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，以显着提高分布扭曲下的数据驱动决策。数据驱动优化是许多行业中常用的工具，用于支持复杂的决策制定，但最终的决策通常容易受到数据质量差的影响。例如，随机优化方法可能会受到异常值的过度影响，而稳健优化方法可能会提供过于谨慎的解决方案。本研究项目研究了一个数据驱动优化的新框架，旨在专门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一个针对对STEM感兴趣的高中女生的夏令营模块，与当地科学博物馆的合作，以及一个基于互动优化的拦截游戏。本项目将建立分布式有利优化（DFO）的理论和算法基础，并研究其在分布扭曲下的操作工程领域的应用。分布有利优化包括检验输入数据的分布假设，并在最有利的分布下选择最优决策的方法。具体而言，本研究将(i)建立可以大大减少异常值影响的DFO基本框架；（ii）研究有效的基于分解的解决方案，以解决大规模DFO模型，这些模型计算效率高，具有吸引人的收敛特性；（iii）探索和利用非凸DFO模型的子模块化、聚类和覆盖等结构，以理论性能保证刺激求解算法；（iv）开发学习和优化框架，以探索DFO模型中的内生不确定性。DFO可以显著减少异常值的影响，潜在地实现更准确和可靠的决策。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.