On the sample complexity of finding good search strategies

A satisficing search problem consists of a set of probabilistic experiments to be performed in some order, without repetitions, until a satisfying configuration of successes and failures has been reached. The cost of performing the experiments depends on the order chosen. Earlier work has concentrated on finding optimal search strategies in special cases of this model, such as search trees and and-or graphs, when the cost function and the success probabilities for the experiments are given. In contrast, we study the complexity of “learning” an approximately optimal search strategy when some of the success probabilities are not known at the outset. Working in the fully general model, we show that if n is the number of unknown probabilities, and C is the maximum cost of performing all the experiments, then 2( nC ) ln 2n δ trials of each undetermined experiment are sufficient to identify, with confidence 1 − δ, a search strategy whose cost is within of the optimal.