Optimal information blending with measurements in the L2 sphere

Boris Defourny, Ilya O. Ryzhov, Warren Buckler Powell

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

A sequential information collection problem, where a risk-averse decision maker updates a Bayesian belief about the unknown objective function of a linear program, is used to investigate the informational value of measurements performed to refine a robust optimization model. The information is collected in the form of a linear combination of the objective coefficients, subject to random noise. We have the ability to choose the weights in the linear combination, creating a new, nonconvex continuous-optimization problem, which we refer to as information blending. We develop two optimal blending strategies: (1) an active learning method that maximizes uncertainty reduction and (2) an economic approach that maximizes an expected improvement criterion. Semidefinite programming relaxations are used to create efficient convex approximations to the nonconvex blending problem.

Original languageEnglish (US)
Pages (from-to)1060-1088
Number of pages29
JournalMathematics of Operations Research
Volume40
Issue number4
DOIs
StatePublished - Nov 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

Keywords

  • Optimal learning
  • Risk
  • Semidefinite programming
  • Stochastic programming
  • Value of information

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