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

• URL: http://arxiv.org/abs/2302.08783v2
• Date: Sun, 11 Jun 2023 15:59:35 GMT
• Title: SGD with AdaGrad Stepsizes: Full Adaptivity with High Probability to Unknown Parameters, Unbounded Gradients and Affine Variance
• Authors: Amit Attia and Tomer Koren
• Abstract summary: We show that AdaGrad stepsizes a popular adaptive (self-tuning) method for first-order optimization. In both the low-noise and high-regimes we find sharp rates of convergence in both the low-noise and high-regimes.
• Score: 33.593203156666746
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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