In this paper, we study the use of anticipation mappings in learning classifier systems. At first, we enrich the eXtended Classifier System (XCS) with two types of anticipation mappings: one based on array of perceptrons array, one based on neural networks. We apply XCS with anticipation mappings (XCSAM) to several multistep problems taken from the literature and compare its anticipatory performance with that of the Neural Classifier System X-NCS which is based on a similar approach. Our results show that, although XCSAM is not a “true” Anticipatory Classifier System like ACS, MACS, or X-NCS, nevertheless XCSAM can provide accurate anticipatory predictions while requiring smaller populations than those needed by X-NCS.

1. Anticipation Mappings for Learning Classifier Systems Larry Bull, Pier Luca Lanzi, Toby O’hara University of the West of England, Bristol, UK Politecnico di Milano, Italy Illinois Genetic Algorithms Laboratory, University of Illinois at Urbana Champaign, USA CEC 2007, September 27th, 2007, Singapore TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A

2. A Brief Look at Classifier Systems If condition C holds in state S , then action A will produce a payoff p , this prediction has an accuracy F

5. Learning Anticipatory Functions s t s t+1 a t s t a t -> s t+1

11. Woods

12. Simple Sequential Problems (1) (2) (3)

13. Anticipation Accuracy (1) accuracy MSE

14. Anticipation Accuracy (2) accuracy MSE

15. Anticipation Accuracy (3) accuracy MSE

16. Alias

17. Sequential Problems with Aliasing (1) (2) Extension of anticipatory Classifier Systems for problem with noise was developed by Martin Butz, Dave G. Goldberg, and Wolfgang Stolzmann (2000)

18. Anticipation Accuracy (1) accuracy MSE

19. Anticipation Accuracy (2) accuracy MSE

20. We presented a very simple approach to anticipatory behavior Compute the anticipation of the next state based on the previous state and the action performed Very simple, but provide accurate predictions, while requiring smaller populations Simpler than ACSs, probably less powerful Even simple perceptron can be powerful enough Generalizes to real-valued and/or noisy domains

21. Any Question? Thank you!