Near Optimal Bayesian Active Learning for Decision Making

How should we gather information to make effective decisions? We address Bayesian active learning and experimental design problems, where we sequentially select tests to reduce uncertaintyaboutasetofhypotheses. Instead ofminimizinguncertaintyperse,weconsidera set of overlappingdecision regions of these hypotheses. Our goal is to drive uncertainty into a single decision region as quickly as possible. We identify necessary and sucient conditionsforcorrectlyidentifyingadecisionregion that contains all hypotheses consistent with observations. We develop a novel Hyperedge Cutting (HEC) algorithm for this problem, and prove that is competitive with the intractable optimal policy. Our ecient implementation of the algorithm relies on computingsubsetsofthecompletehomogeneoussymmetric polynomials. Finally, we demonstrate its eectiveness on two practical applications: approximate comparison-based learning and activelocalizationusingarobotmanipulator.