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Convergence of Preconditioned Hamiltonian Monte Carlo on Hilbert Spaces

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 نشر من قبل Jakiw Pidstrigach
 تاريخ النشر 2020
  مجال البحث الهندسة المعلوماتية
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 تأليف Jakiw Pidstrigach




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In this article, we consider the preconditioned Hamiltonian Monte Carlo (pHMC) algorithm defined directly on an infinite-dimensional Hilbert space. In this context, and under a condition reminiscent of strong log-concavity of the target measure, we prove convergence bounds for adjusted pHMC in the standard 1-Wasserstein distance. The arguments rely on a synchronous coupling of two copies of pHMC, which is controlled by adapting elements from arXiv:1805.00452.



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