Decentralized Online Riemannian Optimization for Strongly Geodesically Convex Functions
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 ge...
| Authors | Zhanyuan Cai, Emre Sahinoglu, Shahin Shahrampour |
|---|---|
| Primary category | math.OC |
| Published | 22 July 2026 |
| Last updated at source | 22 July 2026 |
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