Abstract
A bandit problem is interesting only if there are arms with unknown characteristics. To choose among the available arms a decision maker must first decide how to handle this uncertainty. In the first eight chapters of this monograph the approach used is to average the payoff over the unknown characteristics with respect to a specified prior distribution — a Bayesian approach, in statistical parlance.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bather, J. A. (1983) Personal communication.
Bather, J. A. and Simons, G. (1985) The minimax risk for clinical trials. J.R. Statist. Soc. B (to appear).
Feller, W. (1968) An Introduction to Probability Theory and Its Applications, Vol. I, 3rd edn, Wiley, New York.
Fristedt, B. (1974) Sample functions of stochastic processes with stationary, independent increments. Advances in Probability, Vol. 3 (eds P. Ney and S. Port), pp. 241–396, Marcel-Dekker, New York.
Parthasarathy, T. and Raghavan, T. E. S. (1971) Some Topics in Two-Person Games, American Elsevier, New York.
Vogel, W. (1960a) A sequential design for the two-armed bandit. Ann. Math. Statist. 31: 430–443.
Vogel, W. (1960b) An asymptotic minimax theorem for the two-armed bandit problem. Ann. Math. Statist. 31: 444–451.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 D. A. Berry and B. Fristedt
About this chapter
Cite this chapter
Berry, D.A., Fristedt, B. (1985). Minimax Approach. In: Bandit problems. Monographs on Statistics and Applied Probability. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-3711-7_9
Download citation
DOI: https://doi.org/10.1007/978-94-015-3711-7_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-015-3713-1
Online ISBN: 978-94-015-3711-7
eBook Packages: Springer Book Archive