CAREER: Modern nonconvex optimization for machine learning: foundations of geometric and scalable techniques

职业：机器学习的现代非凸优化：几何和可扩展技术的基础

基本信息

批准号：
1846088
负责人：
Suvrit Sra
金额：
$ 50万
依托单位：
Massachusetts Institute of Technology
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-03-15 至 2024-02-29
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1846088&HistoricalAwards=false
关键词：
CAREER Modern nonconvex optimization machine

项目摘要

Mathematical optimization lies at the heart of machine learning (ML) and artificial intelligence (AI) algorithms. Key challenges herein are to decide what criteria to optimize, and what algorithms to use for performing the optimization. These challenges underlie the motivation for the present project. More specifically, this project seeks to make progress on three fundamental topics in optimization for ML: (i) theoretical foundations for a rich new class of optimization problems that can be solved efficiently (i.e., in a computationally tractable manner); (ii) a set of algorithms that apply to large-scale optimization problems in machine learning (e.g., for accelerating the training of neural networks); and (iii) theory that seeks to understand and explain why do neural networks succeed in practice. By focusing on topics of foundational importance, this project should spur a variety of followup research that deepends the connection of ML and AI with both mathematics and the applied sciences. More broadly, the this project may have a lasting societal impact too, primarily because of (i) its focus on optimization particularly relevant to ML and AI; (2) the non-traditional application domains it connects with (e.g., synthetic biology); and (3) because the investigator is in an environment that fosters such impact (namely, the Institute for Data, Systems, and Society (IDSS), a cross-disciplinary institute at MIT whose mission to drive solutions to problems of societal relevance). Finally, the project has an education centric focus; it involves intellectual and professional development of students, as well as development of curricular material based on the topics of research covered herein.This project lays out an ambitious agenda to develop foundational theory for geometric optimization, large-scale nonconvex optimization, and deep neural networks. The research on geometric optimization (which is a powerful new subclass of nonconvex optimization), is originally motivated by applications in ML and statistics; however, it stands to have a broader impact across all disciplines that consume optimization. The investigator seeks to develop a theory of polynomial time optimization for a class strictly larger than usual convex optimization problems, and thereby endow practitioners with new polynomial time tools and models; if successful, this investigation could open an entire subarea of research and applications. Beyond geometric optimization, the project also focuses on large-scale nonconvex optimization and on the theory of optimization and generalization for deep learning. Within these topics, the project will address key theoretical challenges, develop scalable new algorithms that could greatly speed up neural network training, and also make progress that reduces the gap between the theory and real-world practice of nonconvex optimization.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.

数学优化是机器学习（ML）和人工智能（AI）算法的核心。这里的主要挑战是决定要优化的标准以及用于执行优化的算法。这些挑战是本项目的动机。更具体地说，该项目旨在在ML优化的三个基本主题上取得进展：（i）可以有效解决的丰富新的优化问题的理论基础（即以计算障碍方式）；（ii）一组适用于机器学习中大规模优化问题的算法（例如，用于加速神经网络的培训）；（iii）试图理解和解释为什么神经网络在实践中成功的理论。通过关注基础重要性的主题，该项目应刺激各种后续研究，从而深深地了解ML和AI与数学和应用科学的联系。更广泛地说，该项目也可能具有持久的社会影响，主要是因为（i）专注于与ML和AI特别相关的优化；（2）它与（例如，合成生物学）连接的非传统应用域；（3）由于研究人员处于促进这种影响的环境（即，数据，系统和社会研究所（IDSS），MIT的跨学科研究所，其使命是推动解决社会问题问题的解决方案）。最后，该项目以教育为重点。它涉及学生的智力和专业发展，以及基于本文涵盖的研究主题的课程材料的开发。本项目提出了一个雄心勃勃的议程，以开发几何优化，大规模非凸优化和深层神经网络的基础理论。几何优化的研究（这是一个强大的非凸优化的新子类），最初是由ML和统计数据中的应用进行的。但是，它在所有消费优化的学科中都具有更大的影响。研究者试图针对严格比通常更大的凸优化问题的班级开发多项式时间优化的理论，从而赋予了从业者使用新的多项式时间工具和模型。如果成功的话，这项调查可能会开放整个研究和应用的子区域。除了几何优化外，该项目还侧重于大规模的非凸优化以及深度学习的优化和概括理论。在这些主题中，该项目将解决关键的理论挑战，开发可扩展的新算法，这些算法可以极大地加快神经网络训练的速度，并取得了进步，从而减少了非convex优化的理论和现实世界实践之间的差距。该奖项反映了NSF的法定任务，并通过使用基金会的智力效果和广泛的评估来进行评估，并通过评估值得评估。