Quickest Detection with Social Learning: Interaction of local and global decision makers

摘要

We consider how local and global decision policies interact in stopping timeproblems such as quickest time change detection. Individual agents make myopiclocal decisions via social learning, that is, each agent records a privateobservation of a noisy underlying state process, selfishly optimizes its localutility and then broadcasts its local decision. Given these local decisions,how can a global decision maker achieve quickest time change detection when theunderlying state changes according to a phase-type distribution? The paperpresents four results. First, using Blackwell dominance of measures, it isshown that the optimal cost incurred in social learning based quickestdetection is always larger than that of classical quickest detection. Second,it is shown that in general the optimal decision policy for social learningbased quickest detection is characterized by multiple thresholds within thespace of Bayesian distributions. Third, using lattice programming andstochastic dominance, sufficient conditions are given for the optimal decisionpolicy to consist of a single linear hyperplane, or, more generally, athreshold curve. Estimation of the optimal linear approximation to thisthreshold curve is formulated as a simulation-based stochastic optimizationproblem. Finally, the paper shows that in multi-agent sensor management withquickest detection, where each agent views the world according to its prior,the optimal policy has a similar structure to social learning.