Metropolis Adjusted Langevin Trajectories: a robust alternative to Hamiltonian Monte Carlo

Understand

We introduce MALT: a new Metropolis adjusted sampler built upon the (kinetic) Langevin diffusion.

• Compared to Generalized Hamiltonian Monte Carlo (GHMC), the Metropolis correction is applied to whole Langevin trajectories, which prevents momentum flips, and allows for larger step-sizes.
• We argue that MALT yields a neater extension of HMC, preserving many desirable properties.
• We extend optimal scaling results of HMC to MALT for isotropic targets, and obtain the same scaling with respect to the dimension without additional assumptions.