## Keywords (3)

Publications
A Bernoulli Two-armed Bandit

# A Bernoulli Two-armed Bandit,10.1214/aoms/1177692553,The Annals of Mathematical Statistics,Donald A. Berry

A Bernoulli Two-armed Bandit
One of two independent Bernoulli processes (arms) with unknown expectations $\rho$ and $\lambda$ is selected and observed at each of $n$ stages. The selection problem is sequential in that the process which is selected at a particular stage is a function of the results of previous selections as well as of prior information about $\rho$ and $\lambda$. The variables $\rho$ and $\lambda$ are assumed to be independent under the (prior) probability distribution. The objective is to maximize the expected number of successes from the $n$ selections. Sufficient conditions for the optimality of selecting one or the other of the arms are given and illustrated for example distributions. The stay-on-a-winner rule is proved.
Journal: The Annals of Mathematical Statistics , vol. 43, no. 1972, pp. 871-897, 1972
View Publication
 The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
 ( projecteuclid.org )

## Citation Context (9)

• ...Note that Berry [3] made a similar conjecture regarding a Bernoulli two-armed bandit, which has not been resolved (cf...

### Yi-Ching Yao. Some results on the Gittins index for a normal reward process

• ...See Berry (1972, 1978), Hayre and Turnbull (1981), and Berry and Fristedt (1985) for a detailed discussion of the bandit problem...

### Atanu Biswas. Contribution of Milton Sobel in Selection Problem Following Ethical Al...

• ...INCE the publication of [1], bandit problems have attracted much attention in various areas of statistics, control, learning, and economics (e.g., see [2], [3], [4], [5], [6], [7], [8], [9], [10])...

### Chih-chun Wang, et al. Bandit Problems with Side Observations

• ...Due to the inherent nature of coordinated learning and control, bandit problems have drawn much attention in various areas of statistics, control, learning, and economics, as in [Ada01, Ber72, Che72, GP91, Git79a, Git79b, LR84, LR85, LY95, Rob52]...

### Chih-Chun Wang, et al. Arbitrary side observations in bandit problems

• ...The above problem is known as the “bandit” problem in the literature (Berry (1972), Whittle (1980), Berry and Fristedt (1985), Gittins (1989))...

Sort by:

## Citations (35)

### Prior Ordering and Monotonicity in Dirichlet Bandits

Published in 2011.

### On the optimal amount of experimentation in sequential decision problems

Journal: Statistics & Probability Letters - STAT PROBAB LETT , vol. 80, no. 5, pp. 381-385, 2010

### A Bayesian analysis of human decision-making on bandit problems(Citations: 11)

Journal: Journal of Mathematical Psychology - J MATH PSYCHOL , vol. 53, no. 3, pp. 168-179, 2009

### Dynamic Pricing in e-Services under Demand Uncertainty(Citations: 4)

Journal: Production and Operations Management - PROD OPER MANAG , vol. 16, no. 6, pp. 701-712, 2009

### Some results on the Gittins index for a normal reward process(Citations: 3)

Published in 2007.