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- W4321594140 abstract "We provide a framework to prove convergence rates for discretizations of kinetic Langevin dynamics for $M$-$nabla$Lipschitz $m$-log-concave densities. Our approach provides convergence rates of $mathcal{O}(m/M)$, with explicit stepsize restrictions, which are of the same order as the stability threshold for Gaussian targets and are valid for a large interval of the friction parameter. We apply this methodology to various integration methods which are popular in the molecular dynamics and machine learning communities. Finally we introduce the property ``$gamma$-limit convergent (GLC) to characterise underdamped Langevin schemes that converge to overdamped dynamics in the high friction limit and which have stepsize restrictions that are independent of the friction parameter; we show that this property is not generic by exhibiting methods from both the class and its complement." @default.
- W4321594140 created "2023-02-24" @default.
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- W4321594140 date "2023-02-21" @default.
- W4321594140 modified "2023-09-28" @default.
- W4321594140 title "Contraction and Convergence Rates for Discretized Kinetic Langevin Dynamics" @default.
- W4321594140 doi "https://doi.org/10.48550/arxiv.2302.10684" @default.
- W4321594140 hasPublicationYear "2023" @default.
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