Speaker: Trung Vu
Time: 4:00 pm - 5:00 pm on Tuesday 7/12
Room: KEC 1005
Title of the seminar: On Asymptotic Linear Convergence of Projected Gradient Descent for Constrained Least Squares
Abstract:
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent is a simple yet efficient method for solving such constrained optimization problems. Local convergence analysis furthers our understanding of its asymptotic behavior near the solution, offering sharper bounds on the convergence rate compared to global convergence analysis. However, local guarantees often appear scattered in problem-specific areas of machine learning and signal processing. This manuscript presents a unified framework for the local convergence analysis of projected gradient descent in the context of constrained least squares. The proposed analysis offers insights into pivotal local convergence properties such as the conditions for linear convergence, the region of convergence, the exact asymptotic rate of convergence, and the bound on the number of iterations needed to reach a certain level of accuracy. To demonstrate the applicability of the proposed approach, we present a recipe for the convergence analysis of projected gradient descent and demonstrate it via a beginning-to-end application of the recipe on four fundamental problems, namely, linear equality-constrained least squares, sparse recovery, least squares with the unit norm constraint, and matrix completion.
Speaker Bio:
Trung Vu received the B.S. degree in Computer Science from Hanoi University of Science and Technology, Hanoi, Vietnam, in 2014. He has been working toward the Ph.D. degree in Computer Science since 2016 at the School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, Oregon, USA. His current research interests include both theory and practice of scalable optimization methods for machine learning and signal processing.
Our seminars are held on Tuesdays at 4:00 - 5:00 PM.
Dates |
Presenter |
June 14 |
Dr. Xiao Fu |
June 21 |
Colin Shea-Blymyer |
June 28 |
Leonardo Cavalcanti |
July 12 |
Trung Vu |
August 9 |
Dr. Tim Marrinan |
August 23 |
Shahana Ibrahim |
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