A statistical foundation for machine learning, with application to Go-Moku

AbstractIn the context of the research study reported here, “learning” refers to identification of optimal parameters in value and graph traversing procedures. Of course, graph traversing lies at the heart of artificial intelligence (AI) schemes. We abstract the learning problem to the problem of choosing value functions and traversing rules on the basis of performance during repetitive AI solutions, to achieve improvement as time goes on. Viewed in this fashion, for many AI problems and games, the learning problem is equivalent to the problem of trying to find the minimum of a function f(x) on the basis of noisy measurements Y(i) = f[x(i)] + W[x(i)] at domain points x(i) which are to be chosen by the decision maker (e.g. a computer) on the basis of past sample values. This particular random search problem does not seem to have been addressed in the statistical or optimization literature. This study reports some theoretical properties of a minimization method and results of computational experiments on Go-Moku, a tic-tac-toe style game