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

• URL: http://arxiv.org/abs/2310.18774v3
• Date: Thu, 12 Sep 2024 20:23:48 GMT
• Title: Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo in the nonconvex stochastic gradient case
• Authors: Martin Chak, Pierre Monmarché,
• Abstract summary: Contraction in Wasserstein 1-distance with explicit rates is established for generalized Hamiltonian Monte Carlo with gradients under possibly non diffusion conditions. The algorithms considered include kinetic splitting schemes of Langevin, commonly used in molecular dynamics simulations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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