Adaptively Incorporating Directional Hints into Zeroth-Order Optimization

2026-09-08

AI Summary

研究利用方向提示改进非凸函数的零阶优化问题，提出CV-ZOD框架，自适应地结合方向提示，提高收敛速度，减少对提示质量的依赖。

Abstract

We study zeroth-order optimization of non-convex 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 non-convex landscapes where zeroth-order descent is slower and existing guided methods stall as guidance deteriorates.

Problem

• zeroth-order optimization
• directional hints
• non-convex functions

Innovation

• Control-Variate Zeroth-Order Descent (CV-ZOD)
• directional hints
• convergence rate
• non-convex optimization
• zeroth-order gradient estimator