Minimax-Optimal Strategies for the Best-Choice Problem When a Bound is Known for the Expected Number of Objects
نویسندگان
چکیده
For the best-choice (or secretary) problem with an unknown number N of objects, minimax-optimal strategies for the observer and minimax distributions for N are derived under the assumption that N is a random variable with expected value at most M, where M is known. The solution is derived as a special case of the situation where N is constrained by Ef(N) <_ M, where f is increasing with f(i) f(i 1) convex. Key words, best-choice problem; secretary problem; minimax strategies" optimal stopping; convexity" Lagrangian; Lagrange multiplier AMS subject classification. 60G40
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تاریخ انتشار 2010