Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics
This work addresses the challenge of slow convergence in Langevin samplers for Bayesian inference, offering an incremental improvement by combining irreversible perturbations with Riemannian manifold Langevin dynamics.
The authors tackled the problem of accelerating convergence in Langevin dynamics for Bayesian computation by introducing a geometry-informed irreversible perturbation, which improved estimation performance over non-geometric perturbations in numerical examples.
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.