On the Price of Decentralization in Decentralized Detection

TL;DR

This paper investigates the fundamental limits of decentralized detection algorithms, showing that a modified social learning rule can achieve error decay rates comparable to centralized systems, thus minimizing the impact of decentralization.

Contribution

It introduces a modified social learning rule that closes the error exponent gap between decentralized and centralized detection methods.

Findings

Original social learning rule has a gap in error exponents.

Modified rule achieves centralized error exponents.

Decentralization incurs no first-order penalty in error decay rate.

Abstract

Fundamental limits on the error probabilities of a family of decentralized detection algorithms (eg., the social learning rule proposed by Lalitha et al. over directed graphs are investigated. In decentralized detection, a network of nodes locally exchanging information about the samples they observe with their neighbors to collectively infer the underlying unknown hypothesis. Each node in the network weighs the messages received from its neighbors to form its private belief and only requires knowledge of the data generating distribution of its observation. In this work, it is first shown that while the original social learning rule of Lalitha et al. achieves asymptotically vanishing error probabilities as the number of samples tends to infinity, it suffers a gap in the achievable error exponent compared to the centralized case. The gap is due to the network imbalance caused by the local weights that each node chooses to weigh the messages received from its neighbors. To close this gap, a modified learning rule is proposed and shown to achieve error exponents as large as those in the centralized setup. This implies that there is essentially no first-order penalty caused by decentralization in the exponentially decaying rate of error probabilities.