Minimax-Optimal Strategies for the Best-Choice Problem When a Bound is Known for the Expected Number of Objects
Theodore Preston Hill, Douglas P. Kennedy · SIAM Journal on Control and Optimization · 1994
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 $Ef(N) \leq M$, where f is increasing with $f(i) - f(i - 1)$ convex.