CAREER: Favorable Optimization under Distributional Distortions: Frameworks, Algorithms, and Applications

This Faculty Early Career Development Program (CAREER) award will support the investigation of new methods to significantly enhance data-driven decision-making under distributional distortions. Data-driven optimization is a commonly used tool in many industries to support complex decision making, but the resulting decisions are often susceptible to poor data quality. Stochastic optimization methods, for example, may be unduly influenced by outliers, while robust optimization methods may provide solutions that are overly cautious. This research project investigates a new framework for data-driven optimization, intended to specifically take into account the sensitivity of solutions to data quality, and to develop methods to improve these decisions. In addition to new undergraduate and graduate-level course modules on optimistic optimization, the educational components of this project include a summer camp module for high school girls interested in STEM, collaboration with a local science museum, and an interactive optimization-based interdiction game. This project will establish theoretical and algorithmic foundations for Distributionally Favorable Optimization (DFO) and investigate its applications to the areas of operations engineering under distributional distortions. Distributionally Favorable Optimization incorporates methods to examine distributional assumption on the input data and select the optimal decision under the most-favorable distribution. Specifically, this research will (i) establish fundamental frameworks for DFO that can substantially reduce the effects of outliers; (ii) investigate effective decomposition-based solution schemes for solving large-scale DFO models that are computationally efficient and have attractive convergent properties; (iii) explore and exploit structures such as submodularity, clustering, and covering of nonconvex DFO models, stimulating solution algorithms with theoretical performance guarantees; and (iv) develop learning-and-optimization frameworks to explore endogenous uncertainty in the DFO models. DFO can significantly reduce the effects of outliers, potentially enabling more accurate and reliable decisions. 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.