Published in SIAM Journal of Control and Optimization, Volume 32, Issue 4, July 1, 1994, pages 937-951.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1137/S0363012992234724.
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.