CAREER: A Data-driven Robust Approach for Large Scale Dynamic Optimization

这个教师早期职业发展（CAREER）计划奖的研究目标是开发数据驱动的易处理和鲁棒的方法，用于不确定性下的大规模动态优化。这是一个根本问题，尤其是在当今的大数据世界中，我们希望有效地使用大量可用数据进行决策。由于其广泛的适用性，该领域的任何进展都将在实践中产生重大影响。这个项目将解决动态优化中的两个基本问题。第一个是关于从数据中建模优化问题中的潜在不确定性。传统上，概率论已被用来模拟这些不确定性，但它往往是计算上棘手的，特别是在高维遭受灾难的维度。这项研究将开发新的数据驱动的范例，以模型的不确定性，同时确保易处理性和良好的性能。第二个问题涉及开发有效的和强大的算法产生的多周期优化问题。我们的目标是追求的发展和分析的强大的，实用的，易于实现的算法，通过简单的功能性政策的近似与潜在的强大的理论性能guarantee.If成功的，这项研究的结果将发展基础理论的易处理的动态优化和提供基础和实用的新工具，广泛的真实的世界的问题。这些结果将被用来开发实际的解决方案，在电力市场和智能电网应用中出现的优化问题，这是一个重要的领域，动态优化是非常适用的。研究生和本科生将受益于参与研究和将结果融入课堂教学。这项研究将通过推广计划广泛传播到当地高中，目标是增加学生的参与，特别是来自STEM教育和研究中代表性不足的少数民族的学生。

The research objective of this Faculty Early Career Development (CAREER) Program award is to develop data-driven tractable and robust approach for large-scale dynamic optimization under uncertainty. This is a fundamental problem especially in today's world of BigData where we want to efficiently use vast amount of available data for decision-making. Due to its wide applicability, any progress in this field will have significant impact in practice. This project will address two fundamental problems in dynamic optimization. The first is related to modeling the underlying uncertainties in the optimization problem from data. Traditionally, probability theory has been used to model these uncertainties but it is often computationally intractable especially in high dimensions suffering from the curse of dimensionality. This research will develop new data-driven paradigms to model uncertainty that simultaneously ensure tractability and good performance. The second problem concerns developing efficient and robust algorithms for resulting multi-period optimization problems. The goal is to pursue the development and analysis of robust, practical and easy to implement algorithms through simple functional policy approximations with potentially strong theoretical performance guarantees.If successful, the results of this research will develop foundational theory for tractable dynamic optimization and provide fundamental and practical new tools for a broad spectrum of real world problems. These results will be used to develop practical solutions for optimization problems arising in electricity markets and smart grid applications, which is an important area where dynamic optimization is very applicable. The graduate and undergraduate students will benefit from involvement in research and integration of the results into classroom instruction. The research will be broadly disseminated through outreach programs to local high schools with a goal of increasing the participation of students especially from underrepresented minorities in STEM education and research.