Speaker: Qin Li, University of Wisconsin-Madison

Title: Accelerating optimization over probability measure space

Abstract: In the past decade, there has been a significant shift in the types of mathematical objects under investigation, moving from vectors and matrices in Euclidean space to functions residing in Hilbert or Banach spaces, and ultimately extending to probability measures within the probability measure space. Many questions that were originally posed in the context of linear function spaces are now being revisited in the realm of probability measures. One such question is to the efficiently find a probability measure that minimizes a given objective functional.

In Euclidean space, we devised optimization techniques like gradient descent and introduced momentum-based methods to accelerate convergence. Now, the question arises: Can we employ analogous strategies to expedite convergence within the probability measure space?

We provide an affirmative answer to this question, and show that momentum based acceleration for Euclidean optimization now translates to Hamiltonian flow, and it can achieve arbitrary high-order of convergence. This opens the door of developing methods beyond standard gradient flow.

Bio: Qin Li is an associate professor at UW-Madison mathematics department. She is affiliated with The Wisconsin Institutes for Discovery, and is a senior P.I. at Institute for Foundations of Data Science. The core of her research focuses on numerical analysis and scientific computing.

Host: Kui Ren

This talk will be offered in a hybrid format. If you wish to participate remotely, please send an email to [email protected].