报告题目：A Riemannian Exponential Augmented Lagrangian Method for Computing the Projection Robust Wasserstein Distance
报 告 人：姜波，南京师范大学
报告摘要：Projection robust Wasserstein (PRW) distance is recently proposed to efficiently mitigate the curse of dimensionality in the classical Wasserstein distance. In this paper, by equivalently reformulating the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints, we propose a Riemannian exponential augmented Lagrangian method (REALM) for solving this problem. Compared with the existing Riemannian exponential penalty based approaches, REALM can potentially avoid too small penalty parameters and exhibit more stable numerical performance. To solve the subproblems in REALM efficiently, we design an inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS), which selects the stepsizes adaptively rather than tuning the stepsizes in efforts as done in the existing methods. We show that iRBBS can return an $\epsilon$-stationary point of the original PRW distance problem within $\mathcal{O}(\epsilon^{-3})$ iterations, which matches the best known iteration complexity result. Extensive numerical results demonstrate that our proposed methods outperform the state-of-the-art solvers for computing the PRW distance. This is a joint work with Ya-Feng Liu.
报告人简介：姜波，2008年本科毕业于中国石油大学（华东），2013年博士毕业于中国科学院数学与系统科学研究院，2014年8月入职南京师范大学。研究兴趣为：带特殊结构优化问题的理论和算法，在Math. Program., SIAM J. Optim, SIAM J. Sci. Comput., IEEE汇刊系列等期刊发表数篇学术论文。2022年获中国运筹学会青年科技奖。
报告时间：2023年10月27日 15:00-16:00
报告地点：文渊楼B408教室
主办单位：伟德国际1946源自英国
