Universal Scheme for Optimal Search and Stop

TL;DR

This paper introduces a universal adaptive search and stop scheme that achieves optimal reliability without knowing the target distribution, significantly improving search efficiency and reliability in detecting missing targets.

Contribution

The paper proposes a universal sequential search and stop scheme that operates with only the absence distribution knowledge and achieves asymptotic optimality.

Findings

Universal scheme achieves vanishing error probability.

Scheme attains optimal reliability universally for all target distributions.

Adaptivity provides a multiplicative gain proportional to the number of searched locations.

Abstract

The problem of universal search and stop using an adaptive search policy is considered. When the target location is searched, the observation is distributed according to the target distribution, otherwise it is distributed according to the absence distribution. A universal sequential scheme for search and stop is proposed using only the knowledge of the absence distribution, and its asymptotic performance is analyzed. The universal test is shown to yield a vanishing error probability, and to achieve the optimal reliability when the target is present, universally for every target distribution. Consequently, it is established that the knowledge of the target distribution is only useful for improving the reliability for detecting a missing target. It is also shown that a multiplicative gain for the search reliability equal to the number of searched locations is achieved by allowing adaptivity in the search.