{
  "id": "2403.13219",
  "version": "v1",
  "published": "2024-03-20T00:41:12.000Z",
  "updated": "2024-03-20T00:41:12.000Z",
  "title": "Diffusion Model for Data-Driven Black-Box Optimization",
  "authors": [
    "Zihao Li",
    "Hui Yuan",
    "Kaixuan Huang",
    "Chengzhuo Ni",
    "Yinyu Ye",
    "Minshuo Chen",
    "Mengdi Wang"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2307.07055",
  "categories": [
    "cs.LG",
    "math.OC"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-20T00:41:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "data-driven black-box optimization",
      "latent structure",
      "model efficiently generates high-fidelity designs",
      "low-dimensional latent subspace structure",
      "establish sub-optimality error bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}