Talk Abstract: Speeding up optimization methods used in machine learning applications is an issue of significant practical and theoretical interest. Most research has focused on optimization over Euclidean spaces. Since many machine learning tasks involve optimization over the space of probability measures, attention must be paid to speeding up optimization methods in this setting as well. We introduce a Hamiltonian flow approach analogous to moment-based approaches in Euclidean space. We demonstrate that algorithms based on this approach can achieve high order convergence rates.

Bio: Shi Chen earned his Ph.D. in Mathematics from the University of Wisconsin-Madison in 2024 under the supervision of Qin Li. He is currently a C.L.E. Moore Instructor of Mathematics at Massachusetts Institute of Technology, mentored by Philippe Rigollet. His research interests lie broadly in applied mathematics, with a current focus on machine learning, gradient flows and optimization, inverse problems, and their applications to physics and data science.