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Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices

2020-02-21 | |  34 |   29 |   0

Abstract

We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability distribution 图片.png We prove a convergence guarantee in KullbackLeibler (KL) divergence assuming 图片.png 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 Rényi divergence of order q > 1 assuming the limit of ULA satisfies either log-Sobolev or Poincaré inequality.

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