Probably Approximately Optimal Satisscing Strategies

A satisscing search problem consists of a set of probabilistic experiments to be performed in some order, seeking a satisfying connguration of successes and failures. The expected cost of the search depends both on the success probabilities of the individual experiments, and on the search strategy, which speciies the order in which the experiments are to be performed. A strategy that minimizes the expected cost is optimal. Earlier work has provided \optimizing functions" that compute optimal strategies for certain classes of search problems from the success probabilities of the individual experiments. We extend those results by providing a general model of such strategies, and an algorithm pao that identiies an approximately optimal strategy when the probability values are not known. The algorithm rst estimates the relevant probabilities from a number of trials of each undetermined experiment, and then uses these estimates, and the proper optimizing function, to identify a strategy whose cost is, with high probability , close to optimal. We also show that if the search problem can be formulated as an and-or tree, then the pao algorithm can also \learn while doing", i.e. gather the necessary statistics while performing the search.