The two-armed bandit with delayed responses
type: Item
instance of: scholarly article
title: The two-armed bandit with delayed responses
zbMATH Open document ID: 0637.62074
author: Stephen G. Eick
published in: The Annals of Statistics
publication date: 1988-01-01T00:00:00Z
review text: A general model for a two-armed bandit with delayed responses is introduced and solved with dynamic programming. One arm has geometric lifetime with parameter \(\theta\), which has prior distribution \(\mu\). The other arm has known lifetime with mean \(\kappa\). The response delays completely change the character of the optimal strategies from the no delay case; in particular, the bandit is no longer a stopping problem. The delays also introduce an extra parameter p into the state space. In clinical trial applications, this parameter represents the number of patients previously treated with the unknown arm who are still living. The value function is introduced and investigated as p, \(\mu\) and \(\kappa\) vary. Under a regularity condition on the discount sequence, there exists a manifold in the state space such that both arms are optimal on the manifold, arm x is optimal on one side and arm y on the other. Properties of the manifold are described.
Mathematics Subject Classification ID: 62L05
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 62L15
zbMATH DE Number: 4039059
zbMATH Keywords: randomized clinical trials
zbMATH Keywords: two-armed bandit with delayed responses
zbMATH Keywords: geometric lifetime
zbMATH Keywords: optimal strategies
zbMATH Keywords: value function
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350703
OpenAlex ID: W2053005272
DOI: 10.1214/AOS/1176350703
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description: scientific article; zbMATH DE number 4039059