Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions

תקציר מקורי באנגליתarXiv:2607.20316v1 Announce Type: cross Abstract: We study decentralized online optimization for strongly geodesically convex (strongly g-convex) losses on Riemannian manifolds with bounded sectional curvature, including positively curved manifolds. In centralized Riemannian optimization, strong g-convexity tightens the optimal regret from $O(\sqrt{T})$ to $O(\log T)$, where $T$ is the time horizon; in the decentralized Riemannian setting, however, existing methods address only g-convex losses, leaving the strongly g-convex regime unexplored. One challenge is that the required decaying step size in the centralized regime is incompatible with existing network-error analyses, which typically assume a fixed step size. First, we provide a general network-error analysis for time-varying schedul