Accelerated sampling using SamAdams variable timesteps and position-adaptive Langevin dynamics
For practitioners of Bayesian inference and molecular dynamics, this method offers faster sampling in stiff or anisotropic systems, though it is an incremental improvement over existing Langevin methods.
The paper introduces SA-PAL, a Langevin-based sampling method combining SamAdams adaptive timestepping and position-adaptive Langevin dynamics, achieving 1.5-3x mixing rate improvements on some potentials and over an order of magnitude efficiency gains on others.
We introduce an accelerated Langevin-based sampling method that is based on two complementary devices: \emph{SamAdams} adaptive timestepping, which automatically shrinks the effective integration step in stiff regions of phase space using a relaxed stiffness monitor, and \emph{position-adaptive Langevin} (PAL) dynamics, which concentrates friction along the local force direction while preserving the canonical distribution as the exact invariant measure. The resulting combined scheme (SA-PAL) is implemented in a palindromic integrator which requires only one force evaluation per iteration through suitable organisation of the integration steps and by exploiting the rank-one-plus-scalar structure of the PAL friction tensor. We test the method on various model problems: the Rosenbrock function, a thin entropic channel, the Mueller-Brown potential, and a Bayesian parameterisation problem with a sparsity-inducing shrinkage prior. On the Rosenbrock and Mueller-Brown potentials mixing rates are improved by 1.5-3 times compared to fixed stepsize integration. Efficiency gains of more than an order of magnitude are documented in the other examples.