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

本学院早期职业发展（Career）项目奖的研究目标是开发数据驱动的、可处理的、鲁棒的方法，用于不确定性下的大规模动态优化。这是一个基本问题，特别是在当今的大数据世界中，我们希望有效地利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对实践产生重大影响。本项目将解决动态优化中的两个基本问题。第一个是通过数据对优化问题中的潜在不确定性进行建模。传统上，概率论已被用来对这些不确定性进行建模，但它往往在计算上难以处理，特别是在高维情况下，受到维数诅咒的影响。本研究将开发新的数据驱动范式来模拟不确定性，同时确保可追溯性和良好的性能。第二个问题涉及开发高效和鲁棒的算法来解决由此产生的多周期优化问题。目标是通过具有潜在强大理论性能保证的简单功能策略近似，追求鲁棒性，实用性和易于实现的算法的开发和分析。如果成功，这项研究的结果将为可处理的动态优化提供基础理论，并为广泛的现实世界问题提供基础和实用的新工具。这些结果将用于开发电力市场和智能电网应用中出现的优化问题的实际解决方案，这是动态优化非常适用的一个重要领域。研究生和本科生将受益于参与研究并将结果整合到课堂教学中。这项研究将通过外展项目在当地高中广泛传播，目的是提高学生，特别是来自代表性不足的少数民族的学生对STEM教育和研究的参与。

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.