SGD with AdaGrad Stepsizes: Full Adaptivity with High Probability to Unknown Parameters, Unbounded Gradients and Affine Variance

Amit Attia, Tomer Koren
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:1147-1171, 2023.

Abstract

We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings: they either assume some knowledge of the problem parameters, impose strong global Lipschitz conditions, or fail to give bounds that hold with high probability. We provide a comprehensive analysis of this basic method without any of these limitations, in both the convex and non-convex (smooth) cases, that additionally supports a general “affine variance” noise model and provides sharp rates of convergence in both the low-noise and high-noise regimes.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-attia23a, title = {{SGD} with {A}da{G}rad Stepsizes: Full Adaptivity with High Probability to Unknown Parameters, Unbounded Gradients and Affine Variance}, author = {Attia, Amit and Koren, Tomer}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {1147--1171}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/attia23a/attia23a.pdf}, url = {https://proceedings.mlr.press/v202/attia23a.html}, abstract = {We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings: they either assume some knowledge of the problem parameters, impose strong global Lipschitz conditions, or fail to give bounds that hold with high probability. We provide a comprehensive analysis of this basic method without any of these limitations, in both the convex and non-convex (smooth) cases, that additionally supports a general “affine variance” noise model and provides sharp rates of convergence in both the low-noise and high-noise regimes.} }
Endnote
%0 Conference Paper %T SGD with AdaGrad Stepsizes: Full Adaptivity with High Probability to Unknown Parameters, Unbounded Gradients and Affine Variance %A Amit Attia %A Tomer Koren %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-attia23a %I PMLR %P 1147--1171 %U https://proceedings.mlr.press/v202/attia23a.html %V 202 %X We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings: they either assume some knowledge of the problem parameters, impose strong global Lipschitz conditions, or fail to give bounds that hold with high probability. We provide a comprehensive analysis of this basic method without any of these limitations, in both the convex and non-convex (smooth) cases, that additionally supports a general “affine variance” noise model and provides sharp rates of convergence in both the low-noise and high-noise regimes.
APA
Attia, A. & Koren, T.. (2023). SGD with AdaGrad Stepsizes: Full Adaptivity with High Probability to Unknown Parameters, Unbounded Gradients and Affine Variance. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:1147-1171 Available from https://proceedings.mlr.press/v202/attia23a.html.

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