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

主讲人：户将

户将，清华大学数学科学中心助理教授。他的主要研究兴趣包括流形优化和机器学习，研究成果发表在SIAM 系列、NM、MOR、IEEE 系列、JMLR 和NeurIPS 等期刊和会议，参与编写教材《最优化：建模、算法与理论》和《最优化计算方法》。

1  报告信息

时间 

2025年11月21日（周五） 

16:00-17:00

地点 

中国人民大学中关村校区

明德主楼1016会议室

2  报告摘要

We consider decentralized optimization over a compact Riemannian submanifold in a network of n agents, where each agent holds a smooth, nonconvex local objective defined by its private data. The goal is to collaboratively minimize the sum of these local objective functions. In the presence of data heterogeneity across nodes, existing algorithms typically require communicating both local gradients and iterates to ensure exact convergence with constant step sizes. In this work, we propose REXTRA, a Riemannian extension of the EXTRA algorithm [Shi et al., SIOPT, 2015], to address this limitation. On the theoretical side, we leverage proximal smoothness to overcome the challenges of manifold nonconvexity and establish a global sublinear convergence rate of O(1/k), matching the best-known results. To our knowledge, REXTRA is the first algorithm to achieve a global sublinear convergence rate under a constant step size while requiring only a single round of local iterate communication per iteration. Numerical experiments show that REXTRA achieves superior performance compared to state-of-the-art methods, while supporting larger step sizes and reducing total communication by over 50%.