# The Power of Adaptivity in SGD: Self-Tuning Step Sizes with Unbounded Gradients and Affine Variance

@inproceedings{Faw2022ThePO, title={The Power of Adaptivity in SGD: Self-Tuning Step Sizes with Unbounded Gradients and Affine Variance}, author={Matthew Faw and Isidoros Tziotis and Constantine Caramanis and Aryan Mokhtari and Sanjay Shakkottai and Rachel A. Ward}, booktitle={Annual Conference Computational Learning Theory}, year={2022} }

We study convergence rates of AdaGrad-Norm as an exemplar of adaptive stochastic gradient methods (SGD), where the step sizes change based on observed stochastic gradients, for minimizing non-convex, smooth objectives. Despite their popularity, the analysis of adaptive SGD lags behind that of non adaptive methods in this setting. Speciﬁcally, all prior works rely on some subset of the following assumptions: (i) uniformly-bounded gradient norms, (ii) uniformly-bounded stochastic gradient…

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