Adjustable Risk Management under Ambiguous Decision Preferences and Data Uncertainty

由于现实问题中信息不确定性的存在，决策者往往需要在不知道自己确切的决策标准和偏好的情况下平衡风险和收益结果。该奖项支持基础研究，为当前现有方法的不确定性下的决策制定开发新的范式。该研究将适用于广泛的工业和科学部门。特别是，在电网和运输系统中的预期应用将促进不同学科之间的协同作用，并将推进用于分析各种国家关键基础设施的最先进技术。研究结果将通过教育传播，以改善学生在科学和工程方面的学习，并促进代表性不足的群体参与研究。该项目的目标是开发新的模型和方法，使用机会约束规划和数据驱动的优化方法，用于在模糊的决策偏好和数据不确定性下管理风险。建议的研究重点是随机程序与概率（机会）的约束，制定保证服务质量。此外，我们考虑可调整的风险参数在相关的机会约束及其对整体目标值的影响。给定已知或模糊的不确定性分布信息，我们研究了相应的数据知情或数据驱动的风险管理建模范式。我们的计算方法的可扩展性和有效性是通过数据挖掘的凸表示和二值化技术建立的。该提案还包括调查两个相关的应用程序在最佳的电力流操作和传感器部署监测运输系统。我们的目标是证明（i）在多个机会约束下区分风险有效地平衡了不确定性下的成本和可靠性，以及（ii）在不完美信息的问题中，风险水平的选择可以通过数据驱动的优化方法来指导和改进。

Due to the existence of information uncertainty in real-world problems, decision makers often need to balance risk and return outcomes even without knowing their exact decision criteria and preferences. This award supports fundamental research to develop new paradigms for decision making under uncertainty to currently existing approaches. The research will have applicability in a wide range of industry and science sectors. In particular, the intended applications to electric power grids and to transportation systems will promote synergy among different disciplines, and will advance the state-of-the-art techniques for analyzing a variety of the nation's critical infrastructures. The results will be disseminated through education, to improve students' learning in science and engineering, and promote the participation of underrepresented groups in research. The objective of this project is to develop new models and approaches, using chance-constrained programming and data-driven optimization approaches, for managing risk under ambiguous decision preferences and data uncertainty. The proposed research focuses on stochastic programs with probabilistic (chance) constraints formulated for guaranteeing the quality of service. Moreover, we consider adjustable risk parameters in related chance constraints and their effects on the overall objective value. Given known or ambiguous distributional information of the uncertainty, we study the corresponding data-informed or data-driven modeling paradigms for risk management. The scalability and efficacy of our computation approaches are built through convex representations and binarization techniques from data mining. The proposal also includes investigations of two related applications in optimal power flow operations and sensor deployment for monitoring transportation systems. We aim to demonstrate that (i) differentiating risk in multiple chance constraints effectively balances cost and reliability under uncertainty, and (ii) the selection of risk levels can be guided and improved by data-driven optimization approaches in problems with imperfect information.