CAREER: Dynamic Decision-Making Under Uncertainty via Distributionally Robust Optimization

在过程控制、能源系统运行、供应链管理、投资计划、项目管理、工程、经济等领域中出现的决策问题，都涉及到决策者在决策时未知的不确定参数。忽视这种不确定性通常会导致较差的解决方案，由于平均的臭名昭著的缺陷，在实践中表现不佳，即基于平均条件预估的计划通常是错误的。这些决策问题往往也是动态的，它们跨越多个时间阶段，涉及高维的非预期追索权决策，这进一步增加了问题的复杂性。因此，对于这些决策问题的有效和高效的解决方案是非常必要的。然而，传统的解决方案受到维度诅咒的困扰，求解起来极具挑战性。分布稳健优化(DRO)的最新进展已经成功地缓解了不确定条件下各种单阶段决策问题的困难。在DRO中，我们寻求在考虑到与可用统计和结构信息一致的不确定参数的最不利分布的情况下执行最好的决策。因此，DRO不仅提高了计算的可处理性，而且还缓解了传统解格式的过拟合效应。通过利用和发明DRO中的新技术，拟议的研究工作旨在显著推进最先进的方法，以解决动态决策问题的挑战，并启动工业规模应用的努力。这项工作的研究成果将对能源、工程、机器学习、运营管理、金融等领域的重要应用以及机器人学和自动控制中的学习问题产生重大而直接的实际影响。这项职业工作还将通过开发一门综合课程来推动教育学的发展，该课程将弥合不确定情况下决策的深刻理论与现实生活实践之间的差距。拟议的课程面向未来的实践者和研究人员，旨在使这些专家具备分析技能和工具，以处理现实生活中的不确定性决策问题。拟议的研究工作旨在解决不确定性决策理论和实践中的一个重大差距。它集中于四个主要的研究方向：1)推导出凸动态问题和离散决策的动态问题的精确混合整数锥规划(MICP)重构式；2)处理内生不确定性的情况，其表示明确地取决于所选择的决策；3)系统地将数据集成到不确定性的描述中。从所得到的数据驱动的DRO模型中获得可证明的样本外性能保证4)为动态设置中的逆优化问题导出精确的MICP重新公式。拟议的研究工作致力于开发更强大的解决方案，利用标准的现成MICP解算器来解决不确定情况下的各种棘手决策问题。这项工作将在一般动态DRO模型和著名的混合整数二次规划之间建立一种新的联系。由此产生的联系将使我们更好地了解决策问题的内在困难，并使我们能够为新的解决方案方案获得有吸引力的性能保证。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

A wide spectrum of decision problems arising in process control, energy systems operation, supply chain management, investment planning, project management, engineering, economics, etc., involve uncertain parameters whose values are unknown to the decision maker when the decisions are made. Ignoring this uncertainty typically leads to inferior solutions that perform poorly in practice due to the notorious flaw of averages, whereby plans based on the assumption that average conditions pre-vail are usually wrong. These decision problems are often also dynamic in nature they span across multiple time stages and involve high dimensional non-anticipative recourse decisions which further increase the problem complexity. Thus, effective and efficient solution schemes for these decision problems are highly desirable. Traditional solution schemes, however, suffer from the curse of dimensionality and are extremely challenging to solve. Recent advances in distributionally robust optimization (DRO) have been successful in mitigating the intractability of various single-stage decision problems under uncertainty. In DRO, we seek a decision that performs best in view of the most adverse distribution of uncertain parameters that is consistent with the available statistical and structural information. Thus, DRO not only improves computational tractability but also alleviates the overfitting effects characteristic of the traditional solution schemes. By leveraging and inventing new techniques in DRO, the proposed research work aims to significantly advance the state-of-the-art methodologies for addressing the challenges of dynamic decision problems and to initiate the effort for industrial-size applications. The research outputs of this work will have a significant and immediate practical impact on important applications in energy, engineering, machine learning, operations management, finance, etc., and on learning problems in robotics and automatic control. This CAREER work will also advance the state of pedagogy by developing an integrated curriculum that bridges the gap between the deep theory of decision-making under uncertainty and the real-life practice. The proposed curriculum is aimed at future practitioners and researchers, and is designed to equip these experts with the analytical skills and tools to deal with real-life decision-making problems under uncertainty.The proposed research work is aimed at addressing a major gap in the theory and practice of decision-making under uncertainty. It concentrates on four main research thrusts: 1) Derive exact mixed-integer conic programming (MICP) reformulations for convex dynamic problems as well as for dynamic problems with discrete decisions 2) Deal with the case of endogenous uncertainty whose representation depends explicitly on the chosen decisions 3) Systematically integrate data into the description of uncertainty. Obtain provable out-of-sample performance guarantees from the resulting data-driven DRO models 4) Derive exact MICP reformulations for inverse optimization problems in the dynamic setting. The proposed research effort endeavors to develop more powerful solution schemes which leverage standard off-the-shelf MICP solvers for various intractable decision-making problems under uncertainty. The work will establish a new connection between generic dynamic DRO models and renowned classes of mixed-integer conic programs. The resulting connection will give us a better understanding of the inherent difficulty of the decision problems and enable us to derive attractive performance guarantees for the new solution schemes.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.