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Optimal stopping and dynamic allocation

Published online by Cambridge University Press:  01 July 2016

Fu Chang  and
Tze Leung Lai
Fu Chang*
Affiliation:
AT & T Bell Laboratories
Tze Leung Lai*
Affiliation:
Columbia University
*
∗Postal address: AT & T Bell Laboratories, Crawfords Corner Road, Holmdel, NJ 07733, USA.
∗∗Postal address: Dept. of Statistics, Box 10 Mathematics, Columbia University, New York, NY 10027, USA.
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Abstract

A class of optimal stopping problems for the Wiener process is studied herein, and asymptotic expansions for the optimal stopping boundaries are derived. These results lead to a simple index-type class of asymptotically optimal solutions to the classical discounted multi-armed bandit problem: given a discount factor 0<β <1 and k populations with densities from an exponential family, how should x1, x2,… be sampled sequentially from these populations to maximize the expected value of Ʃ∞1 βi−1xi, in ignorance of the parameters of the densities?

Keywords

STOPPING BOUNDARYASYMPTOTIC EXPANSIONGITTINS INDEXWIENER PROCESSEXPONENTIAL FAMILY
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 4 , December 1987 , pp. 829 - 853
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Research supported by the National Science Foundation and the Army Research Office.

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