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The knowledge-gradient policy for correlated normal beliefs. (English) Zbl 1243.91014

Summary: 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 use this dependence to perform efficiently even when the number of alternatives is very large. We propose a fully sequential sampling policy called the knowledge-gradient policy, which is provably optimal in some special cases and has bounded suboptimality in all others. We then demonstrate how this policy may be applied to efficiently maximize a continuous function on a continuous domain while constrained to a fixed number of noisy measurements.

MSC:

91A26 Rationality and learning in game theory
62C10 Bayesian problems; characterization of Bayes procedures
91B06 Decision theory

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