On the One Arm Bandit Problem.
GEORGE WASHINGTON UNIV WASHINGTON D C DEPT OF STATISTICS
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The author considers the one arm bandit problem when future losses are discounted by a factor gamma per time period, 0 gamma 1. The author adopts a Bayesian approach and formulates the problem as an optimal stopping problem. In the case of a uniform distribution with an unknown range or normal distribution with an unknown mean, it is shown that the boundaries of the continuation region in the parameter space of the conjugate prior family approach limits as gamma nears 1 after appropriate normalization in the normal case. Modified author abstract
- Statistics and Probability