An Analysis of Generalization in XCS with Symbolic Conditions
- 1. An Analysis of Generalization in XCS with Symbolic Conditions Pier Luca Lanzi Politecnico di Milano, Italy Illinois Genetic Algorithms Laboratory, University of Illinois at Urbana Champaign, USA CEC 2007, Singapore, September 25-28, 2007
- 2. One Minute Intro to Classifier Systems Problem Representation Search Evaluate Condition-action rules Genetic Algorithm Online RL
- 3. One Minute Intro to Classifier Systems Learning viewed as online interaction Knowledge representation Population of condition-action-prediction rules, the classifiers Solution evaluation Reinforcement learning evaluates the classifiers Solution search & problem decomposition A genetic algorithm selects, recombines, and mutates classifiers to find better ones
- 4. Generalization = Evolving maximally accurate, maximally compact solutions Generalization is a major feature of learning classifier systems Generalization relies on the representation The better the representation, the better the generalization
- 5. Generalization in Classifier Systems Standard GP for symbolic conditions Input variables x 0 , x 1 , … Constants 0, 1 Functions AND, OR, NOT Previous findings: not optimal when ORs are included Input 010100 Ternary Conditions 01#1## Symbolic Condition?
- 6. Symbolic Conditions How To Classifiers Keep the usual structure Classifier condition is a GP-tree Matching Performed by evaluating the condition expression Covering Randomly generated covering subexpressions Disjunctions used to build up the condition Genetic search Implemented using standard GP
- 9. 6-multiplexer: number of classifiers
- 10. 6-multiplexer: example of population Four classifiers (55677, 55268, 54217, 55308) represent 6-multiplexer completely 55677 covers the first prime implicant 55268 covers the three remaining prime implicants; 54217 and 55308 cover respectively one and three of the four conditions that represent the zeros of 6-multiplexer.
- 11. Optimal performance reached (thanks to recent new fitness definition) not evolved, why? Overlapping concepts share the total fitness, the more the overlaps, the lower the fitness “ A” has a higher fitness than “A OR B” Only generalization pressure works towards “A OR B” Maximally general solution difficult to evolve, Especially without fitness pressure “ A” has a higher fitness than “A OR B”
- 13. 11-multiplexer: number of classifiers
- 14. 11-multiplexer: example of population
- 16. 20-multiplexer: number of classifiers
- 17. 20-multiplexer: example of population
- 18. EQ5,3
- 19. Another Boolean Function: EQ 5,3
- 20. EQ 5,3 : Performance
- 21. EQ 5,3 : Number of Classifiers
- 22. EQ 5,3 : example of population
- 23. Summary
- 24. Early results showed that XCSGP could not reach optimal performance when “or” clauses are involved Here we showed why disjunctions are more difficult Symbolic conditions are highly overlapping Highly overlapping classifiers have a low fitness When disjunctions are not important, XCS tends to evolve solutions without disjunctions When disjunctions are relevant, XCS tends to use them much more
- 25. Thank you! Any question?