Dynamic Programming and Linear Programming for Odds Problem
Abstract
This paper discusses the odds problem, proposed by Bruss in 2000, and its variants. A recurrence relation called a dynamic programming (DP) equation is used to find an optimal stopping policy of the odds problem and its variants. In 2013, Buchbinder, Jain, and Singh proposed a linear programming (LP) formulation for finding an optimal stopping policy of the classical secretary problem, which is a special case of the odds problem. The proposed linear programming problem, which maximizes the probability of a win, differs from the DP equations known for long time periods. This paper shows that an ordinary DP equation is a modification of the dual problem of linear programming including the LP formulation proposed by Buchbinder, Jain, and Singh.
Cite
@article{arxiv.2107.13146,
title = {Dynamic Programming and Linear Programming for Odds Problem},
author = {Sachika Kurokawa and Tomomi Matsui},
journal= {arXiv preprint arXiv:2107.13146},
year = {2021}
}
Comments
12 pages, 1 figure