非强制性检查的潘多拉问题
Pandora's Problem with Nonobligatory Inspection
摘要：
马丁·魏茨曼的“潘多拉问题”为经济学中的最优搜索理论提供了数学基础。近40年后，劳拉·多瓦尔（Laura Doval）提出了一个问题的版本，在这个版本中，参与者没有义务在选择之前支付检查选项价值的费用。与最初的潘多拉问题不同，非强制性检查的版本不能通过任何简单的基于排名的策略来最优解决，并且不知道是否存在任何多项式时间算法来计算最优策略。这激发了对简单且计算效率高的近似最优策略的研究。在这项工作中，我们提供了第一个非平凡的近似保证这个问题。我们引入了一个家庭的“提交政策”，这样它是计算上很容易找到和实施的最佳提交政策。我们证明了最优提交策略保证在一个$1-\frac1e = 0.63\ldots$因子内逼近完全最优策略，对于两个盒子的特殊情况，我们将这个因子改进为4/5，并证明了这种逼近对于提交策略类是紧的.
英文摘要：
Martin Weitzman's "Pandora's problem" furnishes the mathematical basis for optimal search theory in economics. Nearly 40 years later, Laura Doval introduced a version of the problem in which the searcher is not obligated to pay the cost of inspecting an alternative's value before selecting it. Unlike the original Pandora's problem, the version with nonobligatory inspection cannot be solved optimally by any simple ranking-based policy, and it is unknown whether there exists any polynomial-time algorithm to compute the optimal policy. This motivates the study of approximately optimal policies that are simple and computationally efficient. In this work we provide the first non-trivial approximation guarantees for this problem. We introduce a family of "committing policies" such that it is computationally easy to find and implement the optimal committing policy. We prove that the optimal committing policy is guaranteed to approximate the fully optimal policy within a $1-\frac1e = 0.63\ldots$ factor, and for the special case of two boxes we improve this factor to 4/5 and show that this approximation is tight for the class of committing policies.
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