First-order methods in optimization have become the workhorse tool in modern data-driven applications. Although various general methods with optimal iteration complexities have been known for decades, their standard analysis often appears unintuitive. In this talk, I will present a simple unifying framework based on the numerical discretization of a continuous-time dynamics. Further, I will present a novel accelerated method that is naturally obtained from this framework. The method matches the iteration complexity of the well-known Nesterov’s method, and is, in some cases, more stable under noise-corrupted gradients. Time permitting, I will talk about other applications of the framework, such as in obtaining width-independent parallel algorithms for problems with positive linear constraints, and the extensions of the framework to various settings, including that of block coordinate descent.
Jelena Diakonikolas is a Postdoctoral Associate at Boston University. Prior to joining BU, she completed her Ph.D. degree in electrical engineering at Columbia University in 2016. Her research interests include large-scale optimization with a focus on first-order methods and specific applications in wireless and networked systems. She is a recipient of the Morton B. Friedman Prize for Excellence at Columbia Engineering, co-winner of a Qualcomm 2015 Innovation Fellowship, and was listed as “10 Women in Networking/Communications That You Should Watch” by Networking Networking Women in 2016.