Distributed Chernoff Test: Optimal decision systems over networks

Abstract

We study "active" decision making over sensor networks where the sensors' sequential probing actions are actively chosen by continuously learning from past observations. We consider two network settings: with and without central coordination. In the first case, the network nodes interact with each other through a central entity, which plays the role of a fusion center. In the second case, the network nodes interact in a fully distributed fashion. In both of these scenarios, we propose sequential and adaptive hypothesis tests extending the classic Chernoff test. We compare the performance of the proposed tests to the optimal sequential test. In the presence of a fusion center, our test achieves the same asymptotic optimality of the Chernoff test, minimizing the risk, expressed by the expected cost required to reach a decision plus the expected cost of making a wrong decision, when the observation cost per unit time tends to zero. The test is also asymptotically optimal in the higher moments of the time required to reach a decision. Additionally, the test is parsimonious in terms of communications, and the expected number of channel uses per network node tends to a small constant. In the distributed setup, our test achieves the same asymptotic optimality of Chernoff's test, up to a multiplicative constant in terms of both risk and the higher moments of the decision time. Additionally, the test is parsimonious in terms of communications in comparison to state-of-the-art schemes proposed in the literature. The analysis of these tests is also extended to account for message quantization and communication over channels with random erasures.