Title: Capitalizing Deep Generative AI: Cracking High-D Modeling Towards Generative Optimization

Abstract: Deep generative AI, e.g., diffusion models, achieves state-of-the-art performance in various high-dimensional data modeling tasks. Such empirical successes have been challenging conventional wisdom. In this talk, we will focus on diffusion models to explore their methodology and theory. In the first part of the talk, we will understand how diffusion models efficiently model complex high-dimensional data, especially when there are low-dimensional structures in them. We prove the first efficient sample complexity bound of diffusion models, circumventing the notorious curse of dimensionality issue. In the second part, we leverage our understanding of diffusion models to motivate a next-generation optimization method, termed "generative optimization". Specifically, we utilize diffusion models as a data-driven solution generator to an unknown objective function. We propose a learning-labeling-generating algorithm incorporating the targeted function value as guidance to the diffusion model. Theoretically, we show that in the offline setting, the generated solutions yield large function values on average. Meanwhile, the generated solutions closely respect the data intrinsic structures in the training set. Empirically, we demonstrate a good synergy of generative optimization with reinforcement learning.

Bio: Minshuo Chen is a postdoctoral researcher in the Department of Electrical and Computer Engineering at Princeton University. He completed his Ph.D. from the School of Industrial and Systems Engineering at Georgia Tech, majoring in Machine Learning. His research focuses on developing principled methodologies and theoretical foundations of deep learning, with a particular interest in 1) generative models including diffusion models, 2) foundations of machine learning, such as optimization and sample efficiency, and 3) reinforcement learning. He serves as an area chair at NeurIPS conference and receives the IDEaS-TRIAD Scholarship and ARC-TRIAD Student Fellowship at Georgia Tech.