题    目：Riemannian Optimization for Projection Robust Optimal Transport

报告人：马士谦

单    位：Rice University

时    间：8月3日10:00

地    点：腾讯会议862-610-761

摘要：The optimal transport problem is known to suffer the curse of dimensionality. A recently proposed approach to mitigate the curse of dimensionality is to project the sampled data from the high dimensional probability distribution onto a lower-dimensional subspace, and then compute the optimal transport between the projected data. However, this approach requires to solve a max-min problem over the Stiefel manifold, which is very challenging in practice. In this talk, we propose a Riemannian block coordinate descent (RBCD) method to solve this problem. We analyze the complexity of arithmetic operations for RBCD to obtain an $\epsilon$-stationary point, and show that it significantly improves the corresponding complexity of existing methods. Numerical results on both synthetic and real datasets demonstrate that our method is more efficient than existing methods, especially when the number of sampled data is very large. If time permits, we will also talk about the projection robust Wasserstein barycenter problem.

报告人简介：Shiqian Ma is currently an associate professor in the Department of Computational Applied Mathematics and Operations Research at Rice University, and in the Department of Mathematics at University of California, Davis (on leave). He received his BS in Mathematics from Peking University in 2003, MS in Computational Mathematics from the Chinese Academy of Sciences in 2006, and PhD in Industrial Engineering and Operations Research from Columbia University in 2011. Shiqian was an NSF postdoctoral fellow in the Institute for Mathematics and its Applications at the University of Minnesota during 2011-2012 and an assistant professor in the Department of Systems Engineering and Engineering Management at the Chinese University of Hong Kong during 2012-2017. His current research interests include theory and algorithms for large-scale optimization, and their various applications in machine learning, signal processing and statistics. Shiqian received the INFORMS Optimization Society Best Student Paper Prize in 2010, and an honorable mention in the INFORMS George Nicholson Student Paper Competition in 2011. He was one of the finalists for the 2011 IBM Herman Goldstine fellowship. He received the Journal of the Operations Research Society of China Excellent Paper Award in 2016. Shiqian has served as the area chairs for machine learning conferences such as ICML and NeurIPS, and currently serves on the editorial board of Journal of Scientific Computing.