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cs.LG updates on arXiv.org

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Finding Stationary Points by Comparisons
[Submitted on 25 Jun 2026] · 2026-06-26 · via cs.LG updates on arXiv.org

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Abstract: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 $\epsilon$-stationary point using $\widetilde O(n^2/\epsilon^{1.5})$ queries. Our approach uses a subroutine that estimates the normalized Hessian to accuracy $\delta$ using $\widetilde O(n^2\log(1/\delta))$ queries. We further study this problem with a quantum comparison oracle model where queries can be made in superpositions, and develop the first quantum algorithm that finds an $\epsilon$-stationary point, which takes $\widetilde O(n/\epsilon^{1.5})$ queries.

Submission history

From: Helin Wang [view email]
[v1] Thu, 25 Jun 2026 14:20:03 UTC (38 KB)

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