Acknowledgments We Want to Thank

Learning eecient classiication procedures and their application to chess and games. A formal analysis of machine learning systems for knowledge acquisition. tion is much more powerful than simple linear combination of features. Samuel's evaluation function was restricted to hyperplanes, a fact considered to be a major drawback of his program. Our method, however, allows surfaces such as t 2 1 ? t 2 2 shown in gure 9 to be learned, that could not had been learned using simple linear combination of features. t1 t2 Figure 9: Representable non linear surface Conclusions Genetic algorithm is a natural candidate for learning in games. In this paper we study the use of genetic algorithms in game-playing learning programs, emphasising on learning a static evaluation function. Instead of blindly tting the problem to genetic algorithm, we modiied genetic algorithms to t the problem, achieving better results. We began by deciding to invest our eeorts in learning an evaluation function (rather than learn a complete strategy from scratch). We further determined that the precise learning task is nding an order relation (rather than absolute classiications). We then concluded that it is beneecial to learn an evaluation function by its derivatives, and designed a derivative crossover operator that combines good building blocks. A heuristic continuity assumption has proven advantageous in the genetic search. In a series of experiments performed with the new framework, the program acquired an evaluation function component for the game of Checkers, an arbitrary continuous function, and a non linear combination of features. Previous work that use genetic algorithms to learn, either apply too demanding techniques that are not applicable for complex games, or perform a very restricted type of learning. We assumed the control to be known a priori, and left the learner with the task of learning the evaluation function. This is diierent than Koza's approach 9] that induces Lisp programs from scratch. There is another diierence in approaches between other systems and ours concerning the coding policy. We claim that relative representation is more beneecial than absolute representation, for achieving generalization using genetic algorithms. The 1-bounded slops assumption may be generalized to M-bounded slops, increasing the expressive power of the representation , paying in search time. The derivative operators were designed for evolving game-playing evaluation functions, but may be useful for other order-preserving representations as well. We hope that the methodology of learning the derivatives instead of the function …