The objective of this research is to enable computationally-efficient numerical solutions to extremely high-dimensional, nonstationary approximate dynamic programming. This project's Dallas-Fort Worth International Airport deicing activities application involves over 7000 dimensions, while the largest solved to-date is Dr. Chen's air quality application with 524 dimensions. The approach develops a novel and challenging integration of perspectives from statistics, optimization, and reinforcement learning to create efficient new hybrid algorithms.
Intellectual Merit: This research's statistical perspective is unique within the approximate dynamic programming community and is the key to parsimony. This project's integrated approach will yield new algorithms for exploration of state and decision spaces, critical for the popular reinforcement learning approach; simultaneous adaptive design and modeling, beneficial to the larger modeling community; and nonconvex optimization of statistical models, useful for general global optimization. The success of this integration will potentially transform the way researchers conduct exploration and modeling in approximate dynamic programming.
Broader Impacts: This research is important because it can yield practical methods for complex, uncertain, and dynamic decision-making systems, including environmental policy, health care and medicine, energy distribution and diversity, homeland security, and disaster mitigation. Current solutions use oversimplifications that typically compromise social benefits to satisfy economic constraints, while this project seeks to efficiently represent the true system via an intelligent and parsimonious approach. As a major gateway, the airport must address issues involving many of the above systems, and a long-term collaboration with the airport will yield motivating applications benefiting education, such as dissertations, seminars, and course material.
