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Some memoryless bandit policies

Part of: Sequential methods Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Erol A. Peköz
Erol A. Peköz*
Affiliation:
Boston University
*
∗ Postal address: School of Management, Boston University, Boston, MA 02215, USA. Email address: [email protected]
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Abstract

We consider a multiarmed bandit problem, where each arm when pulled generates independent and identically distributed nonnegative rewards according to some unknown distribution. The goal is to maximize the long-run average reward per pull with the restriction that any previously learned information is forgotten whenever a switch between arms is made. We present several policies and a peculiarity surrounding them.

Keywords

Bandit problemmultiarmed bandit problemaverage reward criteria

MSC classification

Primary: 62L05: Sequential design 90B36: Scheduling theory, stochastic 62L15: Optimal stopping
Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 1 , March 2003 , pp. 250 - 256
Copyright
Copyright © Applied Probability Trust 2003 

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References

[1] Bellman, R. (1956). A problem in the sequential design of experiments. Sankhyā 16, 221–229.Google Scholar
[2] Berry, D. A., and Fristedt, B. (1985). Bandit Problems: Sequential Allocation of Experiments. Chapman and Hall, London.Google Scholar
[3] Berry, D. A. et al. (1997). Chen, R. W., Zame, A., Heath, D. C., Shepp, L. A. Bandit problems with infinitely many arms. Ann. Statist. 25, 2103–2116.Google Scholar
[4] Cover, T. (1987). Pick the largest number. In Open Problems in Communication and Computation, eds Cover, T. and Gopinath, B., Springer, New York, p. 152.Google Scholar
[5] Durrett, R. (1996). Probability: Theory and Examples, 2nd edn. Wadsworth Publishing, Belmont, CA.Google Scholar
[6] Gittins, J. C., and Jones, D. M. (1974). A dynamic allocation index for the sequential design of experiments. In Progress in Statistics (Europ. Meeting Statisticians, Budapest, 1972), Vol. 1, eds Gani, J., Sarkadi, K. and Vincze, I., North-Holland, Amsterdam, pp. 241–266.Google Scholar
[7] Herschkorn, S. J., Peköz, E., and Ross, S. M. (1996). Policies without memory for the infinite-armed Bernoulli bandit under the average-reward criterion. Prob. Eng. Inf. Sci. 10, 21–28.Google Scholar
[8] Lai, T. L., and Robbins, H. (1985). Asymptotically efficient adaptive allocation rules. Adv. Appl. Math. 6, 4–22.Google Scholar
[9] Lin, C.-T., and Shiau, C.J. (2000). Some optimal strategies for bandit problems with beta prior distributions. Ann. Inst. Statist. Math. 52, 397–405.Google Scholar
[10] Psounis, K., and Prabhakar, B. (2001). A randomized web-cache replacement scheme. In Proc. IEEE Infocom 2001 (Anchorage, AK, 22–26 April 2001), pp. 1407–1415. Available at http://www.ieee-infocom.org/2001/.Google Scholar