Active Search with a Cost for Switching Actions

TL;DR

This paper extends active sequential hypothesis testing by incorporating switching costs, demonstrating that a modified Chernoff procedure remains asymptotically optimal even when switching costs are considered.

Contribution

It introduces Sluggish Procedure A, a modification of Chernoff's policy, and proves its asymptotic optimality with switching costs included.

Findings

Sluggish Procedure A is asymptotically optimal with switching costs.

Total cost growth rate remains unchanged despite switching costs.

The policy maintains optimality as false detection probability and switching parameters approach zero.

Abstract

Active Sequential Hypothesis Testing (ASHT) is an extension of the classical sequential hypothesis testing problem with controls. Chernoff (Ann. Math. Statist., 1959) proposed a policy called Procedure A and showed its asymptotic optimality as the cost of sampling was driven to zero. In this paper we study a further extension where we introduce costs for switching of actions. We show that a modification of Chernoff's Procedure A, one that we call Sluggish Procedure A, is asymptotically optimal even with switching costs. The growth rate of the total cost, as the probability of false detection is driven to zero, and as a switching parameter of the Sluggish Procedure A is driven down to zero, is the same as that without switching costs.