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Convergence in total variation for the kinetic Langevin algorithm

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arxiv 2407.09301 v3 pith:FIMJB74Y submitted 2024-07-12 math.PR cs.CCmath.AP

Joseph Lehec This is my paper · ORCID
classification math.PRcs.CCmath.AP
keywords algorithmkineticdimensionlangevintotalvariationasymptoticbound
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abstract

We prove non asymptotic total variation estimates for the kinetic Langevin algorithm in high dimension when the target measure satisfies a Poincar\'e inequality and has gradient Lipschitz potential. The main point is that the estimate improves significantly upon the corresponding bound for the non kinetic version of the algorithm, due to Dalalyan. In particular the dimension dependence drops from $O(n)$ to $O(\sqrt n)$.

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Cited by 2 Pith papers

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  1. Space-time divergence lemmas and optimal non-reversible lifts of diffusions on Riemannian manifolds with boundary

    math.PR 2024-12 conditional novelty 7.0 of 10

    For diffusions on Riemannian manifolds with boundary, the paper establishes a quantitative space-time divergence lemma and proves that randomized Hamiltonian Monte Carlo and Langevin dynamics achieve the optimal squar...

  2. Hypocoercivity meets lifts

    math.PR 2024-12 conditional novelty 6.0 of 10

    A unified hypocoercivity framework shows adaptive Langevin dynamics is a near-optimal lift, and proves the generalized Langevin equation cannot beat square-root speedup.

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