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Bilevel Optimization with Learning

带学习的双层优化

基本信息

批准号：
1634835
负责人：
Oleg Prokopyev
金额：
$ 22.76万
依托单位：
University of Pittsburgh
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-09-01 至 2020-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1634835&HistoricalAwards=false
关键词：
Bilevel Optimization Learning

项目摘要

Bilevel optimization involves mathematical models that describe hierarchical decision-making processes between multiple, usually two, decision-makers, referred to as a leader and a follower. A typical bilevel mathematical program assumes that one of the decision-makers, namely, the leader, knows the parameters of the follower's problem. Yet, there are various applications where the leader has incomplete information about the problem faced by the follower. In particular, this research is focused on practical settings, where the leader faces a classical exploitation vs. exploration trade-off: the leader and the follower interact during multiple time periods and the leader has an opportunity to update her knowledge of the follower's problem, and to incorporate this information into the decision-making process. Bilevel optimization has been a popular modeling and solution tool applied in different areas such as law enforcement, economics, transportation, health care and energy. However, standard bilevel optimization does not address this exploration vs. exploitation trade-off arising in many important applications. Therefore, the results of this work will provide improved methods for decision-makers. This project will also have educational impacts for graduate and undergraduate students through courses and direct participation in the research; participation of students from the underrepresented groups will be encouraged, including undergraduate via the REU supplement.The research will result in a new set of models and solution methods for sequential decision-making problems with uncertainty and learning in bilevel settings by combining bilevel, online and robust optimization techniques. The interface between these methods is a fairly unexplored topic. In addition, a new class of benchmarks will be developed based on the notion of a semi-oracle for validating the effectiveness of the different policies. Finally, the decision-making policies and benchmarks will require development of sophisticated algorithms. Thus, the results of this research will also enhance the overall ability to solve hard classes of bilevel and sequential optimization problems, including those under uncertainty.

双层优化涉及描述多个（通常是两个）决策者（称为领导者和追随者）之间的分层决策过程的数学模型。一个典型的二层数学规划假设决策者之一，即领导者，知道跟随者问题的参数。然而，在许多应用中，领导者对跟随者所面临的问题的信息不完全。特别是，这项研究的重点是实际的设置，领导者面临着一个经典的开发与探索权衡：领导者和追随者在多个时间段的互动和领导者有机会更新她的知识追随者的问题，并将这些信息纳入决策过程。双层优化已经成为一种流行的建模和求解工具，应用于不同的领域，如执法，经济，交通，医疗保健和能源。然而，标准的双层优化并没有解决在许多重要应用中出现的这种探索与开发的权衡。因此，这项工作的结果将为决策者提供改进的方法。该项目还将通过课程和直接参与研究，对研究生和本科生产生教育影响;将鼓励代表性不足的群体的学生参与，包括通过REU补充的本科生。该研究将通过结合双层，在线和鲁棒优化技术。这些方法之间的接口是一个相当未开发的主题。此外，将根据半预言的概念开发一类新的基准，以验证不同政策的有效性。最后，决策政策和基准将需要开发复杂的算法。因此，这项研究的结果也将提高整体能力，解决困难的类的双层和顺序优化问题，包括那些不确定性。