  We consider random walks on the torus arising from the action of the group of
affine transformations. We give a quantitative equidistribution result for this
random walk under the assumption that the Zariski closure of the group
generated by the linear part acts strongly irreducibly on $\mathbb{R}^d$ and is
either Zariski connected or contains a proximal element. Specifically, we give
quantitative estimates (depending only on the linear part of the random walk)
for how fast the random walk equidistributes unless the initial point and the
translation part of the affine transformations can be perturbed so that the
random walk is trapped in a finite orbit of small cardinality. In particular,
we prove that the random walk equidistributes in law to the Haar measure if and
only if the random walk is not trapped in a finite orbit.
