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

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

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.