Lower Bounds for Smooth Nonconvex Zeroth-Order Optimization: The Price of Determinism under Low Curvature Trace
Low curvature trace, an effective rank condition, is a common explanation for why randomized zeroth-order methods scale to high-dimensional tasks such as language model fine-tuning. Can deterministic methods achieve the same savings? We show that they cannot. We study finding $\varepsilon$-stationary points of $L$-smooth nonconvex functions on $\mathbb{R}^d$ from exact function values, assuming that below the starting value the Hessian is dominated by a fixed matrix with trace at most $LE$; this is the effective rank condition used to explain zeroth-order fine-tuning. When $ET\le d$, the Gaussian two-point method that such fine-tuning uses needs only $O(ET)$ calls if it rejects steps that...
| Authors | Yuxing Peng, Zhiqing Tang, Weijia Jia |
|---|---|
| Primary category | cs.LG |
| Published | 20 October 2026 |
| Last updated at source | 20 October 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 21 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.