Optimization of detection networks. I. Tandem structures

A distributed binary detection problem with binary communications, wherein the nodes (sensors, decision-makers) of the system are organized in a series configuration, is considered. It is shown that this problem is isomorphic to a deterministic, multistage nonlinear optimal control problem. Necessary and sufficient conditions of optimality are derived using Bayes risk as the optimization criterion, and a physical interpretation of how the costates relate to the decision threshold at each node is provided. A computationally efficient algorithm based on the min-H method is proposed to solve for the optimal decision strategy, and is extended to solve the problem with a Neyman-Pearson criterion to obtain the optimal team (network) receiver operating characteristic curve. The optimal strategies are illustrated by several numerical examples related to organizational design. The results can be extended to directed acyclic networks with at most a single directed path between any pair of nodes (which include directed tree networks as a special case)