  We introduce a novel geometry-informed irreversible perturbation that
accelerates convergence of the Langevin algorithm for Bayesian computation. It
is well documented that there exist perturbations to the Langevin dynamics that
preserve its invariant measure while accelerating its convergence. Irreversible
perturbations and reversible perturbations (such as Riemannian manifold
Langevin dynamics (RMLD)) have separately been shown to improve the performance
of Langevin samplers. We consider these two perturbations simultaneously by
presenting a novel form of irreversible perturbation for RMLD that is informed
by the underlying geometry. Through numerical examples, we show that this new
irreversible perturbation can improve estimation performance over irreversible
perturbations that do not take the geometry into account. Moreover we
demonstrate that irreversible perturbations generally can be implemented in
conjunction with the stochastic gradient version of the Langevin algorithm.
Lastly, while continuous-time irreversible perturbations cannot impair the
performance of a Langevin estimator, the situation can sometimes be more
complicated when discretization is considered. To this end, we describe a
discrete-time example in which irreversibility increases both the bias and
variance of the resulting estimator.
