## The Annals of Statistics

### Further Contributions to the "Two-Armed Bandit" Problem

Robert Keener

#### Abstract

A version of the two-armed bandit with two states of nature and two repeatable experiments is studied. With an infinite horizon and with or without discounting, an optimal procedure is to perform one experiment whenever the posterior probability of one of the states of nature exceeds a constant $\xi^\ast$, and perform the other experiment whenever the posterior is less than $\xi^\ast$ with indifference when the posterior equals $\xi^\ast. \xi^\ast$ is expressed in terms involving expectations of ladder variables and can be calculated using Spitzer series.

#### Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 418-422.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346603

Digital Object Identifier
doi:10.1214/aos/1176346603

Mathematical Reviews number (MathSciNet)
MR773178

Zentralblatt MATH identifier
0567.62067

JSTOR