Analysis of Langevin Monte Carlo from Poincare to Log-Sobolev

Sinho Chewi, Murat A Erdogdu, Mufan Bill Li, Ruoqi Shen, Shunshi Zhang

Abstract: Classically, the continuous-time Langevin diffusion converges exponentially fast to its stationary distribution $\pi$ under the sole assumption that $\pi$ satisfies a Poincaré inequality. Using thi...