The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 19, Number 4 (2009), 1603-1633.
Woodroofe’s one-armed bandit problem revisited
We consider the one-armed bandit problem of Woodroofe [J. Amer. Statist. Assoc. 74 (1979) 799–806], which involves sequential sampling from two populations: one whose characteristics are known, and one which depends on an unknown parameter and incorporates a covariate. The goal is to maximize cumulative expected reward. We study this problem in a minimax setting, and develop rate-optimal polices that involve suitable modifications of the myopic rule. It is shown that the regret, as well as the rate of sampling from the inferior population, can be finite or grow at various rates with the time horizon of the problem, depending on “local” properties of the covariate distribution. Proofs rely on martingale methods and information theoretic arguments.
Ann. Appl. Probab., Volume 19, Number 4 (2009), 1603-1633.
First available in Project Euclid: 27 July 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Goldenshluger, Alexander; Zeevi, Assaf. Woodroofe’s one-armed bandit problem revisited. Ann. Appl. Probab. 19 (2009), no. 4, 1603--1633. doi:10.1214/08-AAP589. https://projecteuclid.org/euclid.aoap/1248700629