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

职业：通过分布稳健优化在不确定性下进行动态决策

基本信息

批准号：
2342505
负责人：
Grani Adiwena Hanasusanto
金额：
$ 50万
依托单位：
University of Illinois at Urbana-Champaign
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2023
资助国家：
美国
起止时间：
2023-06-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2342505&HistoricalAwards=false
关键词：
CAREER Dynamic Decision Making Under

项目摘要

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.

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、经济学等领域中出现的广泛决策问题，涉及决策者在做出决策时不知道其值的不确定参数。忽略这种不确定性通常会导致低劣的解决方案在实践中表现不佳，这是由于众所周知的平均缺陷，即基于平均条件预先假设的计划通常是错误的。这些决策问题通常在本质上也是动态的，它们跨越多个时间阶段，涉及高维的非预期资源决策，这进一步增加了问题的复杂性。因此，迫切需要针对这些决策问题的有效且高效的解决方案。然而，传统的解决方案受到维度的诅咒，并且极具挑战性。分布鲁棒优化（DRO）的最新进展已经成功地缓解了不确定性下各种单阶段决策问题的棘手性。在DRO中，我们寻求在与可用的统计和结构信息一致的不确定参数的最不利分布中表现最佳的决策。因此，DRO不仅提高了计算的可追溯性，而且减轻了传统求解方案的过拟合效应。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解决动态决策问题挑战的最先进方法，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，以及机器人和自动控制领域的学习问题产生重大而直接的实际影响。这一职业生涯的工作也将通过开发一个综合课程来推动教育学的发展，该课程在不确定性下决策的深层理论和现实生活实践之间架起了一座桥梁。建议的课程是针对未来的从业者和研究人员，并旨在装备这些专家的分析技能和工具，以处理不确定的现实生活中的决策问题。提出的研究工作旨在解决不确定性下决策理论与实践的主要差距。它集中在四个主要的研究重点：1)导出精确的混合整数二次规划（MICP）重新表述凸动态问题以及具有离散决策的动态问题2)处理内源性不确定性的情况，其表示明确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。从结果数据驱动的DRO模型中获得可证明的样本外性能保证4)在动态环境下，推导出逆优化问题的精确MICP重新公式。提出的研究工作旨在开发更强大的解决方案，利用标准的现成的MICP求解器来解决各种不确定情况下的棘手决策问题。这项工作将在通用动态DRO模型和著名的混合整数二次规划类之间建立新的联系。由此产生的联系将使我们更好地理解决策问题的内在困难，并使我们能够为新的解决方案得出有吸引力的性能保证。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。