数学与统计学院学术报告[2021] 054号

(高水平大学建设系列报告554号)

报告题目: A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters

报告人：杨磊 博士 (新加坡国立大学)

报告时间：2021年6月18日16：30-17：30

报告地点：汇星楼514

报告内容：

We consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in areas such as statistics, machine learning and image processing. When the support points of the barycenter are pre-specified, this problem can be modeled as a linear programming (LP) problem whose size can be extremely large. To handle this large-scale LP, we analyse the structure of its dual problem, which is conceivably more tractable and can be reformulated as a well-structured convex problem with 3 kinds of block variables and a coupling linear equality constraint. We then adapt a symmetric Gauss-Seidel based alternating direction method of multipliers (sGS-ADMM) to solve the resulting dual problem and establish its global convergence and global linear convergence rate. As a critical component for efficient computation, we also show how all the subproblems involved can be solved exactly and efficiently. This makes our method suitable for computing a Wasserstein barycenter on a large-scale data set, without introducing an entropy regularization term as is commonly practiced. In addition, our sGS-ADMM can be used as a subroutine in an alternating minimization method to compute a barycenter when its support points are not pre-specified. Numerical results on synthetic data sets and image data sets demonstrate that our method is highly competitive for solving large-scale Wasserstein barycenter problems, in comparison to two existing representative methods and the commercial software Gurobi.

报告人简历：

杨磊，本硕毕业于天津大学（导师：黄正海教授），于2017年在香港理工大学获得博士学位（导师：陈小君教授和庞鼎基副教授），2018年起在新加坡国立大学(合作导师: Kim-Chuan Toh教授)从事博士后研究工作至今。主要从事最优化理论、算法和应用研究，特别专注于重要应用领域（如机器与统计学习、数据科学、图像与信号处理等）中出现的大规模结构优化问题，致力于设计和分析高效稳健的求解算法以及相关求解器的开发。目前已在SIAM Journal on Optimization、SIAM Journal on Imaging Science、Journal of Machine Learning Research、IEEE Transactions on Signal Processing等期刊发表多篇论文，其中1篇论文为ESI高被引论文。其博士学位论文《First-order Splitting Algorithms for Nonconvex Matrix Optimization Problems》于2019年荣获香港数学会颁发的“最佳博士学位论文奖”。

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　　　　　　　　　　　　　　　　　　　　　　　2021年6月16日