Decentralized Detection with Signaling

TL;DR

This paper studies a sequential decentralized detection problem where two observers communicate via signaling, revealing that traditional threshold-based stopping rules are suboptimal due to signaling effects, and provides a new characterization of optimal policies.

Contribution

It introduces a novel analysis of decentralized detection with signaling, showing the limitations of threshold policies and deriving a new parametric framework for optimal stopping rules.

Findings

Threshold policies are not always optimal due to signaling.

A new parametric characterization of optimal policies is proposed.

Signaling alters the structure of optimal stopping rules.

Abstract

We consider a sequential problem in decentralized detection. Two observers can make repeated noisy observations of a binary hypothesis on the state of the environment. At any time, any of the two observers can stop and send a final message to the other observer or it may continue to take more measurements. After an observer has sent its final message, it stops operating. The other observer is then faced with a different stopping problem. At each time instant, it can decide either to stop and declare a final decision on the hypothesis or take another measurement. At each time, the system incurs an operating cost depending on the number of observers that are active at that time. A terminal cost that measures the accuracy of the final decision is incurred at the end. We show that, unlike in other sequential detection problems, stopping rules characterized by two thresholds on an observer's posterior belief no longer guarantee optimality in this problem. Thus the potential for signaling among observers alters the nature of optimal policies. We obtain a new parametric characterization of optimal policies for this problem.