CAREER: Submodular Optimization in Complex Environments: Theory, Algorithms, and Applications

职业：复杂环境中的子模优化：理论、算法和应用

• 批准号: 1943064
• 负责人: Hamed Hassani
• 金额: $ 40万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-06-01 至 2025-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1943064&HistoricalAwards=false
• 关键词: CAREER; Submodular; Optimization; Complex; Environments

Discrete optimization is an inherent challenge in algorithm design arising in various domains such as artificial intelligence, robotics, and smart cities. Even though discrete optimization problems are hard in general, prior work has shown that many real-world instances satisfy a natural diminishing property called submodularity. Playing an analogous role as convexity does for continuous optimization, submodularity has been transformational for algorithm design, leading to efficient optimization methods with strong theoretical guarantees. Despite this progress, the existing methodologies suffer known limitations and can benefit from a reexamination inspired by the challenges set forth by today's technological advances. This project aims to develop a research plan that builds the foundations of discrete and submodular optimization in complex, dynamic environments, addressing the challenges of scalability and uncertainty, and facilitating distributed and sequential learning in much broader settings. This project is interdisciplinary, featuring a synergistic education plan that incorporates development of both graduate and undergraduate courses at the University of Pennsylvania with the specific goal of identifying gaps in educational training and enriching the curriculum for teaching data science to engineers. It also aims to use available public education platforms to build a pipeline for STEM majors entering college, advance public communication around data science, and disseminate research results.The overarching goal of the proposed research program is to develop novel and foundational frameworks for submodular optimization in (i) stochastic, uncertain, dynamically evolving, and adversarially changing environments; (ii) distributed and multi-agent systems; and (iii) adaptive scenarios enabling sequential selection of data and observations. The project seeks to establish fundamental trade-offs between the best attainable solution quality and various types of complexities (specifically, computation, communication, and sample complexities), and devise algorithmic frameworks that meet such trade-offs. The resultant theory and algorithms will be applied to real-world scenarios.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.

在人工智能、机器人和智能城市等各个领域，离散优化是算法设计中固有的挑战。尽管离散优化问题总体上是困难的，但先前的工作已经表明，许多现实世界的实例满足一种称为子模的自然递减性质。子模块的作用类似于凸性对连续优化的作用，对算法设计起到了转化作用，从而产生了具有强大理论保证的高效优化方法。尽管取得了这一进展，但现有的方法仍存在已知的局限性，并可以从由当今技术进步提出的挑战引发的重新审查中受益。该项目旨在制定一项研究计划，在复杂、动态的环境中建立离散和子模块优化的基础，解决可伸缩性和不确定性的挑战，并在更广泛的环境中促进分布式和顺序学习。该项目是跨学科的，以协同教育计划为特色，该计划结合了宾夕法尼亚大学研究生和本科课程的发展，具体目标是找出教育培训方面的差距，并丰富向工程师教授数据科学的课程。它还旨在利用现有的公共教育平台为STEM专业的学生建立进入大学的渠道，促进围绕数据科学的公共交流，并传播研究成果。拟议研究计划的总体目标是为(I)随机、不确定、动态演变和不利变化的环境；(Ii)分布式和多智能体系统；以及(Iii)能够顺序选择数据和观测的自适应场景中的子模块优化开发新的基础框架。该项目寻求在可获得的最佳解决方案质量和各种类型的复杂性(特别是计算、通信和样本复杂性)之间建立基本的权衡，并设计出满足这些权衡的算法框架。由此产生的理论和算法将应用于现实世界的场景。这一奖项反映了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。

项目成果

Collaborative Learning of Discrete Distributions under Heterogeneity and Communication Constraints

• 发表时间: 2022-06
• 作者: Xinmeng Huang;Dong-hwan Lee;Edgar Dobriban;Hamed Hassani

Demystifying Disagreement-on-the-Line in High Dimensions

• DOI: 10.48550/arxiv.2301.13371
• 发表时间: 2023-01
• 期刊: ArXiv
• 作者: Dong-Hwan Lee;Behrad Moniri;Xinmeng Huang;Edgar Dobriban;Hamed Hassani