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

这项教师早期职业发展(Career)计划奖的研究目标是开发数据驱动、易处理和健壮的方法，用于不确定条件下的大规模动态优化。这是一个根本性的问题，特别是在当今的BigData世界，我们希望有效地使用大量可用数据进行决策。由于它的广泛适用性，这一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对优化问题中潜在的不确定性进行建模。传统上，概率论一直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，特别是在遭受维度诅咒的高维情况下。这项研究将开发新的数据驱动范式，以建模不确定性，同时确保易管理性和良好的性能。第二个问题涉及为所产生的多周期优化问题开发高效和健壮的算法。其目标是通过简单的泛函策略近似和潜在的强大的理论性能保证来追求开发和分析健壮、实用和易于实现的算法。如果成功，该研究结果将为易处理的动态优化发展基础理论，并为广泛的现实世界问题提供基本和实用的新工具。这些结果将用于为电力市场和智能电网应用中出现的优化问题开发实用的解决方案，这是一个非常适用于动态优化的重要领域。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方案广泛传播到当地高中，目的是增加学生，特别是来自代表人数较少的少数族裔的学生参与STEM教育和研究。

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.