Contemporary nonconvex learning approaches in signal processing and machine learning are revolutionizing our ability to process data in their natural form, bringing transformative changes to modern life ranging from web searches and social networks to healthcare, commerce, and imaging. Despite wide empirical success in applications, these learning schemes lack a clear mathematical foundation that can enable not only rigorous performance analysis but can guide system designs based on an understanding of what would work, when and why. This project aims to develop a unified framework to design and analyze efficient nonconvex optimization algorithms. The resulting signal estimation and learning algorithms will be deployed in novel applications aimed at learning understandable models from data, which in turn will allow for better systems that can acquire data faster and at higher resolution and quality. Components from this project are integrated into an advanced graduate class and select results will serve to motivate K-12 students to pursue careers in STEM (Science, Technology, Engineering and Math).
In this project, the investigator studies a family of iterative algorithms for nonconvex data fitting problems that arise in modern signal processing and artificial intelligence, such as phaseless imaging and neural network training. The overarching goal of the project is to understand when these algorithms converge to globally optimal solutions and to characterize their behavior and convergence rate in terms of key quantities such as the number of data samples/observations, prior knowledge about the model, initialization accuracy, etc. The theoretical investigations utilize techniques from high-dimensional probability, statistics, optimization and nonlinear dynamics in control. The theoretical analysis guides the design of more reliable learning algorithms that can seamlessly scale to massive data sizes and are robust to node failures that arise in modern distributed computing environments.
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.