Fast Epigraphical Projection-based Incremental Algorithms for Wasserstein Distributionally Robust Support Vector Machine


Speaker CHEN Caihua, Nanjing University
HostLI Xudong, Fudan University
Time2020-6-22, 10:00-11:30
Zoom ID911 962 70054
AbstractWasserstein Distributionally Robust Optimization (DRO) is concerned with finding decisions that perform well on data that are drawn from the worst-case probability distribution within a Wasserstein ball centered at a certain nominal distribution. In recent years, it has been shown that various DRO formulations of learning models admit tractable convex reformulations. However, most existing works propose to solve these convex reformulations by general-purpose solvers, which are not well-suited for tackling large-scale problems. In this paper, we focus on a family of Wasserstein distributionally robust support vector machine (DRSVM) problems and propose two novel epigraphical projection-based incremental algorithms to solve them. The updates in each iteration of these algorithms can be computed in a highly efficient manner. Moreover, we show that the DRSVM problems considered in this paper satisfy a Hölderian growth condition with explicitly determined growth exponents. Consequently, we are able to establish the convergence rates of the proposed incremental algorithms.
BioDr. CHEN Caihua is an associate professor of School of Management and Engineering at Nanjing University. His research interests focus on optimization theory and algorithms, as well as their applications to management science and machine learning.