2025/09/09 by Emre Sahinoglu, Shahin Shahrampour, Sahinoglu, Emre +1 · 3 citations
Computer Science · Decision Sciences · #Stochastic Gradient Optimization Techniques #Advanced Bandit Algorithms Research #Distributed Control Multi-Agent Systems
paper · pdf · doi:10.48550/arxiv.2509.07779
We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techniques rely on a consensus step that is well understood in Euclidean spaces because of their linearity. However, in positively curved Riemannian spaces, a main technical challenge is that geodesic distances may not induce a globally convex structure. In this work, we first analyze a curvature-aware Riemannian consensus step that enables a linear convergence beyond Hadamard manifolds. Building on this step, we establish a O(√(T)) regret bound for the decentralized online Riemannian gradient descent algorithm. Then, we investigate the two-point bandit feedback setup, where we employ computationally efficient gradient estimators using smoothing techniques, and we demonstrate the same O(√(T)) regret bound through the subconvexity analysis of smoothed objectives.