  We propose and analyze a variant of the classic Polyak-Ruppert averaging
scheme, broadly used in stochastic gradient methods. Rather than a uniform
average of the iterates, we consider a weighted average, with weights decaying
in a geometric fashion. In the context of linear least squares regression, we
show that this averaging scheme has a the same regularizing effect, and indeed
is asymptotically equivalent, to ridge regression. In particular, we derive
finite-sample bounds for the proposed approach that match the best known
results for regularized stochastic gradient methods.
