SOME RESULTS FOR A MULTI-ARMED BANDIT PROBLEM

抄録

A multi-armed bandit problem is the problem of the sequential design of experiments in which the trial to select and pull one of m arms at each stage is performed sequentially n times and by pulling one arm, an observation is obtained from the distribution with unknown parameters. There is a prior information about the values of the parameters. The objective is to maximize the sum of n observations. Even if the number of arms is 2, the problem is difficult to solve. If it is possible to find the arm which will never be used in the remaining n stages whatever observations will be obtained under the optimal strategy, that arm may be neglected. In this paper, we consider the twoarmed bandit problem with one arm known for the family of distributions with positive means and show how to find this unuseful arm by using critical value functions.