Advanced Artifical Intelligence Avoiding Bloat with Stochastic GrammarBased Genetic Programming

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Advanced Artifical Intelligence-Avoiding Bloat
with Stochastic Grammar-Based Genetic
Programming-
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Table of Contence

• Introduction
• Problem
• Repetition
• Dimensionally Awareness
• Distribution Based Evolution
• SG-GP
• Test Problem
• Results
• Conclusion

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Introduction
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion

• Aim
• Automatic discovery of Imperical Laws
• Limitations in GP
• 1. No incorporation of domain knowledge beside
  Operators
• 2. Requires huge computational Resources

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Introduction
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion

• 1. No incorporation of domain knowledge beside
  Operators
• Solution
• Application of CFG-based Grammar
• Enforcing syntactic constrains on GB solution
• dimensional consistency

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Introduction
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion

• 2. Requires huge computational Resources
• Reason
• Bloat Phenomenon (Introns)
• Early termination of GP runs due to lack of
  resources
• Increase of fitness computation cost

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Introduction
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion

• 2. Requires hudge computational Resources caused
  by Introns
• Solution
• Application of Stochastic Grammar Based GP
• Represent the distribution of the Search Space by
  a stochastic grammar

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Problem

• Why Stochastic Grammar Based GP
• Introns grow unwanted
• Pruning Introns on each generation decreases
  overall GP performance
• Why do introns appear?
• Unwanted growth of introns due to their
  statistical appearance (more long genotype)
• Crossover facilitates the production of larger
  trees (smaller trees are usually poorer fit)

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Problem

• Why Stochastic Grammar Based GP
• but
• Introns provide backup
• Protect good building blocks from destructive
  crossover
• Introns provide larger variety for crossover

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Problem

• Why Stochastic Grammar Based GP
• Reduction of Introns by
• No crossover
• No larger individuals
• No necessity of Intron backup
• Argument
• If Intron growth is per se beneficial
• SG-GP will either produce Introns despite the
  efforts of avoiding
• Or the result will be overall degraded

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Repetition
Context Free Grammar
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
GP Grammar
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Repetition
CFG Based GP Derivation Tree
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Repetition

• CFG Based GP Genetic Operators
• Crossover
• Swapping subtrees built on the same
  non-terminal symbol
• Mutation
• Replace subtree by new derivation tree built on
  the same nonterminal Symbol

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Dimensionally Awareness

• Dimensionally Aware GP introducing Bias
• Expressing domain Variables
• Vector of Elementary Units (Meter,Seconds)
• Finite amount of compound units
• Associate non terminal Symbols to any compound
  unit allowed
• E.g.
• Newton mass length time-2
• 1,1,-2

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Dimensionally Awareness

• Dimensionally Aware GP introducing Bias
• Input in automatic grammar generator
• Elementary Units
• Set of compound units allowed
• Output
• Dimensionally consistent expressions
• CFG size may be exponentional
• Linear grow of crossover complexity
• No change in mutation complexity

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Distribution Based Evoluation

• Distribution Based Evolution
• Distribution Based Evolution (PBIL,PIPE)
• High level description of the best individuals
  encountered so far
• Probability distribution on the solution space
• Model of distribution
• Expoitation of the distribution
• Update mechanism
• Genetic Evolution
• Description of the current population

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Distribution Based Evoluation

• Probabilistic Incremental Program Evolution
  (PIPE)
• Distribution Based Evolution and GP
• Distribution represented as a PPT
• Each node contains the probabilities for
  selecting any Variable and Operator in this Node.
• After construction and evaluation PPT update
• Probability for each variable/operator has to be
  defined for each possible position in the tree

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Stochastic Grammar Based GP

• Stochastic Grammar Based GP
• Initialisation
• Analog to CFG-GP
• Iteratively rewriting each non terminal Symbol
• Selection is uniform (all weights introduces with
  1) but will includes past experience by
  selecting probabilities on the derivations

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Stochastic Grammar Based GP
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Stochastic Grammar Based GP

• Stochastic Grammar Based GP
• Distribution representation
• Distribution is represented by stochastic grammar
• Each derivation in a product rule has attached
  weight
• Selection proportional to weight

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Stochastic Grammar Based GP

• Stochastic Grammar Based GP
• Distribution expoitation
• For each occurance of a non-terminal Symbol all
  admissable derivations determined by
• max tree size
• Position of the non terminal symbol
• Selection of derivation determined by

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Stochastic Grammar Based GP

• Stochastic Grammar Based GP
• Distribution update
• After evaluating all individuals of current
  population
• Multiply weight of dervivation carried by best
  individuals
• Divide weight of derivation carried by worst
  individuals
• Mutate random weight with probability pm (divide
  or multiply)

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Stochastic Grammar Based GP

• Stochastic Grammar Based GP
• Scalar and Vectorial approach
• Problem with fixed vector to represent weights of
  derivations
• Introduces total order
• Derivation might be good at lower level but bad
  for higher level
• Introduce a Vector on each level of the tree
• Update Distribution independant on each level

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Test Problem

• Test Problem
• Identification of rheological models
• Target Kelvin Voigt Model

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
Examples are generated by random values of
material parameters K, C and load F
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Test Problem

• SG-GP is compared with standart elitist GP
• In Terms of
• Quality of Solution
• Memory use
• Parameters are set due to preelemary experiments
• GP larger Population
• Smaller number of generations
• SG-GP vice versa

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Results
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
Even Scalar SG-GP provides better results than GP
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Results
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
Lower learning rate seems to improve results
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Results
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
Larger Mutation Rate seems to improve results
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Results
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
Vectorial SG-GP performes better than Scalar
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Results
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
SG-GP resists the Bloat
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Results
Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
SG-GP near constant best individual size
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Conclusion

• Conclusion
• SG-GP overcomes bloat with using stochastic
  grammar
• SG-GP shows good identification abilities(5/20)
• SG-GP shows good generalization abilities (even
  when target law was missed)
• No Intron growth

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Conclusion

• Conclusion
• Intron growth not necessary to archieve non
  parametic learning in a fitness based context.
• Instead probably side effect of crossover

Table of Contence Introduction Problem Repetition
Dimensionally Awarenes Distribution Based
Evolution SG-GP Test Problem Results Conclusion
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Thanks for your attention