CAREER: Efficient computational methods for nonlinear optimization and machine learning problems with applications to power systems

职业：非线性优化和机器学习问题的有效计算方法及其在电力系统中的应用

基本信息

批准号：
2045829
负责人：
Somayeh Sojoudi
金额：
$ 50万
依托单位：
University of California-Berkeley
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-01-15 至 2025-12-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2045829&HistoricalAwards=false
关键词：
CAREER Efficient computational methods nonlinear

项目摘要

Optimization is an important tool for the design, analysis, control and operation of real-world systems, such as power systems. It also plays a central role in machine learning and artificial intelligence, particularly in deep learning, reinforcement leaning, and statistical learning. The mathematical foundation of optimization has heavily relied on the notion of convexity since convex optimization problems can be solved using fast algorithms. Nevertheless, many optimization problems in real-world applications are non-convex, and therefore it is extremely difficult to solve those problems reliably and efficiently using the existing methods. As an example, this issue is one of the main bottlenecks in the upgrade of the legacy power grids and has been incurring billions of dollars annually in the United States. This CAREER project aims to develop a set of computational tools for solving complex optimization and learning problems using efficient computational methods. This project has a significant impact on many societal problems through the development of a rich mathematical foundation for non-convex optimization, and its outcomes can be exploited in a variety of fields. The developed techniques enable solving large-scale computational problems for improving the efficiency, reliability, resiliency and sustainability of power grids, which has major societal, economical, and environmental impacts. Moreover, these tools significantly extend the application of artificial intelligence to safety-critical systems. This project has a wide range of outreach plans for K-12 and underrepresented students, and it also has several educational activities at both undergraduate and graduate levels. The state-of-the-art techniques for solving non-convex problems are based on various approximation and relaxation methods, whose practical use remains limited due to their scalability issues for real-world systems. On the other hand, the staggering advances made in artificial intelligence in the last 5 years (e.g., in deep learning) are due, in part, to handling computationally-intensive machine learning problems directly as non-convex optimization without relying on convex optimization. Motivated by the resounding success of local search methods for artificial intelligence, this CAREER project aims to design low-complexity computational methods for non-convex optimization problems. To this end, it studies the notion of spurious solutions, which are those solutions of an optimization problem that satisfy the local optimality conditions but are not globally optimal. The main property of convex optimization is the absence of spurious solutions. This project introduces the class of global functions which is far broader than the class of convex functions but benefits from the same spurious-solution-free property. Using the notions of global functions and kernel structure property, four objectives will be addressed: (i) analysis of the spurious solutions of key non-convex problems in machine learning and studying how the amount of data and the structural properties of each problem affects the inexistence of such solutions, (ii) analysis of the spurious solutions of an arbitrary polynomial optimization problem via its conversion to a machine learning problem and then discovering what structural properties guarantee the inexistence of spurious solutions, (iii) approximation of an arbitrary polynomial optimization problem having a spurious solution with a sequence of spurious-minima-free non-convex problems in a higher-dimensional space, (iv) software development and performing case studies on key problems for power systems and machine learning. This project is interdisciplinary and contributes to the areas of optimization theory, machine learning, control theory, and energy.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.

