Locality-aware Surrogates for Gradient-based Black-box Optimization

TL;DR

This paper introduces locality-aware surrogate models for gradient-based black-box optimization, improving efficiency in complex, non-differentiable simulation tasks through a novel theoretical framework and scalable training algorithm.

Contribution

It establishes a theoretical link between gradient alignment and a new GradPIE loss, and develops a scalable method for offline and online optimization of black-box functions.

Findings

Improved optimization efficiency on real-world tasks.

Consistent performance under limited query budgets.

Effective in offline and online settings.

Abstract

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.