Minimax-Optimal Stop Rules and Distributions in Secretary Problems

Abstract

For the secretary(o r best-choicep)r oblemw itha n unknownn umberN of objects, m inimax-optimsatlo p rules and (worst-cased) istributionasr e derivedu, ndert he assumptionth at N is a randomv ariablew ithu nknown distributionb,u t knownu pperb ound n. Asymptoticalltyh,e probabilitoyf selectingt he best object in this situationi s of order of (log n)-Y. For examplee, veni ft heo nlyi nformatioanv ailablei s thatt herea re somewhere between1 and 100 objectst, herei s stilla strategyw hichw ills electt heb est itema bouto ne timei n five