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Poster

Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices

Santosh Vempala · Andre Wibisono

East Exhibition Hall B, C #181

Keywords: [ Information Theory ] [ Theory ] [ Algorithms ] [ Stochastic Methods ]


Abstract: We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability distribution ν=ef on \Rn. We prove a convergence guarantee in Kullback-Leibler (KL) divergence assuming ν satisfies log-Sobolev inequality and f has bounded Hessian. Notably, we do not assume convexity or bounds on higher derivatives. We also prove convergence guarantees in R\'enyi divergence of order q>1 assuming the limit of ULA satisfies either log-Sobolev or Poincar\'e inequality.

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