[2603.00023] Riemannian Dueling Optimization

Mathematics > Optimization and Control arXiv:2603.00023 (math) [Submitted on 3 Feb 2026] Title:Riemannian Dueling Optimization Authors:Yuxuan Ren, Abhishek Roy, Shiqian Ma View a PDF of the paper titled Riemannian Dueling Optimization, by Yuxuan Ren and 2 other authors View PDF HTML (experimental) Abstract:Dueling optimization considers optimizing an objective with access to only a comparison oracle of the objective function. It finds important applications in emerging fields such as recommendation systems and robotics. Existing works on dueling optimization mainly focused on unconstrained problems in the Euclidean space. In this work, we study dueling optimization over Riemannian manifolds, which covers important applications that cannot be solved by existing dueling optimization algorithms. In particular, we propose a Riemannian Dueling Normalized Gradient Descent (RDNGD) method and establish its iteration complexity when the objective function is geodesically L-smooth or geodesically (strongly) convex. We also propose a projection-free algorithm, named Riemannian Dueling Frank-Wolfe (RDFW) method, to deal with the situation where projection is prohibited. We establish the iteration and oracle complexities for RDFW. We illustrate the effectiveness of the proposed algorithms through numerical experiments on both synthetic and real applications. Subjects: Optimization and Control (math.OC); Machine Learning (cs.LG) Cite as: arXiv:2603.00023 [math.OC]   (or arXiv:2603.00023...