On the optimal search problem: the case when the target distribution is unknown

We consider the problem of searching for an object in a set of N locations (or bins) (C₁,…,C_N). The probability of the object being in the location C_i is p(i). Also, the probability of locating the object in the bin within a specified time, given that it is in the bin, is given by a function called the detection function. This is typically specified by an exponential function. The intention is to allocate the available resources so as to maximize the probability of locating the object. This problem has applications in searching large databases and in developing various military and strategic policies. All of the research done in this area has assumed the knowledge of the {p(i)}-the target distribution. We consider the problem of obtaining error bounds and estimating the target distribution. To our knowledge these are the first available results in this area, and are particularly interesting because the target distribution, in itself, is unobservable