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

2025-02-24

AI Summary

To address the poor scalability of Bayesian optimization (BO) and weak uncertainty quantification in generative approaches for high-dimensional (≥100D) black-box function optimization, this paper proposes DiBO—a novel framework that introduces diffusion models to black-box optimization for the first time. DiBO formulates optimization as a posterior inference task and enables efficient amortized inference via fine-tuning. It jointly integrates ensemble surrogate models for robust uncertainty estimation and iteratively refines candidate solutions in a generative manner. DiBO overcomes fundamental dimensionality and evaluation-budget limitations of conventional BO, achieving significant improvements over state-of-the-art methods across diverse synthetic and real-world black-box benchmarks—particularly under kilo-scale (≈1,000) function evaluations. The implementation is publicly available.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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 extbf{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 an ensemble of proxies 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}

Problem

• High-dimensional black-box optimization
• Curse of dimensionality
• Uncertainty estimation in optimization

Innovation

• Diffusion models for optimization
• Ensemble proxies for uncertainty
• Posterior inference balancing exploration