The Annals of Statistics

Bayesian Nonparametric Bandits

Murray K. Clayton and Donald A. Berry

Full-text: Open access

Abstract

Sequential selections are to be made from two stochastic processes, or "arms." At each stage the arm selected for observation depends on past observations. The objective is to maximize the expected sum of the first $n$ observations. For arm 1 the observations are identically distributed with probability measure $P$, and for arm 2 the observations have probability measure $Q; P$ is a Dirichlet process and $Q$ is known. An equivalent problem is deciding sequentially when to stop sampling from an unknown population. Optimal strategies are shown to continue sampling if the current observation is sufficiently large. A simple form of such a rule is expressed in terms of a degenerate Dirichlet process which is related to $P$.

Article information

Source
Ann. Statist., Volume 13, Number 4 (1985), 1523-1534.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349753

Digital Object Identifier
doi:10.1214/aos/1176349753

Mathematical Reviews number (MathSciNet)
MR811507

Zentralblatt MATH identifier
0587.62151

JSTOR
links.jstor.org

Subjects
Primary: 62L05: Sequential design
Secondary: 62L15: Optimal stopping [See also 60G40, 91A60]

Keywords
Sequential decisions nonparametric decisions optimal stopping one-armed bandits two-armed bandits Dirichlet bandits

Citation

Clayton, Murray K.; Berry, Donald A. Bayesian Nonparametric Bandits. Ann. Statist. 13 (1985), no. 4, 1523--1534. doi:10.1214/aos/1176349753. https://projecteuclid.org/euclid.aos/1176349753


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