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Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo in the nonconvex stochastic gradient case

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arxiv 2310.18774 v3 pith:3O7NFCBF submitted 2023-10-28 math.PR stat.COstat.ML

Martin Chak , Pierre Monmarché This is my paper · ORCID
classification math.PRstat.COstat.ML
keywords carlocontractioncouplingdistancegeneralizedhamiltonianmontenonconvex
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Contraction in Wasserstein 1-distance with explicit rates is established for generalized Hamiltonian Monte Carlo with stochastic gradients under possibly nonconvex conditions. The algorithms considered include splitting schemes of kinetic Langevin diffusion commonly used in molecular dynamics simulations. To accommodate the degenerate noise structure corresponding to inertia existing in the chain, a characteristically discrete-in-time coupling and contraction proof is devised. As consequence, quantitative Gaussian concentration bounds are provided for empirical averages. Convergence in Wasserstein 2-distance and total variation are also given, together with numerical bias estimates.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Theoretical guarantees for stochastic gradient sampling methods via Gaussian convolution inequalities

    stat.CO 2026-04 unverdicted novelty 8.0 of 10

    Stochastic-gradient UBU Langevin sampling has O(h) Wasserstein invariant-measure bias under moment and spectral assumptions on gradient noise, proved via new Gaussian convolution inequalities.

  2. Non-asymptotic entropic bounds for non-linear kinetic Langevin sampler with second-order splitting scheme

    math.PR 2024-12 conditional novelty 6.0 of 10

    A non-asymptotic relative entropy bound for unadjusted kinetic Langevin Monte Carlo with a second-order splitting scheme, under defective log-Sobolev and Lyapunov conditions more general than prior work.

  3. Conditions for uniform in time convergence: applications to averaging, numerical discretisations and mean-field systems

    math.PR 2024-12 conditional novelty 4.0 of 10

    A unified three-assumption theorem (contraction, local error, uniform control) converts finite-time bounds into global-in-time bounds for stochastic approximations.

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