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

离散优化是算法设计中的一个固有挑战，出现在人工智能、机器人和智慧城市等各个领域。尽管离散优化问题通常很难，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块性的自然递减性质。与凸性在连续优化中的作用类似，子模块性在算法设计中具有变革性，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，现有的方法受到已知的限制，并可以受益于重新审查所提出的挑战，由今天的技术进步。该项目旨在制定一项研究计划，为复杂动态环境中的离散和子模块优化奠定基础，解决可扩展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，具有协同教育计划，结合了宾夕法尼亚大学研究生和本科课程的开发，具体目标是确定教育培训的差距，并丰富工程师数据科学教学课程。它还旨在利用现有的公共教育平台，为进入大学的STEM专业学生建立一个管道，推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中的子模块优化开发新的基础框架;（ii）分布式和多智能体系统;（iii）分布式和多智能体系统。以及（iii）能够按顺序选择数据和观测的适应性情景。该项目旨在建立最佳可实现的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）之间的基本权衡，并设计满足这种权衡的算法框架。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.