Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices
NeurIPS, pp. 8092-8104, 2019.
We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability distribution ⌫ = e f on R n. We prove a convergence guarantee in Kullback-Leibler (KL) divergence assuming ⌫ satisfies log-Sobolev inequality and f has bounded Hessian. Notably, we do not assume convexity or bounds on higher derivatives. We also prove converg...More
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