CAREER: Hierarchical Commit or Defer Problems with Learning: Methods and Applications

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。这项教师早期职业发展计划（Career）资助的研究将调查理论和计算方法，以提交或推迟决策层次问题。疫苗设计、灾害应对和走私预防等方面的问题设置涉及决策者观察系统随时间的演变，他们定期决定是否投入不可再生资源或推迟其使用，以优化系统的整体性能。系统的演化受制于随机性，其性能可能取决于其他决策者，关于他们的信息可能不完整，他们寻求优化自己的性能。该奖项支持的研究旨在确定在这些设置中应该使用哪些规则来指导提交或推迟决策，决策者应该如何以及在多大程度上使用所观察到的信息反馈，以及如何在特定问题设置中通过计算找到提交或推迟决策。教育活动包括创建一个在线游戏，向K-12学生教授多阶段决策的基础知识。标准提交或延迟问题（cdp）假设只有一个决策者，并且不能对涉及多个决策者的问题进行建模，例如，一个领导者和一个追随者，他们以分层方式交互。该项目将建立一个数学和算法框架来解决分层cdp。该框架将增进我们对现实生活中的cdp及其实际需求的理解。该项目将同时解决一些技术挑战。首先，领导者可能面临全球性的资源限制，例如在一个时期内消耗的资源无法在未来的时期内补充；第二，领导者的表现取决于追随者的最佳行动；第三，领导者通过观察追随者对领导者行为的反应来了解追随者问题的不确定参数。通过使用分层优化和在线优化的接口方法，该项目将严格建立在不确定的分层设置下提交或推迟决策的方式。此外，该项目将使用数学规划和概率的工具来揭示决策者应该如何以及在多大程度上使用所学到的信息，然后在相关应用程序的大型实例中制定和解决最优或接近最优的策略。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).This Faculty Early Career Development Program (CAREER) grant supports research that will investigate theoretical and computational approaches to commit or defer problems with decision-making hierarchies. Problem settings in vaccine design, disaster response, and smuggling prevention, among others, involve decision-makers observing a system evolving over time who periodically decide whether to commit non-renewable resources, or defer their use, to optimize the system's overall performance. The evolution of the system is subject to randomness and its performance may depend on other decision makers, about whom there may be incomplete information, who seek to optimize their own performance. The research supported by this award seeks to determine what rules should guide commit or defer decisions in these settings, how and to what extent the decision-maker should use the information feedback observed, and how to computationally find the commit or defer decisions in specific problem settings. The educational activities include the creation of an online game to teach fundamentals of multistage decision-making to K-12 students. Standard commit or defer problems (CDPs) assume a single decision-maker and cannot model problems that involve multiple decision-makers, e.g., a Leader and a Follower, who interact in a hierarchical manner. This project will establish a mathematical and algorithmic framework to solve hierarchical CDPs. The framework will improve our understanding of real-life CDPs and their practical requirements. The project will simultaneously address a number of technical challenges. First, the Leader may face global resource constraints, such that the resources spent in one period, cannot be replenished in future periods; second, the Leader's performance depends on the optimal actions of the Follower; and third, the Leader learns about the uncertain parameters of the Follower's problem by observing their reaction to the Leader's actions. By using approaches at the interface of hierarchical and online optimization, the project will rigorously establish the manner by which commit or defer decisions should be made in hierarchical settings under uncertainty. Furthermore, the project will use tools from mathematical programming and probability to uncover how and to what extent the decision-maker should use the information that is learned, and then formulate and solve for optimal or near optimal policies in large instances of relevant applications.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.