鲁棒主动偏好获取
Robust Active Preference Elicitation
摘要：
我们研究的问题，通过适度数量的成对比较查询，使他们成为一个高质量的建议，一个特定的问题，引起决策者的偏好。我们的动机是高风险领域的应用，例如选择分配稀缺资源以满足基本需求的政策（例如，肾脏移植或无家可归者的住房），其中需要根据（部分）引出的偏好做出相应的建议。我们将偏好中的不确定性建模为基于设置的，并调查两种设置：a）离线启发设置，其中所有查询都是同时进行的，以及b）在线启发设置，其中查询以自适应方式随着时间的推移顺序选择。我们提出了这些问题的强大的优化配方，集成的偏好诱导和推荐阶段，旨在最大限度地提高最坏情况下的效用或最小化最坏情况下的遗憾，并研究其复杂性。对于离线的情况下，积极的偏好启发采取的形式，两个半阶段的强大的最优化问题与决策相关的信息发现，我们提供了一个等价的重新制定的形式，我们解决了通过列和约束生成的混合二进制线性规划。对于在线设置，主动偏好学习的形式是一个多阶段的强大的最优化问题与决策相关的信息发现，我们提出了一个保守的解决方案。对合成数据的数值研究表明，我们的方法在最坏情况下的排名，遗憾和效用方面优于文献中最先进的方法。我们展示了我们的方法可以用来帮助无家可归的服务机构在选择一项政策，分配稀缺的住房资源的不同类型的人经历无家可归。
英文摘要：
We study the problem of eliciting the preferences of a decision-maker through a moderate number of pairwise comparison queries to make them a high quality recommendation for a specific problem. We are motivated by applications in high stakes domains, such as when choosing a policy for allocating scarce resources to satisfy basic needs (e.g., kidneys for transplantation or housing for those experiencing homelessness) where a consequential recommendation needs to be made from the (partially) elicited preferences. We model uncertainty in the preferences as being set based and} investigate two settings: a) an offline elicitation setting, where all queries are made at once, and b) an online elicitation setting, where queries are selected sequentially over time in an adaptive fashion. We propose robust optimization formulations of these problems which integrate the preference elicitation and recommendation phases with aim to either maximize worst-case utility or minimize worst-case regret, and study their complexity. For the offline case, where active preference elicitation takes the form of a two and half stage robust optimization problem with decision-dependent information discovery, we provide an equivalent reformulation in the form of a mixed-binary linear program which we solve via column-and-constraint generation. For the online setting, where active preference learning takes the form of a multi-stage robust optimization problem with decision-dependent information discovery, we propose a conservative solution approach. Numerical studies on synthetic data demonstrate that our methods outperform state-of-the art approaches from the literature in terms of worst-case rank, regret, and utility. We showcase how our methodology can be used to assist a homeless services agency in choosing a policy for allocating scarce housing resources of different types to people experiencing homelessness.
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