CSE DSI Machine Learning Seminar with Renbo Zhao

Frank-Wolfe-Type Methods for Minimizing Log-Homogenous Self-Concordant Barriers

We present and analyze a new Frank–Wolfe method for minimizing a theta-log-homogenous self-concordant barriers, with applications including positron emission tomography, D-optimal design, TV-regularized Poisson image de-blurring, quantum state tomography. The iteration complexity of our method is essentially O(\theta^2/\epsilon), which recovers that obtained by Khachiyan (1996) on the D-optimal design problem. In addition, we also present and analyze an away-step variant of our proposed Frank–Wolfe method, and we show the global linear convergence of this method. When specialized to the D-optimal design problem, this settles an open problem in Ahipasaoglu, Sun and Todd (2008).

Renbo Zhao is currently an assistant professor in the Tippie College of Business at the University of Iowa. He obtained his PhD in Operations Research from MIT in 2023. His research interests include theory and computational practice for continuous optimization algorithms, with applications in machine learning, data science and operations management. His current research focuses on developing and analyzing efficient first-order methods for convex optimization with “non-standard” structures.