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arXiv · 2112.06844

Optimal friction matrix for underdamped Langevin sampling

Martin Chak·Nikolas Kantas·Tony Lelièvre·Grigorios A. Pavliotis
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Abstract

A systematic procedure for optimising the friction coefficient in underdamped Langevin dynamics as a sampling tool is given by taking the gradient of the associated asymptotic variance with respect to friction. We give an expression for this gradient in terms of the solution to an appropriate Poisson equation and show that it can be approximated by short simulations of the associated first variation/tangent process under concavity assumptions on the log density. Our algorithm is applied to the estimation of posterior means in Bayesian inference problems and reduced variance is demonstrated when compared to the original underdamped and overdamped Langevin dynamics in both full and stochastic gradient cases.

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Martin Chak, Nikolas Kantas, Tony Lelièvre, Grigorios A. Pavliotis. 2021-11-30. Optimal friction matrix for underdamped Langevin sampling. https://doi.org/10.1051/m2an%2F2023083

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