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Modern machine learning paradigms, such as deep learning, occur in or closeto the interpolation regime, wherein the number of model parameters is muchlarger than the number of data samples. In this work, we propose a regularitycondition within the interpolation regime which endows the stochastic gradientmethod with the same worst-case iteration complexity as the deterministicgradient method, while using only a single sampled gradient (or a minibatch) ineach iteration. In contrast, all existing guarantees require the stochasticgradient method to take small steps, thereby resulting in a much slower linearrate of convergence. Finally, we demonstrate that our condition holds whentraining sufficiently wide feedforward neural networks with a linear outputlayer.

Aiming towards the minimizers: fast convergence of SGD for overparametrized problems