Posterior Inference with Diffusion Models for High-dimensional Black-box Optimization

Taeyoung Yun, Kiyoung Om, Jaewoo Lee, Sujin Yun, Jinkyoo Park

Keywords: Diffusion Models, Posterior Inference, High-dimensional Black-box Optimization

TL;DR: We adopt posterior inference with diffusion models to solve high-dimensional black-box optimization problems efficiently

Abstract:

Optimizing high-dimensional and complex black-box functions is crucial in numerous scientific applications.
While Bayesian optimization (BO) is a powerful method for sample-efficient optimization, it struggles with the curse of dimensionality and scaling to thousands of evaluations.
Recently, leveraging generative models to solve black-box optimization problems has emerged as a promising framework.
However, those methods often underperform compared to BO methods due to limited expressivity and difficulty of uncertainty estimation in high-dimensional spaces.
To overcome these issues, we introduce \textbf{DiBO}, a novel framework for solving high-dimensional black-box optimization problems.
Our method iterates two stages. First, we train a diffusion model to capture the data distribution and a surrogate model to predict function values with uncertainty quantification.
Second, we cast the candidate selection as a posterior inference problem to balance exploration and exploitation in high-dimensional spaces. Concretely, we fine-tune diffusion models to amortize posterior inference.
Extensive experiments demonstrate that our method outperforms state-of-the-art baselines across various synthetic and real-world black-box optimization tasks. Our code is publicly available \href{https://github.com/umkiyoung/DiBO}{here}.

Submission Number: 16