For strongly horospherically convex functions, negative curvature preserves or improves the Euclidean-optimal higher-order oracle rate; for strongly geodesically convex functions, growing negative curvature forces a strictly worse rate.
Proceedings of the 36th Conference on Learning Theory , series =
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.OC 1years
2026 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity
For strongly horospherically convex functions, negative curvature preserves or improves the Euclidean-optimal higher-order oracle rate; for strongly geodesically convex functions, growing negative curvature forces a strictly worse rate.