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 ]
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Abstract
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Abstract:
We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability distribution ν=e−f 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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