracySum + k(cl) * numcl
9 for each classifier cl in [A]
10 fcl Å fcl + β * (k(cl) * numcl / accuracySum - fcl)
Appendix B. Knowledge Population
Table: Knowledge Population
Knowledge Condition part Action part
1 111100000011000110000 001
2 011100000001010110100 101
3 111100000111000111010 011
4 111100000011000111100 011
5 011100000111000110000 010
6 000101001000111110011 100
7 000111001000111011100 011
8 100011100000111011111 111
9 000011100000111011111 001
10 000011100100111011001 011
11 110011101100110011000 110
12 000011100100111011000 111
13 000011100110111010111 000
14 100011100000111010010 011
15 000011111000111010010 001
16 000011100000111010001 011
17 100011100000111011101 010
18 010011101000111011100 110
19 000011111000111010100 000
20 000011100111001010001 011
21 000011100000111011000 011
22 110011101111001011000 101
23 110011101111001011111 110
24 010011101000010011100 000
25 100011100100110011000 100
26 111000001011011011000 100
27 111100000111000110000 100
28 011100101001111110110 110
29 001101100000111110110 100