CAREER: Incorporating Decision-Dependent Uncertainty via Distributionally Robust Optimization: Models, Solution Approaches, and Applications

服务行业中的各种决策问题（例如，电力、医疗保健和交通）涉及不确定参数，这些参数部分地取决于决策本身，因此是决策相关的或内生的。在决策过程中阐明这种依赖性是重要的，因为否则这些不确定的参数可能会意外地破坏系统性能。此外，这种依赖性提供了主动操纵不确定性以加强决策的机会。该职业项目将评估纳入决策相关不确定性的潜在好处，并研究应对此类不确定性的新优化方法。如果在服务行业成功实施，该项目的研究成果将提高社会的可持续性和人民的福祉。此外，还将开发电力系统模拟策略类游戏、随机鲁棒优化研究生课程等新教材，以启发下一代工程师。与独立于决策的外生不确定性相比，内生不确定性在应用中受到的关注要少得多。这个CAREER项目的目标是通过分布鲁棒优化来全面量化、建模和操纵内生不确定性。该研究的智力意义包括：（a）为内生不确定性下的决策提供可证明的样本外性能保证;（B）减轻将内生不确定性纳入优化问题的计算挑战。具体而言，研究范围包括（1）量化考虑内生不确定性的价值，当它实际出现时，（2）通过一系列决策相关概率分布对内生不确定性进行建模，（3）主动操纵内生不确定性以提高系统性能，以及（4）将所得方法应用于涉及内生不确定性的应用中，例如，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。

A wide range of decision making problems in the service industries (e.g., power, healthcare, and transportation) involve uncertain parameters, which partially depend on the decision itself and hence are decision-dependent or endogenous. Incorporating such dependency in the decision-making process is significant, because otherwise these uncertain parameters may unexpectedly undermine the system performance. Furthermore, such dependency provides an opportunity of proactively maneuvering the uncertainty to reinforce the decision making. This CAREER project will evaluate the potential benefit of incorporating decision-dependent uncertainty and investigate new optimization approaches to maneuvering such uncertainty. If successfully implemented in the service industries, the research findings of this project will improve the sustainability of the society and the well-being of the people. In addition, this project will develop new educational materials including a power system simulation game and a graduate-level course on stochastic and robust optimization, which help inspire the next generation of engineers.As compared to the exogenous uncertainty that is independent of the decision, endogenous uncertainty has received much less attention in the applications. The goal of this CAREER project is to holistically quantify, model, and maneuver the endogenous uncertainty via distributionally robust optimization. The intellectual significance of this research includes (a) providing provable out-of-sample performance guarantee for making decisions under endogenous uncertainty and (b) mitigating the computational challenges of incorporating endogenous uncertainty in optimization problems. Specifically, the scope of the research includes (1) quantifying the value of considering endogenous uncertainty when it actually arises, (2) modeling the endogenous uncertainty by a family of decision-dependent probability distributions, (3) proactively maneuvering the endogenous uncertainty to improve system performance, and (4) applying the resulting methodology in applications that involve endogenous uncertainty, e.g., do-not-exceed limits, demand response programs, and off-shore oil drilling.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.