Riemannian Online Optimistic Algorithms With Dynamic Regret

• 成果类型: Article
• 署名作者: Wang, Xi; Yuan, Deming; Hong, Yiguang; Hu, Zihao; Wang, Lei; Shi, Guodong
• 署名单位: University of New South Wales Sydney; Nanjing University of Science & Technology; Tongji University; Hong Kong University of Science & Technology; Zhejiang University; University of Sydney
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3557363
• 发表日期: 2025
• 页码: 6481-6496
• 关键词: Heuristic algorithms; MANIFOLDS; Convex functions; optimization; Lower bound; robots; mirrors; Upper bound; training; Machine Learning; dynamic regret; online learning; optimistic algorithm; Riemannian manifold

摘要

this article, we consider Riemannian online convex optimization with dynamic regret, which involves minimizing the cumulative loss difference between a learner's decisions and a sequence of adaptive decisions across dynamic environments over time on Riemannian manifolds. First, we propose Riemannian online optimistic gradient descent (R-OOGD), which extends the classical optimistic algorithms to Riemannian manifolds, requiring one gradient inquiry per round. We then propose Riemannian adaptive online optimistic gradient descent (R-AOOGD) by incorporating the meta-expert framework into R-OOGD. We analyze the dynamic regret of R-OOGD and R-AOOGD in terms of the regularity of the sequence of cost functions and comparators. The dynamic regret bound matches the results in Euclidean space and with a scale ( ' adjustment of O (1+kappa D-2/root 1-KD2) related to the sectional curvature lower bound kappa, sectional curvature upper bound K and feasible set diameter D. Finally, we provide numerical experiments to illustrate the performance of the proposed algorithms.