不要掷骰子，问两次：匹配问题的两个查询扭曲及其他
Don't Roll the Dice, Ask Twice: The Two-Query Distortion of Matching Problems and Beyond
摘要：
在大多数社会选择环境中，参与主体以线性排序的形式表达他们对不同选项的偏好。虽然这显然简化了偏好诱导，但它不可避免地导致在优化基本目标（如社会福利）方面的性能较差，因为代理人的价值实际上仍然未知。由于缺乏信息而造成的性能损失可以用失真的概念来衡量。最近的一系列工作提出了设计机制的议程，通过查询学习代理的价值为少数的替代品，并使用这有限的额外信息，使更明智的决策，从而改善失真。根据这一议程，在这项工作中，我们专注于一类组合问题，包括最知名的匹配问题和他们的几个概括，如单边匹配，双边匹配，一般图匹配，和$k$ -约束资源分配。我们设计了两个查询机制，实现了最好的可能的最坏情况下的失真方面的社会福利，并优于最好的可能的预期失真实现随机顺序机制。
英文摘要：
In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor performance with respect to optimizing a cardinal objective, such as the social welfare, since the values of the agents remain virtually unknown. This loss in performance because of lack of information is measured by the notion of distortion. A recent array of works put forward the agenda of designing mechanisms that learn the values of the agents for a small number of alternatives via queries, and use this limited extra information to make better-informed decisions, thus improving distortion. Following this agenda, in this work we focus on a class of combinatorial problems that includes most well-known matching problems and several of their generalizations, such as One-Sided Matching, Two-Sided Matching, General Graph Matching, and $k$-Constrained Resource Allocation. We design two-query mechanisms that achieve the best-possible worst-case distortion in terms of social welfare, and outperform the best-possible expected distortion achieved by randomized ordinal mechanisms.
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。
