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Prior Information
Probability Distribution
twoarmed bandit
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(8)
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A Bernoulli Twoarmed Bandit
A Bernoulli Twoarmed Bandit,10.1214/aoms/1177692553,The Annals of Mathematical Statistics,Donald A. Berry
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A Bernoulli Twoarmed Bandit
(
Citations: 35
)
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Donald A. Berry
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 stayonawinner rule is proved.
Journal:
The Annals of Mathematical Statistics
, vol. 43, no. 1972, pp. 871897, 1972
DOI:
10.1214/aoms/1177692553
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Citation Context
(9)
...Note that Berry [
3
] made a similar conjecture regarding a Bernoulli twoarmed bandit, which has not been resolved (cf...
YiChing 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])...
Chihchun 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]...
ChihChun 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))...
Tackseung Jun
.
A survey on the bandit problem with switching costs
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Citations
(35)
Prior Ordering and Monotonicity in Dirichlet Bandits
Yaming Yu
Published in 2011.
On the optimal amount of experimentation in sequential decision problems
Dinah Rosenberg
,
Eilon Solan
,
Nicolas Vieille
Journal:
Statistics & Probability Letters  STAT PROBAB LETT
, vol. 80, no. 5, pp. 381385, 2010
A Bayesian analysis of human decisionmaking on bandit problems
(
Citations: 11
)
Mark Steyvers
,
Michael D. Lee
,
EricJan Wagenmakers
Journal:
Journal of Mathematical Psychology  J MATH PSYCHOL
, vol. 53, no. 3, pp. 168179, 2009
Dynamic Pricing in eServices under Demand Uncertainty
(
Citations: 4
)
Cathy H. Xia
,
Parijat Dube
Journal:
Production and Operations Management  PROD OPER MANAG
, vol. 16, no. 6, pp. 701712, 2009
Some results on the Gittins index for a normal reward process
(
Citations: 3
)
YiChing Yao
Published in 2007.