  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.
