  Numerical stochastic perturbation theory is a powerful tool for estimating
high-order perturbative expansions in lattice field theory. The standard
algorithms based on the Langevin equation, however, suffer from several
limitations which in practice restrict the potential of this technique. In this
work we investigate some alternative methods which could in principle improve
on the standard approach. In particular, we present a study of the recently
proposed Instantaneous Stochastic Perturbation Theory, as well as a formulation
of numerical stochastic perturbation theory based on Generalized Hybrid
Molecular Dynamics algorithms. The viability of these methods is investigated
in $\varphi^4$ theory.
