Optimal Simultaneous Search for the Maximum by the Principle of Statistical Information

This paper investigates the problem of estimating an optimal interval containing the location of the maximum of a unimodal function by simultaneous experimentation for the case when an arbitrary probability density function for the distribution of the maximum is given. The payoff of the estimation is taken to be the “statistical information” gained by the search. For an even number of experiments, the optimal strategy selects an interval estimate, containing the maximum point, for which the maximal a priori probability of containing this maximum is minimized. When the probability density is uniform, the optimal strategy minimizes the maximal length of the interval estimate. For an odd number of experiments, an unsymmetric search pattern results.