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

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。该教师早期职业发展计划（CAREER）资助支持研究，将调查理论和计算方法，以解决或推迟决策层次问题。在疫苗设计、灾难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，他们定期决定是否承诺不可再生资源或推迟其使用，以优化系统的整体性能。系统的演变是随机的，其性能可能取决于其他决策者，可能有不完整的信息，谁寻求优化自己的表现。该奖项支持的研究旨在确定在这些环境中应该指导提交或推迟决策的规则，决策者应该如何以及在多大程度上使用观察到的信息反馈，以及如何在特定问题设置中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。 标准提交或推迟问题（CDP）假设单个决策者，并且不能对涉及多个决策者的问题建模，例如，一个领导者和一个追随者，他们以分层的方式互动。本计画将建立一个数学与演算架构，以解决阶层式协同设计问题。该框架将提高我们对现实生活中的CDP及其实际要求的理解。该项目将同时解决若干技术挑战。首先，领导者可能面临全局资源约束，例如在一个时期花费的资源在未来时期无法补充;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动的反应来了解追随者问题的不确定参数。通过使用分层和在线优化接口处的方法，该项目将严格建立在不确定性下在分层设置中做出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，该奖项反映了NSF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进行评估，被认为值得支持的搜索.

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.