Iterate Averaging as Regularization for Stochastic Gradient Descent

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 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.