带有顺序约束的潘多拉魔盒问题
Pandora's Box Problem with Order Constraints
AI总结：
首次研究带顺序约束的潘多拉魔盒问题，证明树状约束下存在贪心最优策略，拟阵或DAG约束下近似求解为NP-hard，并给出近似自适应搜索策略。
摘要：
Pandora's Box Problem（潘多拉魔盒问题）最初由 Weitzman 于 1979 年形式化，用于对评估成本高昂时从一组随机备选方案中进行选择的过程进行建模。例如，这包括雇佣一名熟练工人的问题，其中只能雇佣一人，但对每个候选人的评估是一个昂贵的过程。Weitzman 证明了 Pandora's Box Problem 存在一个优雅且简单的解决方案，即按照 reservation value（保留价值）的递减顺序考虑各个选项，该价值是指使打开盒子的预期边际收益降为零的价值。我们首次研究了在盒子之间施加顺序（或优先级）约束时的这一问题。我们表明，尽管定义考虑到各种选项的深度和广度探索的盒子保留价值存在困难，但对于树状顺序约束，存在贪心最优策略并且可以高效计算。我们还证明，当使用某些拟阵约束进一步限制可以打开的盒子集合，或者当顺序约束作为 DAG 上的可达性约束给出时，寻找近似最优的自适应搜索策略是 NP-hard 的。我们通过基于最优自适应策略与具有有界适应性差距的非自适应策略之间的联系，为该问题的一个精心放宽的版本提供近似自适应搜索策略，从而补充了上述结果。
英文摘要：
The Pandora's Box Problem, originally formalized by Weitzman in 1979, models selection from set of random, alternative options, when evaluation is costly. This includes, for example, the problem of hiring a skilled worker, where only one hire can be made, but the evaluation of each candidate is an expensive procedure. Weitzman showed that the Pandora's Box Problem admits an elegant, simple solution, where the options are considered in decreasing order of reservation value,i.e., the value that reduces to zero the expected marginal gain for opening the box. We study for the first time this problem when order - or precedence - constraints are imposed between the boxes. We show that, despite the difficulty of defining reservation values for the boxes which take into account both in-depth and in-breath exploration of the various options, greedy optimal strategies exist and can be efficiently computed for tree-like order constraints. We also prove that finding approximately optimal adaptive search strategies is NP-hard when certain matroid constraints are used to further restrict the set of boxes which may be opened, or when the order constraints are given as reachability constraints on a DAG. We complement the above result by giving approximate adaptive search strategies based on a connection between optimal adaptive strategies and non-adaptive strategies with bounded adaptivity gap for a carefully relaxed version of the problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
