Extremum Seeking with Surrogate Gradients: Scalable Derivative-Free Optimization for High-Dimensional Black-Box Functions

Kilean Hwang, Jinyu Wan, Alexander Scheinker, Peter N. Ostroumov

Keywords: Extremum Seeking, Surrogate Gradients, Derivative-Free Optimization, High-Dimensional Optimization, Zeroth-order Optimization

TL;DR: We introduce a derivative-free optimizer that blends extremum seeking with surrogate-model gradients to solve time-constrained (moderate per-evaluation cost), high-dimensional black-box problems.

Abstract: Derivative-free optimization remains a central challenge in high-dimensional black-box problems where gradients are unavailable and evaluations are moderately expensive or must be performed under tight, non-parallelizable time budgets. Classical approaches such as Bayesian optimization suffer computational cost from model training and acquisition-function optimization, while many evolutionary strategies can be sample-inefficient. Classical Zeroth-order methods are also often data-inefficient requiring evaluation queries for gradient estimation. We propose a hybrid framework that combines Extremum Seeking (ES) with surrogate-gradient (SG): a Gaussian process surrogate is trained on data collected during the optimization process and used to predict approximate local gradients at the current iterate, while ES provides structured local perturbative exploration via sinusoidal dithering. By using predicted gradients to form direct update directions, the method avoids a separate acquisition-function optimization step and reduces per-iteration overhead in sequential deployments. To improve robustness and adaptive learning rate we project surrogate gradients according to their posterior uncertainty and apply Adam on the surrogate gradient. On high-dimensional synthetic control benchmarks, our approach outperforms standard ES and comparable to the trust-region BO on the tasks studied.

Primary Area: optimization

Submission Number: 9993