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

这个教师早期职业发展计划（CAREER）奖将支持新方法的调查，以显着提高数据驱动的决策下分布扭曲。数据驱动的优化是许多行业支持复杂决策的常用工具，但最终决策往往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，而鲁棒优化方法可能会提供过于谨慎的解决方案。 该研究项目调查了一个新的数据驱动优化框架，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。 除了关于乐观优化的新的本科和研究生课程模块外，该项目的教育部分还包括为对STEM感兴趣的高中女生提供的夏令营模块，与当地科学博物馆的合作，以及基于交互式优化的拦截游戏。本计画将建立分布有利最佳化（DFO）的理论与演算基础，并探讨其在分布扭曲下作业工程领域的应用。 分布有利优化包括检查输入数据的分布假设并在最有利分布下选择最优决策的方法。 具体而言，本研究将（i）建立DFO的基本框架，可以大大减少离群值的影响;（ii）研究有效的基于分解的解决方案，用于解决大规模DFO模型，计算效率高，具有吸引力的收敛特性;（iii）探索和利用非凸DFO模型的子模块化、聚类和覆盖等结构，激励解决方案的算法与理论性能保证;（iv）开发学习和优化框架，探索内生的不确定性DFO模型。 DFO可以显著降低离群值的影响，从而可能实现更准确和可靠的决策。该奖项反映了NSF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.