Abstract
We consider the best-choice problem with disorder and imperfect observation. The decision-maker observes sequentially a known number of i.i.d random variables from a known distribution with the object of choosing the largest. At the random time the distribution law of observations is changed. The random variables cannot be perfectly observed. Each time a random variable is sampled the decision-maker is informed only whether it is greater than or less than some level specified by him. The decision-maker can choose at most one of the observation. The optimal rule is derived in the class of Bayes' strategies.
Highlights
In the papers we consider the following best-choice problem with disorder and imperfect observations
The observations ξ1, . . . , ξθ−1 are from a continuous distribution law F1 x state S1
At the random time θ, the distribution law of observations is changed to continuous distribution function F2 x i.e., the disorder happen—state S2
Summary
In the papers we consider the following best-choice problem with disorder and imperfect observations. The aim of the decision-maker is to maximize the expected value of the accepted discounted observation. The decision-maker accepts the observation xk if and only if it is greater than the corresponding threshold s. This problem is the generalization of the best-choice problem 1, 2 and the quickest determination of the change-point disorder problem 3–5. In 11 , we constructed the solution of the combined best-choice and disorder problem in the class of single-level strategies, and, in this paper, we search the Bayes’ strategy which maximizes the expected reward in the model with imperfect observation
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