优化是现实系统（例如电源系统）设计，分析，控制和操作的重要工具。它在机器学习和人工智能中也起着核心作用，尤其是在深度学习，强化倾向和统计学习中。优化的数学基础已在很大程度上依赖于凸的概念，因为可以使用快速算法解决凸优化问题。然而，现实世界应用中的许多优化问题是非凸的，因此，使用现有方法可靠，有效地解决这些问题非常困难。例如，这个问题是旧版电网升级的主要瓶颈之一，在美国每年都会产生数十亿美元。该职业项目旨在开发一套计算工具，以使用有效的计算方法来解决复杂的优化和学习问题。该项目通过为非凸优化的丰富数学基础的发展开发而对许多社会问题产生重大影响，并且可以在各个领域中利用其结果。已开发的技术使解决大规模计算问题，以提高电网的效率，可靠性，弹性和可持续性，这些电网具有主要的社会，经济和环境影响。此外，这些工具大大扩展了人工智能在安全至关重要系统中的应用。该项目针对K-12和代表性不足的学生制定了广泛的外展计划，并且在本科和研究生级别也有几项教育活动。解决非凸问题的最新技术基于各种近似和放松方法，由于其对现实世界系统的可伸缩性问题，其实际使用仍然有限。另一方面，过去5年中人工智能的惊人进步（例如，在深度学习中）部分归因于在不依赖凸优化的情况下直接处理计算强度的机器学习问题。由于本地搜索方法在人工智能方面的成功，该职业项目旨在设计低复杂性计算方法，以解决非convex优化问题。为此，它研究了虚假解决方案的概念，这些解决方案是满足当地最佳条件但在全球范围内的优化问题的那些解决方案。凸优化的主要特性是缺乏虚假解决方案。该项目介绍了一类全球功能，该类别比凸函数类别宽得多，但受益于同一无虚拟属性的属性。使用全球功能和内核结构属性的概念，将解决四个目标：（i）分析机器学习中关键的非凸问题的杂种解决方案，并研究每个问题的数据量和结构性如何影响此类解决方案的不存在，影响此类解决方案的不存在，（II）通过其构建问题的构建质量属性的构建质量属性的分析，以分析其构建问题的构建质量质量，以实现构建质量的质量质量质量，以构建机器的构建范围。伪造溶液的不存在，（iii）任意多项式优化问题的近似值具有伪造溶液，其中具有一系列较高维空间中的一系列虚假的无米型非凸问题，（iv）软件开发和对电源系统和机器学习的关键问题进行案例研究。该项目是跨学科的，有助于优化理论，机器学习，控制理论和能源的领域。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响来通过评估来支持的。

项目成果

期刊论文数量（22）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Sample Complexity of Block-Sparse System Identification Problem

块稀疏系统辨识问题的样本复杂度

DOI：
发表时间：
2021
期刊：
IEEE transactions on control of network systems
影响因子：
4.2
作者：
Fattahi, Salar;Sojoudi, Somayeh
通讯作者：
Sojoudi, Somayeh

Projected Randomized Smoothing for Certified Adversarial Robustness

DOI：
10.48550/arxiv.2309.13794
发表时间：
2023-09
期刊：
ArXiv
影响因子：
0
作者：
Samuel Pfrommer;Brendon G. Anderson;S. Sojoudi
通讯作者：
Samuel Pfrommer;Brendon G. Anderson;S. Sojoudi

A MILP for Optimal Measurement Choice in Robust Power Grid State Estimation

鲁棒电网状态估计中最优测量选择的 MILP

DOI：
发表时间：
2022
期刊：
IEEE Power Energy Society General Meeting
影响因子：
0
作者：
Glista, Elizabeth;Sojoudi, Somayeh
通讯作者：
Sojoudi, Somayeh

On the Absence of Spurious Local Trajectories in Time-Varying Nonconvex Optimization

DOI：
10.1109/tac.2021.3137147
发表时间：
2020-11
期刊：
IEEE Transactions on Automatic Control
影响因子：
6.8
作者：
S. Fattahi;C. Josz;Yuhao Ding;R. Mohammadi;J. Lavaei;S. Sojoudi
通讯作者：
S. Fattahi;C. Josz;Yuhao Ding;R. Mohammadi;J. Lavaei;S. Sojoudi

A Sequential Framework Towards an Exact SDP Verification of Neural Networks

DOI：
10.1109/dsaa53316.2021.9564161
发表时间：
2020-10
期刊：
2021 IEEE 8th International Conference on Data Science and Advanced Analytics (DSAA)
影响因子：
0
作者：
Ziye Ma;S. Sojoudi
通讯作者：
Ziye Ma;S. Sojoudi