Variable block search with prior information

Consider the problem of optimizing an unknown, unimodal, univariate function by direct function evaluation. This article replaces the classic criterion for evaluating search strategies, minimax, by one we feel to be more practical, minimum expected final interval of uncertainty. This latter measure of effectiveness is useful when the experimenter has some prior knowledge of the underlying function and can specify a probability distribution on the location of the optimum.We show here that for a large class of search strategies under the uniform distribution, minimax is equivalent to minimum expected final interval length, i.e., the uniform distribution represents a ‘worst-case’ prior. In addition, computational procedures are develooed for determining the optimal search strategy for arbitrary a priori distributions. Several examples are included.