Achievable Resolution Limits for the Noisy Adaptive 20 Questions Problem

05/01/2021
by   Lin Zhou, et al.
0

We study the achievable performance of adaptive query procedures for the noisy 20 questions problem with measurement-dependent noise over a unit cube of finite dimension. The performance criterion that we consider is the minimal resolution, defined as the L_∞ norm between the estimated and the true values of the random location vector of a target, given a finite number of queries constrained by an excess-resolution probability. Specifically, we derive the achievable resolution of an adaptive query procedure based on the variable length feedback code by Polyanskiy et al. (TIT 2011). Furthermore, we verify our theoretical results with numerical simulations and compare the performance of our considered adaptive query procedure with that of certain state-of-the-art algorithms, such as the sorted posterior matching algorithm by Chiu and Javadi (ITW 2016). In particular, we demonstrate that the termination strategy adopted in our adaptive query procedure can significantly enhance the asymptotic performance of adaptive query procedures, especially at moderate to large excess-resolution probability constraints.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/15/2020

Resolution Limits of Non-Adaptive Querying for Noisy 20 Questions Estimation

We study fundamental limits of estimation accuracy for the noisy 20 ques...
research
09/27/2019

Resolution Limits of Noisy 20 Questions Estimation

We establish fundamental limits on estimation accuracy for the noisy 20 ...
research
01/18/2021

Resolution Limits of Non-Adaptive 20 Questions Search for Multiple Targets

We study the problem of simultaneous search for multiple targets over a ...
research
04/22/2015

Non-Adaptive Policies for 20 Questions Target Localization

The problem of target localization with noise is addressed. The target i...
research
04/14/2022

Distributed Reconstruction of Noisy Pooled Data

In the pooled data problem we are given a set of n agents, each of which...
research
03/15/2021

Resolution Limits of 20 Questions Search Strategies for Moving Targets

We establish fundamental limits of tracking a moving target over the uni...
research
07/22/2018

Finite Time Adaptive Stabilization of LQ Systems

Stabilization of linear systems with unknown dynamics is a canonical pro...

Please sign up or login with your details

Forgot password? Click here to reset