CAREER: Optimization-Based Computational Discovery of Decision-Making Processes

决策是日常生活的基础，但许多决策过程知之甚少。例如，化工厂的操作专家根据多年的经验做出决策，但他们的决策策略往往没有很好的记录，并且由于这些制造过程的复杂性，甚至难以向同行操作员解释。这意味着将专业知识完全转移给新操作员仍然是一个未解决的问题。同样，在微生物学中，细胞可以被认为是自主的代理人，对基因表达和细胞代谢功能做出决定。虽然我们可以观察到细胞在实验中做出的决定，但我们通常不理解这些选择的动机。解决这个问题将提供基本的见解，可以推进癌症治疗，免疫学研究和生物制造业务。这些挑战为这项研究计划提供了动力，该计划旨在开发一个计算框架，该框架使用对决策的观察来揭示潜在的决策过程。我们的研究将推进这一基本问题的理论和算法表示。通过我们的综合研究和教育活动，我们将教导未来的科学家和工程师使用先进的决策工具，并促进决策科学领域研究人员之间的跨学科合作。我们提出的方法受到最优性原则的启发，该原则强调自治代理通常以某种最优方式做出决策。遵循这一原则，我们建议将决策过程建模为数学优化问题，其中决策被认为是最优解。给定一组观察结果，每个观察结果由在特定情况下做出的决策表示，目标是推断优化模型，其解决方案导致观察到的决策;这被称为逆优化（IO）。IO方法具有数学优化提供的所有建模灵活性，便于结合领域知识，并允许生成内在可解释的决策模型。在这项研究中，我们将开发计算效率高的IO算法，并将其应用于科学和工程中的一系列问题。提出了三个具体的目标：（1）学习未知的目标函数，（2）学习未知的约束条件，（3）优化与IO为基础的模型。目标1和2侧重于发展计算方法，解决IO的挑战性方面，如非线性，离散决策，模型选择和自适应采样。混合整数规划，双层优化和分解将以创新的方式应用，以确保计算的易处理性。在目标3中，我们将展示如何从IO派生的优化模型不仅可以帮助发现隐藏的决策过程，而且还可以作为代理优化器和嵌入模型在分层优化，在生物过程优化和环境政策设计的具体应用。由于最优性原理具有广泛的（尽管通常是近似的）有效性，并且我们研究中开发的IO方法将是可推广的，因此我们的工作有可能广泛影响人工智能研究，机器人，生物学，医疗保健，甚至管理和行为科学。我们将开展一系列活动，包括通过游戏向K-12学生教授决策科学的基本概念，将优化纳入我们的化学工程课程，建立决策制定短期课程，并组织跨学科研讨会。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Decision making is fundamental to everyday life, but many decision-making processes are poorly understood. For example, experts in the operation of chemical plants make decisions based on years of experience, but their decision strategies often are not well documented and, due to the complexity of these manufacturing processes, are difficult to explain even to fellow operators. This means the complete transfer of expert knowledge to new operators remains an unsolved problem. Likewise in microbiology, cells can be considered autonomous agents that make decisions regarding gene expression and cell metabolic function. While we can observe the decisions cells make in experiments, we often do not understand the motivation for these choices. Answering this question would provide fundamental insights that could advance cancer treatment, immunology research, and biomanufacturing operations. These challenges provide the motivation for this research program which aims to develop a computational framework that uses observations of decisions to uncover the underlying decision-making processes. Our research will advance the theory and algorithmic representation of this fundamental problem. Through our integrated research and education activities, we will teach future scientists and engineers to use advanced decision-making tools and promote interdisciplinary collaborations between researchers that work in the field of decision science.Our proposed approach is inspired by the principle of optimality, which conjectures that autonomous agents generally make decisions in some optimal fashion. Following this principle, we propose to model decision-making processes as mathematical optimization problems in which decisions are considered optimal solutions. Given a set of observations, each represented by the decisions made in a specific situation, the goal is to infer the optimization model whose solution results in the observed decisions; this is referred to as Inverse Optimization (IO). The IO approach enjoys all the modeling flexibility provided by mathematical optimization, facilitates incorporation of domain knowledge, and allows the generation of inherently interpretable decision-making models. In this research, we will develop computationally efficient IO algorithms and apply them to a range of problems in science and engineering. Three specific Aims are proposed: (1) learning unknown objective functions, (2) learning unknown constraints, and (3) optimization with IO-based models. Aims 1 and 2 focus on the development of computational methods addressing the challenging aspects of IO, such as nonlinearity, discrete decisions, model selection, and adaptive sampling. Mixed-integer programming, bilevel optimization, and decomposition will be applied in innovative ways to ensure computational tractability. In Aim 3, we will demonstrate how optimization models derived from IO can not only help discover hidden decision-making processes but also serve as surrogate optimizers and embedded models in hierarchical optimization, with specific applications in bioprocess optimization and environmental policy design. Because the principle of optimality enjoys broad (albeit often approximate) validity and the IO methods developed in our research will be generalizable, our work has the potential to broadly impact artificial intelligence research, robotics, biology, healthcare, and even management and behavioral science. We will pursue a set of activities that include teaching K-12 students the basic concepts of decision science through games, incorporating optimization into our chemical engineering curriculum, establishing a short course on decision making, and organizing cross-disciplinary workshops.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.