报告题目：Riemannian EXTRA: Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity

报告人：Jiayuan Wu，博士后研究员，美国宾夕法尼亚大学沃顿商学院统计与数据科学系

报告时间：2026年10月12日9:00（北京时间）

报告地点：腾讯会议ID：709-777-481

校内联系人：宋海明[email protected]

报告摘要：We consider decentralized optimization over a compact Riemannian submanifold in a network of agents, where each agent owns a smooth nonconvex local objective defined by its private data. The goal is to minimize the sum of these local objectives using only local communications. In the presence of data heterogeneity, existing decentralized Riemannian algorithms typically exchange both local iterates and local directions and often require multiple communication rounds per iteration to guarantee exact convergence with constant step sizes.

In this talk, we present projection- and retraction-based Riemannian EXTRA algorithms (REXTRAs), which extend the EXTRA algorithm to manifold optimization and require only a single round of local-iterate communication per iteration. Our convergence analysis uses a primal-perspective reformulation that interprets REXTRA as a network-based Riemannian inexact gradient method with explicitly controllable inexactness. Together with the proximal smoothness of the manifold constraint, this framework allows us to quantify and control both the consensus error and the deviation of the local update direction from the Riemannian gradient of the global objective. We establish a global sublinear convergence rate of O(1/k) under a constant step size, matching the best-known rates for decentralized nonconvex optimization. Numerical experiments on representative manifold-valued learning tasks demonstrate that REXTRA supports larger step sizes and reduces total communication compared with state-of-the-art methods.

报告人简介：Jiayuan Wu，现为美国宾夕法尼亚大学沃顿商学院统计与数据科学系博士后研究员，合作导师为Weijie Su教授。2019年获吉林大学计算数学专业学士学位，2024年获北京大学工学院博士学位，博士导师为宋杰教授。主要研究兴趣包括数学优化、机器学习及其在管理中的应用，研究涉及黎曼流形优化、分布式优化和统计学习。