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

TL;DR

This work introduces GradPIE, a locality-aware surrogate training objective derived from the Gradient Theorem, to align a surrogate’s gradients with those of a non-differentiable black-box. By training surrogates with GradPIE using either offline data or online updates, the method improves gradient estimation and accelerates gradient-based optimization under limited query budgets. Empirical results on CNON, OpAmp, and OWMS show substantial gains in gradient accuracy and optimization efficiency, with notable query-budget reductions and robustness in high-dimensional settings. The approach provides a principled pathway to more reliable gradient estimates for black-box simulators and physical systems, with potential extensions to analog neural networks and reinforcement learning.

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.

Figures (4)

• Figure 1: a Our method calculates the $k$-nearest neighbors for each sample in the dataset. These neighbors are used to train the locality-aware surrogate model with the GradPIE loss function. b Active black-box optimization (ABBO) using the surrogate model trained offline. c ABBO with online training of the surrogate model.
• Figure 2: Relative error and cosine similarity between estimated and exact gradient for input dimensions of $D_i = 7$ (a and b) and $D_i = 10$ (c and d ), as a function of the number of nearest neighbors for CNON. e The improvement in gradient estimation for optimal number of nearest neighbors. Performance of ABBO using the offline-trained surrogate model for the CNON task for f$\mathfrak{\lambda}=0.50$, g$\mathfrak{\lambda}=0.55$, and h$\mathfrak{\lambda}=0.70$.
• Figure 3: Performance of ABBO using the online-trained surrogate model for the CNON task ($\boldsymbol{\lambda} = [-0.55, 0.125, 0.31, -0.38, 0.60]$): a without local sampling ($N_s = 0$) and b with local sampling ($N_s = 1$). c Schematic of the OpAmp circuit task. d Mean ± standard deviation and e median with interquartile range (IQR) of ABBO using the online-trained surrogate model for the OpAmp task.
• Figure 4: a Schematic of the OWMS. An input Gaussian beam is illuminated onto a Spatial Light Modulator (SLM) with 3600 parameters to be optimized such that the output waveform matches the target waveform. b Mean ± standard deviation and c median with interquartile range (IQR) of ABBO using the online-trained surrogate model for the OWMS task.