TY - GEN
T1 - A Combinatorial Proof for the Dowry Problem
AU - Liu, Xujun
AU - Milenkovic, Olgica
AU - Moustakides, George V.
N1 - Funding Information:
Acknowledgment. We thank the anonymous reviewers for their valuable comments. The work was supported in part by the NSF CCF 15-26875 and CIF 1513373 grants.
Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - The Secretary problem is a classical sequential decision-making question that can be succinctly described as follows: a set of rank-ordered applicants are interviewed sequentially for a single position. Once an applicant is interviewed, an immediate and irrevocable decision is made if the person is to be offered the job or not and only applicants observed so far can be used in the decision process. The problem of interest is to identify the stopping rule that maximizes the probability of hiring the highest-ranked applicant. A multiple-choice version of the Secretary problem, known as the Dowry problem, assumes that one is given a fixed integer budget for the total number of selections allowed to choose the best applicant. It has been solved using tools from dynamic programming and optimal stopping theory. We provide the first combinatorial proof for a related new query-based model for which we are allowed to solicit the response of an expert to determine if an applicant is optimal. Since the selection criteria differ from those of the Dowry problem, we obtain nonidentical expected stopping times.
AB - The Secretary problem is a classical sequential decision-making question that can be succinctly described as follows: a set of rank-ordered applicants are interviewed sequentially for a single position. Once an applicant is interviewed, an immediate and irrevocable decision is made if the person is to be offered the job or not and only applicants observed so far can be used in the decision process. The problem of interest is to identify the stopping rule that maximizes the probability of hiring the highest-ranked applicant. A multiple-choice version of the Secretary problem, known as the Dowry problem, assumes that one is given a fixed integer budget for the total number of selections allowed to choose the best applicant. It has been solved using tools from dynamic programming and optimal stopping theory. We provide the first combinatorial proof for a related new query-based model for which we are allowed to solicit the response of an expert to determine if an applicant is optimal. Since the selection criteria differ from those of the Dowry problem, we obtain nonidentical expected stopping times.
UR - http://www.scopus.com/inward/record.url?scp=85164994225&partnerID=8YFLogxK
U2 - 10.1109/ITW55543.2023.10161638
DO - 10.1109/ITW55543.2023.10161638
M3 - Conference Proceeding
AN - SCOPUS:85164994225
T3 - 2023 IEEE Information Theory Workshop, ITW 2023
SP - 538
EP - 543
BT - 2023 IEEE Information Theory Workshop, ITW 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2023 IEEE Information Theory Workshop, ITW 2023
Y2 - 23 April 2023 through 28 April 2023
ER -