Diffusion Model for Data-Driven Black-Box Optimization

• URL: http://arxiv.org/abs/2403.13219v1
• Date: Wed, 20 Mar 2024 00:41:12 GMT
• Title: Diffusion Model for Data-Driven Black-Box Optimization
• Authors: Zihao Li, Hui Yuan, Kaixuan Huang, Chengzhuo Ni, Yinyu Ye, Minshuo Chen, Mengdi Wang,
• Abstract summary: We focus on diffusion models, a powerful generative AI technology, and investigate their potential for black-box optimization. We study two practical types of labels: 1) noisy measurements of a real-valued reward function and 2) human preference based on pairwise comparisons. Our proposed method reformulates the design optimization problem into a conditional sampling problem, which allows us to leverage the power of diffusion models.
• Score: 54.25693582870226
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Generative AI has redefined artificial intelligence, enabling the creation of innovative content and customized solutions that drive business practices into a new era of efficiency and creativity. In this paper, we focus on diffusion models, a powerful generative AI technology, and investigate their potential for black-box optimization over complex structured variables. Consider the practical scenario where one wants to optimize some structured design in a high-dimensional space, based on massive unlabeled data (representing design variables) and a small labeled dataset. We study two practical types of labels: 1) noisy measurements of a real-valued reward function and 2) human preference based on pairwise comparisons. The goal is to generate new designs that are near-optimal and preserve the designed latent structures. Our proposed method reformulates the design optimization problem into a conditional sampling problem, which allows us to leverage the power of diffusion models for modeling complex distributions. In particular, we propose a reward-directed conditional diffusion model, to be trained on the mixed data, for sampling a near-optimal solution conditioned on high predicted rewards. Theoretically, we establish sub-optimality error bounds for the generated designs. The sub-optimality gap nearly matches the optimal guarantee in off-policy bandits, demonstrating the efficiency of reward-directed diffusion models for black-box optimization. Moreover, when the data admits a low-dimensional latent subspace structure, our model efficiently generates high-fidelity designs that closely respect the latent structure. We provide empirical experiments validating our model in decision-making and content-creation tasks.

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