The Department of Mathematical Sciences will host Dr. Murat A. Erdogdu from the University of Toronto, for its math seminar series. Dr. Erdogdu will present, “Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothness.” This free seminar will take place on Friday, April 22, at 11 a.m. in BSB 117. A virtual option is also available: https://tinyurl.com/9nrnveur.
Abstract
We study sampling from a target distribution $e^{ f}$ using the Langevin Monte Carlo (LMC) algorithm. For any potential function $f$ whose tails behave like $|x|^ alpha$ for $ alpha in [1,2]$, and has beta$ H \\”older continuous gradient, we derive the sufficient number of steps to reach the $ eps$ neighbor hood of a $d$ dimensional target distribution as a function of $ alpha$ and $ beta$. Our result is the first convergence guarantee for LMC under a functional inequality interpolating between the Poincar \\’e and log Sobolev settings (also covering the edge c ases).