The Application of Algorithmic Probability to Problems in Artificial Intelligence

We will cover two topics First, Algorithmic Probability — the motivation for defining it, how it overcomes difficulties in other formulations of probability, some of its characteristic properties and successful applications. Second, we will apply it to problems in A.I. — where it promises to give near optimum search procedures for two very broad classes of problems. A strong motivation for revising classical concepts of probability has come from the analysis of human problem solving. When working on a difficult problem, a person is in a maze in which he must make choices of possible courses of action. If the problem is a familiar one, the choices will all be easy. If it is not familiar, there can be much uncertainty in each choice, but choices must somehow be made. One basis for choice might be the probability of each choice leading to a quick solution — this probability being based on experience in this problem and in problems like it. A good reason for using probability is that it enables us to use a relatively simple search procedure to find the solution in near minimal time. The usual method of calculating probability is by taking the ratio of the number of favorable choices to the total number of choices in the past. If the decision to use integration by parts in an integration problem has been successful in the past 43% of the time, then its present probability of success is about .43. This method has very poor accuracy if we only have one or two cases in the