  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. We
show that MALT improves both the robustness to tuning and the sampling
performance of HMC on anisotropic targets. We compare our approach with
Randomized HMC, recently praised for its robustness. We show that, in
continuous time, the Langevin diffusion achieves the fastest mixing rate for
strongly log-concave targets. We then assess the accuracies of MALT, GHMC, HMC
and RHMC when performing numerical integration on anisotropic targets, both on
toy models and real data experiments on a Bayesian logistic regression. We show
that MALT outperforms GHMC, standard HMC, and is competitive with RHMC.
