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Collaborative Research: Computationally Efficient Algorithms for Large-scale Bilevel Optimization Problems

协作研究：大规模双层优化问题的计算高效算法

基本信息

批准号：
2127696
负责人：
Erfan Yazdandoost Hamedani
金额：
$ 22.44万
依托单位：
University of Arizona
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-15 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2127696&HistoricalAwards=false
关键词：
Collaborative Research Computationally Efficient Algorithms

项目摘要

The recent advancements in machine learning and power systems with hierarchical decision-making structure necessitate developing efficient schemes to solve bilevel optimization problems. A bilevel optimization problem is a hierarchical decision-making process and an important class of mathematical models in which finding the optimal decision (the upper-level problem) depends on anticipating another decision-making problem (the lower-level problem). Despite the progress in studying bilevel optimization, most existing methods could be slow or inefficient when applied in large-scale, uncertain, or distributed settings. This project aims to address these challenges by examining novel reformulations of bilevel optimization and developing computationally efficient algorithms for solving hierarchical decision-making problems. The outcomes of this project will be transformational for energy storage systems, investment and operation planning in power systems, recommendation platforms, and speech and image recognition software. On the education front, this project will provide a stimulating and innovative research environment to include under-representative and minority students in the project research; it will also incorporate the development of curricular material for courses in the PIs’ institutions. This project lays out a detailed agenda for exploring bilevel optimization reformulations and developing efficient and scalable schemes to address major limitations of state-of-the-art bilevel optimization frameworks when confronted with the challenges of recently emerged paradigms in machine learning and power systems. The research encompasses three different thrusts: (I) Examining reformulations of nonconvex bilevel optimization and offering new insights on how to reformulate a bilevel optimization problem with the goal of finding a local optimum. (II) Developing computationally efficient methods with fast convergence guarantees for bilevel optimization problems under uncertainty by leveraging tools from stochastic optimization and online learning. (III) Investigating bilevel optimization problems in a decentralized regime with the goal of developing and analyzing distributed algorithms with local computations and communications.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.

在机器学习和具有分层决策结构的电力系统方面的最新进展需要开发有效的方案来解决双层优化问题。双层优化问题是一个递阶决策过程，是一类重要的数学模型，其中寻找最优决策(上层问题)依赖于预测另一个决策问题(下层问题)。尽管双层优化的研究取得了进展，但大多数现有方法在大规模、不确定或分布式环境中的应用可能会很慢或效率低下。这个项目旨在通过研究双层优化的新的重新公式和开发计算效率高的算法来解决分层决策问题，以应对这些挑战。该项目的成果将对储能系统、电力系统投资和运营规划、推荐平台以及语音和图像识别软件产生变革性的影响。在教育方面，这个项目将提供一个激励和创新的研究环境，将代表不足的学生和少数族裔学生纳入项目研究；它还将包括为私人投资机构的课程编制课程材料。这个项目列出了一个详细的议程，探索双层优化重构，并开发有效和可扩展的方案，以解决在面对机器学习和电力系统中最近出现的范例的挑战时，最先进的双层优化框架的主要限制。这项研究包括三个不同的方向：(I)考察非凸双层优化的重构，并为如何重构双层优化问题以找到局部最优解提供了新的见解。(2)利用随机优化和在线学习的工具，开发计算效率高、收敛速度快的方法来解决不确定条件下的双层优化问题。(Iii)研究去中心化制度下的双层优化问题，目的是开发和分析具有本地计算和通信的分布式算法。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。