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

该学院早期职业发展计划(Career)奖将支持对新方法的研究，以显著增强在分布扭曲情况下的数据驱动决策。数据驱动优化是许多行业中支持复杂决策的常用工具，但由此产生的决策往往容易受到数据质量不佳的影响。例如，随机优化方法可能会受到离群值的过度影响，而稳健的优化方法可能会提供过于谨慎的解决方案。这项研究项目调查了一种新的数据驱动优化框架，旨在具体考虑解决方案对数据质量的敏感性，并开发改进这些决策的方法。除了新的本科生和研究生水平的乐观优化课程模块外，该项目的教育部分还包括为对STEM感兴趣的高中女孩开设的夏令营模块、与当地一家科学博物馆的合作，以及基于优化的互动拦截游戏。本项目将为分布有利优化(DFO)建立理论和算法基础，并研究其在分布扭曲下的运营工程领域中的应用。分布有利优化结合了对输入数据的分布假设进行检验的方法，并在最有利分布下选择最优决策。具体地说，本研究将(I)建立能够显著降低离群点影响的DFO的基本框架；(Ii)研究基于分解的求解大规模DFO模型的有效方案，其计算效率高且具有诱人的收敛特性；(Iii)探索和利用非凸DFO模型的子模、聚类和覆盖等结构，以理论性能保证来激励求解算法；以及(Iv)开发学习和优化框架来探索DFO模型中的内生不确定性。DFO可以显著减少离群值的影响，潜在地能够做出更准确和可靠的决定。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.