测试与发现模型

中文摘要 AI 辅助

我们引入了测试与发现（Test and Find，TF）问题，其中决策者（Decision Maker，DM）面临如下场景：k个相同对象根据某分布π被随机分配到n个不同的盒子（位点）中，每个盒子最多放1个对象。决策者对所有盒子进行测试，但测试并非完美，可能出现假阳性或假阴性结果。决策者拥有m个标签（1≤m≤n），在测试完所有盒子后，可在任意她认为藏有对象的盒子上放置1个标签；若猜对盒子i中有对象，将获得奖励c_i，若猜错则受到惩罚d_i。决策者知晓模型的所有参数，目标是最大化期望奖励。我们给出了该问题的显式解，随后转向对称情形，推导了计算效率更高的结果，还考虑了TF模型的若干扩展并给出详细解法，其中一个扩展针对更贴近实际的情形：对象数量k未知且为随机变量。

英文摘要

We introduce the Test and Find (TF) problem, where a decision maker (DM) faces the following situation: $k$ identical objects are randomly allocated to $n$ distinct boxes (sites) according to some distribution $π$, with no more than one object to a box. The DM tests all of the boxes. However, the tests are imperfect: they can give false positive or false negative results. DM has $m$ tags, $1\leq m\leq n$, and, after testing all boxes, she can place a tag on any box that she thinks has a hidden object. She is rewarded $c_i$ for a correct guess and penalized $d_i$ for a wrong guess in box $i$. DM knows all of the parameters of the model and her goal is to maximize the expected reward. We give an explicit solution to this problem. We then turn to the symmetric case, for which we derive more computationally efficient results. We also consider several extensions of the TF model and give detailed solutions. One of these extensions is to the realistic case where $k$, the number of objects, is unknown and random.

发表机构

• University of North Carolina Charlotte（北卡罗来纳大学夏洛特分校）

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