[2310.18774] Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo within the nonconvex stochastic gradient case

View a PDF of the paper titled Reflection coupling for unadjusted generalized Hamiltonian Monte Carlo within the nonconvex stochastic gradient case, by Martin Chak and Pierre Monmarch’e

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Summary:Contraction in Wasserstein 1-distance with express charges is established for generalized Hamiltonian Monte Carlo with stochastic gradients below presumably nonconvex circumstances. The algorithms thought-about embody splitting schemes of kinetic Langevin diffusion generally utilized in molecular dynamics simulations. To accommodate the degenerate noise construction similar to inertia present within the chain, a characteristically discrete-in-time coupling and contraction proof is devised. As consequence, quantitative Gaussian focus bounds are offered for empirical averages. Convergence in Wasserstein 2-distance and complete variation are additionally given, along with numerical bias estimates.