Diff-BBO: Diffusion-Based Inverse Modeling for Black-Box Optimization

Black-box optimization (BBO) aims to optimize an objective function by iteratively querying a black-box oracle in a sample-efficient way. While prior studies focus on forward approaches to learn surrogates for the unknown objective function, they struggle with steering clear of out-of-distribution and invalid inputs. Recently, inverse modeling approaches that map objective space to the design space with classifier-free conditional diffusion models have demonstrated impressive capability in learning the data manifold. They have shown promising performance in offline BBO tasks. However, these approaches require a pre-collected dataset. How to design the acquisition function for inverse modeling to actively query new data remains an open question. In this work, we propose diffusion-based inverse modeling for black-box optimization (Diff-BBO), an inverse approach leveraging diffusion models for online BBO problem. Instead of proposing candidates in the design space, Diff-BBO employs a novel acquisition function Uncertainty-aware Exploration (UaE) to propose objective function values. It leverages the uncertainty of a conditional diffusion model to generate samples in the design space. We demonstrate that using UaE results in optimal optimization outcomes, supported by both theoretical and empirical evidence.