MALA with annealed proposals: a generalization of locally and globally balanced proposal distributions

We introduce a generalized version of the Metropolis-adjusted Langevin algorithm (MALA). The informed proposal distribution of this new sampler features two tuning parameters: the usual step size parameter $$\sigma ^2$$ and an interpolation parameter $$\gamma $$ that may be adjusted to accommodate the dimension of the target distribution. We theoretically study the efficiency of the sampler by making use of the local- and global-balance concepts introduced in Zanella (JASA 115:852–865, 2020) and provide efficient tuning guidelines that work well with a variety of target distributions. Although the usual MALA ( $$\gamma =1$$ ) is shown to be optimal for infinite-dimensional targets, in practice, the generalized MALA ( $$1