The knowledge-gradient policy for correlated normal beliefs

Peter Frazier, Warren Buckler Powell, Savas Dayanik

Research output: Contribution to journalArticlepeer-review

280 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)599-613
Number of pages15
JournalINFORMS Journal on Computing
Issue number4
StatePublished - Sep 2009

All Science Journal Classification (ASJC) codes

  • Software
  • Information Systems
  • Computer Science Applications
  • Management Science and Operations Research


  • Bayesian
  • Decision analysis: sequential
  • Simulation: design of experiments
  • Statistics


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