  Ever since the concepts of dynamic programming were introduced, one of the
most difficult challenges has been to adequately address high-dimensional
control problems. With growing dimensionality, the utilisation of Deep Neural
Networks promises to circumvent the issue of an otherwise exponentially
increasing complexity. The paper specifically investigates the sampling issues
the Deep Galerkin Method is subjected to. It proposes a drift relaxation-based
sampling approach to alleviate the symptoms of high-variance policy
approximations. This is validated on mean-field control problems; namely, the
variations of the opinion dynamics presented by the Sznajd and the
Hegselmann-Krause model. The resulting policies induce a significant cost
reduction over manually optimised control functions and show improvements on
the Linear-Quadratic Regulator problem over the Deep FBSDE approach.
