• Corpus ID: 182952528

# Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices

@inproceedings{Vempala2019RapidCO,
title={Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices},
author={Santosh S. Vempala and Andre Wibisono},
booktitle={Neural Information Processing Systems},
year={2019}
}
• Published in
Neural Information Processing…
20 March 2019
• Mathematics, Computer Science
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. Notably, we do not assume convexity or bounds on higher derivatives. We also prove convergence guarantees in Renyi divergence of order $q > 1$ assuming the limit of ULA satisfies either the log-Sobolev or Poincare…
104 Citations

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