# Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices

Santosh S. VempalaAndre Wibisono

We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability distribution $\nu = e^{-f}$ on $\mathbb{R}^n$. We prove a convergence guarantee in Kullback-Leibler (KL) divergence assuming $\nu$ satisfies a log-Sobolev inequality and the Hessian of $f$ is bounded... (read more)

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