Noisy binary search and its applications

We study a noisy version of the classic binary search problem of inserting an element into its proper place within an ordered sequence by comparing it with elements of the sequence. In the noisy version we can not compare elements directly. Instead we are given a coin corresponding to each element of the sequence, such that as one goes through the ordered sequence the probability of observing heads when tossing the corresponding coin increases. We design online algorithms which adaptively choose a sequence of experiments, each consisting of tossing a single coin, with the goal of identifying the highest-numbered coin in the ordered sequence whose heads probability is less than some specified target value. Possible applications of such algorithms include investment planning, sponsored search advertising, admission control in queueing networks, college admissions, and admitting new members into an organization ranked by ability, such as a tennis ladder.