Discounted Bayesian search problems with unknown detection probabilities

Abstract

In this paper we consider three discrete-time discounted Bayesian search problems with an unknown number of objects and uncertainty about the distribution of the objects among the boxes. Moreover, we admit uncertainty about the detection probabilities. The goal is to determine a policy which finds (dependent on the search problem) at least one object or all objects with minimal expected total cost. We give sufficient conditions for the optimality of the greedy policy which has been introduced in Liebig/Rieder (1996). For some examples in which the greedy policy is not optimal we derive a bound for the error.