Rapid Convergence of the Unadjusted Langevin Algorithm: Log-Sobolev Suffices

03/20/2019

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by   Santosh S. Vempala, et al.

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We prove a convergence guarantee on the unadjusted Langevin algorithm for sampling assuming only that the target distribution e^-f satisfies a log-Sobolev inequality and the Hessian of f is bounded. In particular, f is not required to be convex or have higher derivatives bounded.