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# Iterate Averaging as Regularization for Stochastic Gradient Descent

*Proceedings of the 31st Conference On Learning Theory*, PMLR 75:3222-3242, 2018.

#### Abstract

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.