arXiv:2609. 13646v1 Announce Type: new Abstract: This work addresses decentralized online Riemannian optimization on Hadamard manifolds.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
arXiv:2509. 07779v2 Announce Type: replace-cross Abstract: We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting.
arXiv: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.
arXiv:2606. 02948v1 Announce Type: new Abstract: Curvature adaptivity is a classical theme in online optimization: for convex Lipschitz losses, adaptive methods interpolate between the optimal $O(\sqrt{T})$ regret for general convex losses and $O(\log T)$ regret under strong convexity.
arXiv:2608. 02375v1 Announce Type: cross Abstract: This paper studies the distributed online control problem over a network of linear time-invariant (LTI) systems in the presence of adversarial disturbances and time-varying convex costs.
arXiv:2610. 28058v1 Announce Type: new Abstract: We study universal online convex optimization with delayed feedback.
The paper introduces a new convergence framework for solving distributionally robust optimization problems formulated as nonconvex, nonconcave minimax problems over a Euclidean space and a Riemannian manifold. It defines a "basin saddle point"—a locally defined Nash equilibrium—and proves that a Riemannian gradient ascent–descent algorithm converges to such points under a local Łojasiewicz growth condition. The authors apply this theory to a statistical risk DRO problem over Gaussian measures, deriving explicit convergence rates and constants in terms of data dimension, loss moments, and reference covariance.