A Best-Choice Problem With Linear Travel Cost
研究了旅行者在无限候选者中寻找最佳人选的问题,旅行成本与距离成正比,若选错则损失单位成本,推导了最优策略及其风险,并求解了有限版本。
Abstract The concepts of sampling cost and recall of previously seen applicants are here combined in a natural way: The best, second best, and so forth, of infinitely many applicants are located at points independently and uniformly distributed on the unit interval. A traveler, observing relative ranks, hopes to select the best applicant, and incurs a cost proportional to the total distance traveled, plus a unit loss if the applicant selected is not overall best. The optimal policy and its risk are derived. A finite version of the problem is also solved.