Sharp Convergence Rates for Langevin Dynamics in the Nonconvex Setting

4 May 2018Xiang ChengNiladri S. ChatterjiYasin Abbasi-YadkoriPeter L. BartlettMichael I. Jordan

We study the problem of sampling from a distribution where the negative logarithm of the target density is $L$-smooth everywhere and $m$-strongly convex outside a ball of radius $R$, but potentially non-convex inside this ball. We study both overdamped and underdamped Langevin MCMC and prove upper bounds on the time required to obtain a sample from a distribution that is within $\epsilon$ of the target distribution in $1$-Wasserstein distance... (read more)

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