A CLASS OF BAYESIAN MODELS FOR OPTIMAL EXPLORATION

Each of several locations contains an unknown number of objects of val ue. A single search of a location will discover some of these objects which are then removed. Discoveries yield rewards. A 'distribution of effort' problem is posed concerning how to explore the locations optim ally-i.e. to maximize the expected return from discoveries made. This is formulated as a Bayes sequential decision problem for which index p olicies are optimal. A natural simple case is one in which, conditiona lly on the number of undiscovered objects at a location N, the number of discoveries made in a single search is binomial B(N, p) where p is a detection rate. For this case, we can gain considerable insight into how model structure relates to policy structure. The tail behaviour o f the priors for the number of objects at each location plays an impor tant role.