Samuel Livingstone (UCL)

Robust gradient-based sampling algorithms using skew-symmetric numerical schemes

Abstract: State-of-the-art sampling algorithms for smooth continuous distributions are typically gradient-based, e.g. Langevin or Hamiltonian Monte Carlo. It is known, however, that particular features of the distribution to be sampled can cause them to be unstable/work poorly. The algorithms are typically based on a numerical simulation of some stochastic process (e.g. the overdamped Langevin diffusion), and the instability comes from the choice of numerical scheme. I will introduce a new explicit numerical scheme for diffusions, which has skew-symmetric increments, and can be used to design simple and fast sampling algorithms that are provably more robust. I will show that the resulting ‘unadjusted Barker algorithm’, so called because of its connection to the Barker Metropolis—Hastings algorithm of Livingstone & Zanella (JRSS B, 2022) is well-defined and converges at a geometric rate to an equilibrium which is close to the distribution of interest in many cases when the unadjusted Langevin algorithm is transient.