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

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.