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We consider a Bayesian ranking and selection problem with independent normal rewards and a correlated multivariate normal belief on the mean values of these rewards. Because this formulation of the ranking and selection problem models dependence between alternatives' mean values, algorithms may utilize this dependence to perform efficiently even when the(More)
Bisection search is the most efficient algorithm for locating a unique point X * ∈ [0, 1] when we are able to query an oracle only about whether X * lies to the left or right of a point x of our choosing. We study a noisy version of this classic problem, where the oracle's response is correct only with probability p. The probabilistic bisection algorithm(More)
In a sequential Bayesian ranking and selection problem with independent normal populations and common known variance, we study a previously introduced measurement policy which we refer to as the knowledge-gradient policy. This policy myopically maximizes the expected increment in the value of information in each time period, where the value is measured(More)
We consider the problem of 20 questions with noisy answers, in which we seek to find a target by repeatedly choosing a set, asking an oracle whether the target lies in this set, and obtaining an answer corrupted by noise. Starting with a prior distribution on the target's location, we seek to minimize the expected entropy of the posterior distribution. We(More)
We consider information collection problems, in which we must decide how much and of what type of information to collect. We focus our interest on sequential Bayesian information collection problems. In making such decisions we trade the benefit of information (the ability to make better decisions in the future) against its cost (money, time, or opportunity(More)
Latent feature models are widely used to decompose data into a small number of components. Bayesian nonparametric variants of these models, which use the Indian buffet process (IBP) as a prior over latent features, allow the number of features to be determined from the data. We present a generalization of the IBP, the <italic>distance dependent Indian(More)
This paper considers the task of finding a target location by making a limited number of sequential observations. Each observation results from evaluating an imperfect classifier of a chosen cost and accuracy on an interval of chosen length and position. Within a Bayesian framework, we study the problem of minimizing an objective that combines the entropy(More)
We derive a one-period look-ahead policy for finite-and infinite-horizon online optimal learning problems with Gaussian rewards. Our approach is able to handle the case where our prior beliefs about the rewards are correlated, which is not handled by traditional multi-armed bandit methods. Experiments show that our KG policy performs competitively against(More)