Optimal sampling policy for quickest change detection

Abstract

We consider the problem of quickest change detection (QCD) for a signal that can only be observed using actions selected by a static policy from a finite set of permissible actions. We propose a static sampling policy on the set of permissible actions and a GLR CuSum stopping rule for the QCD problem. Our proposed sampling policy is the solution to a convex optimization problem. We show that our proposed scheme has asymptotically optimal worst case average detection delay as the false alarm rate goes to zero. Finally, we apply our approach to the problem of QCD of a partially observed graph signal. Simulation results demonstrate that our proposed approach achieves a significantly lower average detection delay, compared to a random uniform sampling policy, for large average run lengths.