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A study on the best choice problem based on the ranks of observations

基于观测值排序的最佳选择问题研究

基本信息

批准号：
10680439
负责人：
TAMAKI Mitsuhi
金额：
$ 1.73万
依托单位：
Aichi University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10680439/
关键词：
secretary problem best choice problem optimal stopping relative rank dynamic programming multiple choice rank minimization probability maximization optimal selection urn problem ballot problem random walk multiple choril optiomal

项目摘要

In 1998 and 1999, we mainly studied the secretary problem with rank-dependent rejection probability. The main result is summarized in Section 2.6. The rank minimization problem with refusal is considered in Section 2.7. The problem considered in Section 2.5 also falls into the category of the problem with refusal. Boyce's urn problem, a model of bond-selling problem, is modified as a problem of stopping on the maximum of the trajectory with maximum probability. This is analyzed in Section 2.12. The versions of the so called duration problem, which is concerned with maximizing the expected duration of keeping the relatively best applicant, are considered in Sections 2.2 and 2.3. A multiple-choice secretary problem with a random number of applicants is considered in Section 2.4..In 2000, the problems we considered are probabilistic interpretation of an identity related to the Stirling number of the first kind and an optimal stopping problem related to the random walk. The results are given in Sections 2.8 and 2.10 respectively.In 2001, Bruss odds theorem is generalized to cover the case with uncertain selection. A multiple-choice secretary problem with partial recall whose objective is to minimize the total expected ranks of the applicants chosen is still under consideration. However, its partial result is given in Section 7 of the survey paper given in Section 2.14. Sections 2.1,2.9 and 2.13 are devoted to some related problems.

1998年和1999年，我们主要研究了具有等级依赖拒绝概率的秘书问题。主要结果在2.6节中进行了总结。第2.7节将考虑拒绝的秩最小化问题。第2.5节所考虑的问题也属于拒绝问题的范畴。将债券出售问题模型Boyce's urn问题修正为最大概率在轨迹最大值处停止的问题。第2.12节对此进行了分析。所谓的持续时间问题的不同版本将在2.2节和2.3节中讨论，该问题涉及如何最大化保留相对最佳申请人的预期持续时间。在第2.4节中考虑了一个带有随机申请人数量的秘书选择题。在2000年，我们考虑的问题是与第一类斯特林数相关的恒等式的概率解释和与随机漫步相关的最优停止问题。结果分别在第2.8节和2.10节中给出。2001年，将Bruss几率定理推广到具有不确定选择的情况。一个带有部分回忆的秘书选择题，其目标是最小化所选申请人的总期望等级，目前仍在考虑之中。然而，其部分结果载于第2.14条所载的调查报告第7条。第2.1、2.9和2.13节专门讨论一些相关问题。