← 研踪 PaperTrailarXiv:2609.08277 · v2
Adaptively Incorporating Directional Hints into Zeroth-Order Optimization
首次提交 2026-09-08 13:42
版本更新 2026-11-09 19:20
雷达观测 2026-11-10 15:22
摘要
We study zeroth-order optimization of nonconvex functions with the aid of directional hints, which are cheap but potentially inaccurate approximations of the true gradient direction, given by linear subspaces at each iteration. To leverage these hints adaptively while maintaining robustness to their quality, we introduce Control-Variate Zeroth-Order Descent (CV-ZOD), a new framework that refines the classical zeroth-order gradient estimator with a control variate that can be set based on the directional hints. We first show that the oracle algorithm that optimally sets the reference vector and step size at each iteration achieves a convergence rate that interpolates between the first-order $O(1/T)$ rate and the zeroth-order $O(d/T)$ rate, depending on the quality of the hints along the trajectory. We then develop a practical variant of CV-ZOD that achieves the same oracle guarantee up to logarithmic factors, without any prior knowledge of the hint quality. We validate the method empirically on simulation-based scientific optimization tasks, demonstrating sustained progress on nonconvex landscapes where zeroth-order descent is slower and existing guided methods stall as guidance deteriorates.
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v2 · 2026-11-09 19:20 · 最新观测版本
Adaptively Incorporating Directional Hints into Zeroth-Order Optimization
We study zeroth-order optimization of nonconvex functions with the aid of directional hints, which are cheap but potentially inaccurate approximations of the true gradient direction, given by linear subspaces at each iteration. To leverage these hints adaptively while maintaining robustness to their quality, we introduce Control-Variate Zeroth-Order Descent (CV-ZOD), a new framework that refines the classical zeroth-order gradient estimator with a control variate that can be set based on the directional hints. We first show that the oracle algorithm that optimally sets the reference vector and step size at each iteration achieves a convergence rate that interpolates between the first-order $O(1/T)$ rate and the zeroth-order $O(d/T)$ rate, depending on the quality of the hints along the trajectory. We then develop a practical variant of CV-ZOD that achieves the same oracle guarantee up to logarithmic factors, without any prior knowledge of the hint quality. We validate the method empirically on simulation-based scientific optimization tasks, demonstrating sustained progress on nonconvex landscapes where zeroth-order descent is slower and existing guided methods stall as guidance deteriorates.
查看此版本解读 →查看此版本原文 ↗