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

TL;DR

DiBO introduces a diffusion model-based framework for high-dimensional black-box optimization, effectively balancing exploration and exploitation, and outperforming existing methods in synthetic and real-world tasks.

Contribution

The paper proposes DiBO, a novel diffusion model-based approach that improves uncertainty estimation and scalability in high-dimensional black-box optimization.

Findings

Outperforms state-of-the-art baselines on synthetic tasks

Effective in real-world high-dimensional optimization problems

Balances exploration and exploitation through posterior inference

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 deep ensembles 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 synthetic and real-world tasks. Our code is publicly available \href{https://github.com/umkiyoung/DiBO}{here}.