Finding Stationary Points by Comparisons
We study the problem of finding stationary points of non-convex functions when access to the objective is provided only through a comparison oracle that, given two points, outputs which has the larger function value. For a twice differentiable $f\colon\mathbb R^n\to\mathbb R$ with Lipschitz gradient and Hessian, we develop an algorithm that visits an $ε$-stationary point using $\widetilde O(n^2/ε^{1.5})$ queries. Our approach uses a subroutine that estimates the normalized Hessian to accuracy $δ$ using $\widetilde O(n^2\log(1/δ))$ queries. We further study this problem with a quantum comparison oracle model where queries can be made in superpositions, and develop the first quantum algorit...
| Authors | Helin Wang, Chenyi Zhang, Xiwen Tao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 25 June 2026 |
| Last updated at source | 25 June 2026 |
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