Unadjusted Langevin algorithm for sampling a mixture of weakly smooth potentials
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Abstract (arXiv)
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, it seems to be a considerable restriction when the potentials are often required to be smooth (gradient Lipschitz). This paper studies the problem of sampling through Euler discretization, where the potential function is assumed to be a mixture of weakly smooth distributions and satisfies weakly dissipative. We establish the convergence in Kullback-Leibler (KL) divergence with the number of iterations to reach ε-neighborhood of a target distribution in only polynomial dependence on the dimension. We relax the degenerated convex at infinity conditions of citeterdogdu2020convergence and prove convergence guarantees under Poincar'e inequality or non-strongly convex outside the ball. In addition, we also provide convergence in Lβ-Wasserstein metric for the smoothing potential.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 24 of its 57 references that are in the map. First posted on arXiv 17 Dec 2021.
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24 of 57 references.
References · 24
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12 more
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Citing papers per year: 2022: 1; 2023: 2.
3 papers.