Asymptotic Optimality Theory For Decentralized Sequential Multihypothesis Testing Problems

TL;DR

This paper develops asymptotically optimal decentralized sequential testing methods for multi-hypothesis problems in sensor networks, introducing a two-stage approach with optimized local quantizers that improve decision accuracy.

Contribution

It introduces a novel two-stage testing framework with maximin quantizers for decentralized multi-hypothesis testing, extending to multiple sensors and message types.

Findings

Optimal local quantizers are maximin and are randomizations of ULQs.

The two-stage test achieves asymptotic optimality in decentralized settings.

Extensions to multiple sensors and message alphabets are provided.

Abstract

The Bayesian formulation of sequentially testing $M \ge 3$ hypotheses is studied in the context of a decentralized sensor network system. In such a system, local sensors observe raw observations and send quantized sensor messages to a fusion center which makes a final decision when stopping taking observations. Asymptotically optimal decentralized sequential tests are developed from a class of "two-stage" tests that allows the sensor network system to make a preliminary decision in the first stage and then optimize each local sensor quantizer accordingly in the second stage. It is shown that the optimal local quantizer at each local sensor in the second stage can be defined as a maximin quantizer which turns out to be a randomization of at most $M-1$ unambiguous likelihood quantizers (ULQ). We first present in detail our results for the system with a single sensor and binary sensor messages, and then extend to more general cases involving any finite alphabet sensor messages, multiple sensors, or composite hypotheses.