Non-Adaptive Policies for 20 Questions Target Localization

TL;DR

This paper investigates non-adaptive dyadic questioning strategies for target localization under noise, deriving the optimal asymptotic distortion and introducing a policy that achieves this bound.

Contribution

It provides the first asymptotic analysis of non-adaptive policies for noisy target localization and proposes a new policy that attains the theoretical minimum distortion.

Findings

Derived the asymptotic minimum achievable distortion for non-adaptive policies.

Introduced the Aurelian policy that achieves the asymptotic optimal distortion.

Established theoretical bounds for non-adaptive 20 questions strategies.

Abstract

The problem of target localization with noise is addressed. The target is a sample from a continuous random variable with known distribution and the goal is to locate it with minimum mean squared error distortion. The localization scheme or policy proceeds by queries, or questions, weather or not the target belongs to some subset as it is addressed in the 20-question framework. These subsets are not constrained to be intervals and the answers to the queries are noisy. While this situation is well studied for adaptive querying, this paper is focused on the non adaptive querying policies based on dyadic questions. The asymptotic minimum achievable distortion under such policies is derived. Furthermore, a policy named the Aurelian1 is exhibited which achieves asymptotically this distortion.