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December, 1992 Stay-with-a-Winner Rule for Dependent Bernoulli Bandits
K. Samaranayake
Ann. Statist. 20(4): 2111-2123 (December, 1992). DOI: 10.1214/aos/1176348906

Abstract

The $k$-armed bandit problem on the Bernoulli dependent arms is discussed. Order relations on the prior distributions of the Bernoulli parameters using moments of the posterior are used to prove a monotonicity property of the value function. When $k = 2$, a stay-with-a-winner rule is derived for negatively correlated arms and for a certain class of positively correlated arms. These results are extensions of those given in Berry and Fristedt for independent Bernoulli arms. They also generalize the results of Benzing, Hinderer and Kolonko and Kolonko and Benzing.

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K. Samaranayake. "Stay-with-a-Winner Rule for Dependent Bernoulli Bandits." Ann. Statist. 20 (4) 2111 - 2123, December, 1992. https://doi.org/10.1214/aos/1176348906

Information

Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0765.62074
MathSciNet: MR1193329
Digital Object Identifier: 10.1214/aos/1176348906

Subjects:
Primary: 62L05
Secondary: 90D15

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 4 • December, 1992
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