Curvature-Independent Regret Bounds for Distributed Online Optimization on Hadamard Manifolds

A new arXiv paper studies decentralized online optimization where the decision variables live on Hadamard manifolds, a setting with negative curvature. The authors derive regret guarantees that do not depend on the manifold's curvature, avoiding the finite lower bound on sectional curvature required by earlier analyses built on geodesic convexity. The results apply to distributed multi-agent settings where agents coordinate over a network while optimizing online.