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September, 1962 Contributions to the "Two-Armed Bandit" Problem
Dorian Feldman
Ann. Math. Statist. 33(3): 847-856 (September, 1962). DOI: 10.1214/aoms/1177704454


The Bayes sequential design is obtained for an optimization problem involving the choice of experiments. Given are experiments $A, B$, densities $p_1, p_2$, a positive integer $N$ and a number $\xi \varepsilon \lbrack 0, 1\rbrack$. A sequence of $N$ observations is to be made such that at each stage either $A$ or $B$ is observed, the loss being 1 if the experiment with density $p_2$ is chosen, 0 otherwise. $\xi$ is the prior probability that $A$ has density $p_1$. If the mean of $p_1$ is bigger than the mean of $p_2$ one obtains a more common version of the "two-armed bandit" (see e.g. [1]). The principal result of this paper is a proof of optimality for the procedure which at each stage chooses the experiment with higher posterior probability of being correct. Some attention is also given to the problem of computing risk functions.


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Dorian Feldman. "Contributions to the "Two-Armed Bandit" Problem." Ann. Math. Statist. 33 (3) 847 - 856, September, 1962.


Published: September, 1962
First available in Project Euclid: 27 April 2007

zbMATH: 0113.14801
MathSciNet: MR145625
Digital Object Identifier: 10.1214/aoms/1177704454

Rights: Copyright © 1962 Institute of Mathematical Statistics

Vol.33 • No. 3 • September, 1962
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