Zeroth order optimization improved by adapting to directional hint quality
Adaptively Incorporating Directional Hints into Zeroth-Order Optimization
Machine Learning
Summary
Sometimes, computers need to solve problems where they can't directly see the slope or direction to improve their answer. This work looks at how to use helpful hints about directions, which might not always be accurate, to guide the search better. The authors created a method that smartly adjusts how much it trusts these hints, leading to faster and more reliable solutions. Their approach works well even when the hints are of unknown or changing quality, outperforming older methods in complex problems.
zeroth-order optimizationnon-convex functionsdirectional hintsgradient estimationcontrol variateconvergence rateoracle algorithmstep sizelinear subspaces
Authors
Alexander Ryabchenko, Jian Qian, Wenlong Mou
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.