CAREER: Advancing Theory and Practice of Robust Simulation Analysis Under Input Model Risk

这个教师早期职业发展计划（Career）资助通过为数据驱动的模拟创建一个强大的决策框架来促进国家的健康、繁荣和福利。由于其在捕获系统随机性方面的灵活性，模拟已成为支持制造业、医疗保健、国防、金融和其他领域中出现的决策问题的流行工具。然而，仿真分析存在由于实际系统与仿真模型存在差异而得出错误统计推断的“模型风险”。未能考虑到这种风险可能导致基于这些模型做出的低质量决策。本研究的重点是“输入模型风险”，即当基于可用数据估计仿真模型中驱动随机性的概率分布函数时产生的风险。该项目将研究在输入模型风险下量化、减少和确保稳健决策的方法。特别是，将研究一个新的鲁棒决策框架，以平衡实际用户对可接受次优性的输入和对仿真模型中统计误差的鲁棒性。该基金的教育使命是培训当前和下一代STEM劳动力，使模型风险成为模拟分析的中心焦点，并为他们配备可使用的计算工具。这项研究将使复杂模拟系统的输入模型风险量化成为可能，这些系统由于计算的复杂性，到目前为止实际上是不可行的。应用似然比方法，求解双层优化问题，得到成本最小的仿真实验设计。此外，将创建一个高斯过程（GP）元模型来预测模拟输出均值作为参数和非参数输入模型的函数。这个GP元模型将作为一个工具，为鲁棒模拟分析生命周期的所有三个步骤设计一个全面的框架：(1)风险量化，(2)鲁棒优化，(3)风险降低。“实际稳健”最优性的概念将通过考虑用户指定的实际最优性感兴趣的差距来重新定义。该框架将减少现有方法的保守性，同时达到用户期望的鲁棒性水平。为了找到具有实际鲁棒性的最优解，本文提出了一种高效的仿真优化算法，该算法在GP推理的指导下，对仿真工作进行了顺序分配。最后，通过优化数据收集计划，为降低输入模型风险提供可操作的指导，为实际鲁棒优化提供更强的统计性能保证。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) grant advances the national health, prosperity and welfare by creating a robust decision-making framework for data-driven simulation. Due to its flexibility in capturing system randomness, simulation has been a popular tool to support decision-making problems that arise in manufacturing, healthcare, defense, finance, and other domains. However, simulation analysis is subject to “model risk” of drawing an incorrect statistical inference due to discrepancy between the real system and the simulation model. Failure to account for such risk may lead to poor quality decisions made on the basis of these models. This research focuses on “input model risk” that arises when the probability distribution functions driving randomness in a simulation model are estimated based on the available data. The project will study methods to quantify, reduce, and ensure robust decisions under input model risk. In particular, a new robust decision-making framework will be studied to balance a practical user input on acceptable suboptimality and robustness to the statistical error in the simulation model. The education mission of this grant is to train current and next-generation STEM workforce to make model risk a central focus of simulation analysis and equip them with computational tools to employ. This research will enable input model risk quantification for complex simulated systems that are here-to-fore practically infeasible due to computationally complexity. A minimum-cost simulation experiment design will be obtained by applying the likelihood ratio method and solving a bilevel optimization problem. Moreover, a Gaussian process (GP) metamodel will be created to predict the simulation output mean as a function of both parametric and nonparametric input models. This GP metamodel will serve as a vehicle to design a comprehensive framework for all three steps of the robust simulation analysis life cycle: (1) risk quantification, (2) robust optimization, and (3) risk reduction. The concept of “practically robust” optimality will be newly defined by accounting for the user-specified practical optimality gap of interest. This framework will reduce conservatism of existing methods while achieving the level of robustness the user desires. To find a practically robust optimum, an efficient simulation optimization algorithm, which sequentially allocates simulation effort guided by GP inference, will be created. Finally, an actionable guidance to reduce input model risk will be provided by optimizing the data collection plan to attain a stronger statistical performance guarantee for the practically robust optimum.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.