2023
ICML
ICML 2023
SGD with AdaGrad Stepsizes: Full Adaptivity with High Probability to Unknown Parameters, Unbounded Gradients and Affine Variance
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.
🌉
Interdisciplinary Bridge
— Machine Learning and Mathematics & Optimization
🧭
Keyword Pioneer
— adaptive stepsize
🐝
Cross-Pollinator
— Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Reinforcement Learning, Security & Privacy