Speakers
Jose Blanchet (Stanford) and Renyuan Xu (NYU)
Registration (Required)
Titles and Abstracts
Talk 1:On Highly Parameterized Controls and Fusion of Generative Diffusions
Jose Blanchet (Stanford)
We discuss two recent projects which touch on first order methods in connection with two very active in artificial intelligence. The first one involves the design of efficient gradient estimators for dynamic optimization problems based on highly parameterized controls. The motivation is the application of stochastic gradient descent for the numerical solution of stochastic control problems using neural networks. Our estimator has at least a linear speed-up in the dimension of the parameter space compared to infinitesimal perturbation analysis and it can be applied to situations in which the likelihood ratio estimator may not be applicable (e.g. If the diffusion matrix depends on the parameter of interest). We show very substantial gains in high-dimensional control problems based on experiments.
The second result involves the development of an efficient approach for merging diffusion-based generative models. We assume the existence of several auxiliary models that have been trained with abundance of data. These models are assumed to contain features that, combined, can be useful to enhance the training of a generative diffusion model for a target distribution with limited data. We merge the models using a Kullback-Leibler (KL) Barycenter given set of weights representing the importance of the auxiliaries. In turn, we optimize the weights to improve the overall performance of the fused model. While the double optimization problem (KL Barycenter and optimizing over weights) is challenging to solve, we show that diffusion based generative modeling significantly reduce the complexity of the overall optimization. This approach also provides a mechanistic interpretation of popular fine-tuning approaches used in the literature.
The results are based on two papers, the first one (on gradient estimators) with Peter Glynn and Shengbo Wang, and the second one (on fusion) with Hao Liu, Nian Si, and Tony Ye.
Talk 2: Generative diffusion models: optimization, generalization and fine-tuning
Renyuan Xu (NYU)
Abstract: Recently, generative diffusion models have outperformed previous architectures, such as GANs, in generating high-quality synthetic data, setting a new standard for generative AI. A key component of these models is learning the associated Stein's score function. Though diffusion models have demonstrated practical success, their theoretical foundations are far from mature, especially regarding whether gradient-based algorithms can provably learn the score function. In this talk, I will present a suite of non-asymptotic theory aimed at understanding the data generation process in diffusion models and the accuracy of score estimation. Our analysis addresses both the optimization and generalization aspects of the learning process, establishing a novel connection to supervised learning and neural tangent kernels.
Building on these theoretical insights, another key challenge arises when fine-tuning pre-trained diffusion models for specific tasks or datasets to improve performance. Fine-tuning requires refining the generated outputs based on particular conditions or human preferences while leveraging prior knowledge from the pre-trained model. In the second part of the talk, we formulate this fine-tuning as a stochastic control problem, establishing its well-definedness through the Dynamic Programming Principle and proving convergence for an iterative Bellman scheme.z
This talk is based on joint works with Yinbin Han (NYU) and Meisam Razaviyayn (USC).
