Decentralized dynamic decision making

Problems of decision making in the face of statistical uncertainties have long been of interest to decision theorists in various disciplines. A decentralized detection or hypothesis-testing system is a special case of a decentralized decision-making system in which several local agents or detectors observe a common region of the environment to determine, for example, the presence or absence of a certain phenomenon. Due to such factors as communication constraints, local detectors must make decisions at their local sites and send their decisions, rather than their received measurements or observations, to a central processor, who is responsible for declaring the final decision. Moreover, the local detectors are not permitted to communicate with one another. In this paper, we study a broad class of decentralized multi-stage, multi-detector binary hypothesis-testing problems. It is shown that, under appropriate independence assumptions on the received measurements, local strategies at each time instant are given by threshold tests on the likelihood ratio. Furthermore, it is shown that local decisions of each detector depend not only on his present and past observations, but on his past decisions as well. That is, for each local detector there is a different threshold corresponding to each combination of past decisions.