Collaborative Research: CIF: Small: New Theory, Algorithms and Applications for Large-Scale Bilevel Optimization

合作研究：CIF：小型：大规模双层优化的新理论、算法和应用

• 批准号: 2311275
• 负责人: Shiqian Ma
• 金额: $ 29.95万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2311275&HistoricalAwards=false
• 关键词: Collaborative; Research; CIF; Small; New

In recent years, the world has witnessed significant progress in optimization for emerging fields, including meta-learning, fine-tuning, automated hyperparameter selection, continual learning, fair batch selection, adversarial learning, and artificial intelligence (AI)-aware communication networks. Problems arising from these fields often exhibit a common nested optimization structure, which has motivated the study of bilevel optimization. However, there are many theoretical and computational challenges in large-scale bilevel optimization problems, e.g., those arising from machine learning on massive amounts of data in high-dimensional feature domains that have manifold constraints. This project will provide a comprehensive study of bilevel optimization theory, algorithms, and applications for large-scale problems. The outcomes of this project will benefit researchers in academia, government labs, and industry aiming to solve large-scale nested optimization problems in science and engineering. New applications in information science, signal processing, communications, statistics, and machine learning will be studied. This project consists of three intertwined thrusts. The first thrust focuses on developing fast and scalable Hessian-free bilevel algorithms with convergence rate guarantees. Specifically, several Hessian-free approaches will be designed and analyzed using methods of fully single-loop momentum, finite-difference matrix-vector estimation, and residual response Jacobian estimation. The second thrust aims to develop primal-dual, primal, and pessimistic bilevel methods, in addition to the analysis of convergence in the difficult case where no unique lower-level solution exists. In the third thrust, the investigators will develop algorithms for solving bilevel problems on non-linear manifolds and analyze the associated convergence of these algorithms. The developed algorithms will be implemented in the context of real-world applications, including fairness-aware machine learning, continual learning, resource allocation over communication networks, hyperparameter selection of principal component analysis, and dictionary learning models.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.

近年来，世界在新兴领域的优化方面取得了重大进展，包括元学习、微调、自动超参数选择、持续学习、公平批量选择、对抗性学习和人工智能（AI）感知通信网络。这些领域产生的问题通常表现出共同的嵌套优化结构，这激发了双层优化的研究。然而，大规模双层优化问题存在许多理论和计算挑战，例如，对具有多种约束的高维特征域中的大量数据进行机器学习所产生的问题。该项目将提供对大规模问题的双层优化理论、算法和应用的全面研究。该项目的成果将使学术界、政府实验室和工业界的研究人员受益，旨在解决科学和工程中的大规模嵌套优化问题。将研究信息科学、信号处理、通信、统计和机器学习方面的新应用。该项目由三个相互交织的主力组成。第一个重点是开发具有收敛速度保证的快速且可扩展的无 Hessian 双层算法。具体来说，将使用完全单环动量、有限差分矩阵向量估计和残差响应雅可比估计的方法来设计和分析几种无 Hessian 方法。第二个重点旨在开发原始对偶、原始和悲观双层方法，以及在不存在唯一的低级解的困难情况下的收敛性分析。在第三个重点中，研究人员将开发解决非线性流形上的双层问题的算法，并分析这些算法的相关收敛性。所开发的算法将在现实世界的应用中实现，包括公平感知机器学习、持续学习、通信网络上的资源分配、主成分分析的超参数选择和字典学习模型。该奖项反映了 NSF 的法定使命和通过使用基金会的智力价值和更广泛的影响审查标准进行评估，该项目被认为值得支持。