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.

基于扩散模型的条件采样方法，在黑盒优化中生成接近最佳解且保留设计的潜在结构，通过建立理论模型和进行实验验证，证明了奖励导向扩散模型在黑盒优化中的效率和准确性。