Sequentiality and Adaptivity Gains in Active Hypothesis Testing

TL;DR

This paper analyzes how sequential and adaptive sensing policies improve the speed and efficiency of information gathering in hypothesis testing, providing bounds and characterizing the gains over non-sequential and non-adaptive methods.

Contribution

It offers performance bounds for various sensing policies and quantifies the benefits of sequential and adaptive strategies in hypothesis testing.

Findings

Sequential policies significantly reduce sample size needed.

Adaptive policies improve decision accuracy with fewer observations.

Performance bounds quantify the gains of sequentiality and adaptivity.

Abstract

Consider a decision maker who is responsible to collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest. The policies under which the decision maker selects sensing actions can be categorized based on the following two factors: i) sequential vs. non-sequential; ii) adaptive vs. non-adaptive. Non-sequential policies collect a fixed number of observation samples and make the final decision afterwards; while under sequential policies, the sample size is not known initially and is determined by the observation outcomes. Under adaptive policies, the decision maker relies on the previous collected samples to select the next sensing action; while under non-adaptive policies, the actions are selected independent of the past observation outcomes. In this paper, performance bounds are provided for the policies in each category. Using these bounds, sequentiality gain and adaptivity gain, i.e., the gains of sequential and adaptive selection of actions are characterized.