In physics and engineering, many processes are modeled using non-differentiable black-box simulators, making the optimization of such functions particularly challenging. To address such cases, inspired by the Gradient Theorem, we propose locality-aware surrogate models for active model-based black-box optimization. We first establish a theoretical connection between gradient alignment and the minimization of a Gradient Path Integral Equation (GradPIE) loss, which enforces consistency of the surrogate's gradients in local regions of the design space. Leveraging this theoretical insight, we develop a scalable training algorithm that minimizes the GradPIE loss, enabling both offline and online learning while maintaining computational efficiency. We evaluate our approach on three real-world tasks - spanning automated in silico experiments such as coupled nonlinear oscillators, analog circuits, and optical systems - and demonstrate consistent improvements in optimization efficiency under limited query budgets. Our results offer dependable solutions for both offline and online optimization tasks where reliable gradient estimation is needed.
@article{arxiv.2501.19161,
title = {Locality-aware Surrogates for Gradient-based Black-box Optimization},
author = {Ali Momeni and Stefan Uhlich and Arun Venkitaraman and Chia-Yu Hsieh and Andrea Bonetti and Ryoga Matsuo and Eisaku Ohbuchi and Lorenzo Servadei},
journal= {arXiv preprint arXiv:2501.19161},
year = {2025}
}