A recently proposed class of machine-learning interatomic potentials -Moment tensor potentials (MTPs) -is investigated in this work. MTPs are able to actively select configurations and parametrize the potential on-thefly. It is shown that MTPs accurately reproduce energies, forces and stresses calculated ab initio. As a more comprehensive test, MTPs are employed to calculate vacancy diffusion rates in Al, Mo and Si. We demonstrate that the results are in a good agreement with ab initio data for the materials considered.