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Minimax-Optimal Strategies For The Best-Choice Problem When A Bound Is Known For The Expected Number Of Objects, Theodore P. Hill, D. P. Kennedy
Minimax-Optimal Strategies For The Best-Choice Problem When A Bound Is Known For The Expected Number Of Objects, Theodore P. Hill, D. P. Kennedy
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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.