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Two-armed bandits with a goal, I. One arm known

Published online by Cambridge University Press:  01 July 2016

Donald A. Berry  and
Bert Fristedt
Donald A. Berry
Affiliation:
University of Minnesota
Bert Fristedt
Affiliation:
University of Minnesota
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Abstract

One of two random variables, X and Y, can be selected at each of a possibly infinite number of stages. Depending on the outcome, one's fortune is either increased or decreased by 1. The probability of increase may not be known for either X or Y. The objective is to increase one's fortune to G before it decreases to g, for some integral g and G; either may be infinite.

In the current part of the paper, the distribution of X is unknown and that of Y is known. We characterize the situations in which optimal strategies exist and, for certain kinds of information concerning X and Y, we characterize optimal sequential strategies for choosing to observe X and Y.

In Part II (Berry and Fristedt (1980)), it is known that either X or Y has probability α of increasing the current fortune by 1 and the other has probability β of increasing the fortune by 1, where α and β are known, but which goes with X is not known.

Keywords

ACHIEVING A GOALTWO-ARMED BANDITSHOW TO GAMBLE IF YOU MUSTGAMBLER'S RUINSEQUENTIAL DECISIONSBAYESIAN DECISION MAKINGSEQUENTIAL MEDICAL TREATMENTSSTOCHASTIC CONTROLOPTIMAL DYNAMIC DESIGNS
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 3 , September 1980 , pp. 775 - 798
Copyright
Copyright © Applied Probability Trust 1980 

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References

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