The Annals of Statistics

Bayesian Nonparametric Bandits

Murray K. Clayton and Donald A. Berry

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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

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

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

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


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

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