Optimization for ML and AI Seminar: Stochastic-Gradient and Diagonal-Scaling Algorithms for Constrained Optimization and Learning

Frank E. Curtis, Lehigh University

Abstract: I will motivate and provide an overview of recent efforts in my research group on the design and analysis of stochastic-gradient-based algorithms for solving constrained optimization problems. I will focus in particular on our motivation for informed supervised learning, where constraints in the training problem can be used to impose prior knowledge on the properties that should be possessed by a trained prediction model. In addition, I will provide a detailed look at our newest extensions of heavy-ball and Adam schemes from the unconstrained to the equality-constrained setting, for which we have shown state-of-the-art convergence guarantees. I will demonstrate the impressive practical performance of our methods using a few informed supervised learning problems.

Frank E. Curtis is a Professor in the Department of Industrial and Systems Engineering at Lehigh University, where he has been employed since 2009. He received a bachelor’s degree from the College of William and Mary in 2003 with a double major in Computer Science and Mathematics, received a master’s degree in 2004 and Ph.D. degree in 2007 from the Department of Industrial Engineering and Management Science at Northwestern University, and spent two years as a Postdoctoral Researcher in the Courant Institute of Mathematical Sciences at New York University from 2007 until 2009. His research focuses on the design, analysis, and implementation of numerical methods for solving large-scale nonlinear optimization problems. He received an Early Career Award from the Advanced Scientific Computing Research (ASCR) program of the U.S. Department of Energy (DoE), and has received funding from various programs of the U.S. National Science Foundation (NSF), including through a TRIPODS Phase I grant awarded to him and his collaborators at Lehigh, Northwestern, and Boston University. He has also received funding from the U.S. Office of Naval Research (ONR) and DoE’s Advanced Research Projects Agency-Energy (ARPA-E). He received, along with Leon Bottou (Meta AI) and Jorge Nocedal (Northwestern), the 2021 SIAM/MOS Lagrange Prize in Continuous Optimization. He was awarded, with James V. Burke (U. of Washington), Adrian Lewis (Cornell), and Michael Overton (NYU), the 2018 INFORMS Computing Society Prize. He and team members Daniel Molzahn (Georgia Tech), Andreas Waechter (Northwestern), Ermin Wei (Northwestern), and Elizabeth Wong (UC San Diego) were awarded second place in the ARPA-E Grid Optimization Competition in 2020. He currently serves as Area Editor for Continuous Optimization for Mathematics of Operations Research and serves as an Associate Editor for Mathematical Programming, SIAM Journal on Optimization, Operations Research, IMA Journal of Numerical Analysis, and Mathematical Programming Computation. He previously served as the Vice Chair for Nonlinear Programming for the INFORMS Optimization Society, and is currently very active in professional societies and groups related to mathematical optimization, including INFORMS, the Mathematics Optimization Society, and the SIAM Activity Group on Optimization.

Zoom: https://bit.ly/Opt-AI-ML