CAREER: End-to-end Constrained Optimization Learning

该奖项全部或部分由2021年美国救援计划法案（公法117-2）资助。约束优化在我们的社会中每天都在使用，应用范围从供应链和物流到电网，器官交换，营销活动和制造。尽管这些问题即使对于中等规模的实例也经常具有计算挑战性，但它们构成了许多工业过程优化的基本构建块，对我们的社会和经济产生了深远的影响。然而，许多约束优化问题的复杂性往往使它们无法有效地应用于必须在长期范围内解决许多问题或必须在严格的时间限制下产生解决方案的情况。该项目提出了一种新的范式，将基本优化技术与机器学习算法紧密结合，以实时解决约束优化问题。这项研究有望创造一个新的和变革性的一代优化工具，解决严格的时间限制下的硬约束优化问题，导致显着的经济和社会效益。从科学的角度来看，该项目将开发优化和机器学习工具的新集成，以前所未有的计算速度为大规模硬约束优化问题提供高质量的解决方案。所提出的端到端约束优化学习（e2 e-COL）沿着沿着三个主要方向贡献新的科学知识：（1）它通过将优化的基本方法结合到深度神经网络的训练周期中来适应领域知识或复杂问题约束的存在。(2)它通过设计高效的数据生成程序，将优化方法与模型学习能力联系起来，以及开发需要少量标记数据的半监督模型，来满足生成大型数据集以训练高质量模型的需求。(3)最后，为了扩展到大的问题实例，该提案使e2 e-COL能够学习问题结构的分解和近似。该奖项反映了NSF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 award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).Constrained optimization is used daily in our society with applications ranging from supply chains and logistics to electricity grids, organ exchanges, marketing campaigns, and manufacturing. Although these problems are often computationally challenging even for medium-sized instances, they constitute fundamental building blocks for the optimization of many industrial processes with profound effects on our society and economy. Yet the complexity of many constrained optimization problems often prevents them from being effectively adopted in contexts where many instances must be solved over a long-term horizon or when solutions must be produced under stringent time constraints. This project proposes a new paradigm that tightly integrates fundamental optimization techniques with machine learning algorithms to solve constraint optimization problems in real-time. This research holds the promise to create a new and transformative generation of optimization tools that solve hard constraint optimization problems under stringent time constraints leading to significant economic and societal benefits. From a scientific standpoint, this project will develop a new integration of optimization and machine learning tools that deliver high-quality solutions to large-scale hard constraint optimization problems at unprecedented computational speeds. The proposed end-to-end Constraint Optimization Learning (e2e-COL) contributes to new scientific knowledge along three main directions: (1) It accommodates the presence of domain knowledge or complex problem constraints by combining fundamental methodologies from optimization into the training cycle of deep neural networks. (2) It addresses the need of generating large datasets to train high-quality models by devising efficient data generation procedures, linking methodologies from optimization with the model learning ability, and developing semi-supervised models requiring small amounts of labeled data. (3) Finally, to scale to large problem instances, this proposal enables e2e-COL to learn decompositions and approximations of the problem structure.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.