Diff-BBO: Diffusion-Based Inverse Modeling for Black-Box Optimization (2407.00610v2)

Abstract: 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 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. Subsequently, we employ a conditional diffusion model to generate samples based on these proposed values within the design space. We demonstrate that using UaE results in optimal optimization outcomes, supported by both theoretical and empirical evidence.