Contraction and Convergence Rates for Discretized Kinetic Langevin Dynamics

Research output: Working paperPreprint

Abstract / Description of output

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.
Original languageEnglish
Publication statusPublished - 21 Feb 2023

Keywords / Materials (for Non-textual outputs)

  • math.NA
  • cs.NA
  • stat.CO


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