On acceleration with noise-corrupted gradients
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Citation (published version)Lorenzo Orecchia, Jelena Diakonikolas, Michael Cohen. 2018. "On Acceleration with Noise-Corrupted Gradients." Proceedings of the 35th International Conference on Machine Learning (ICML 2018)
Accelerated algorithms have broad applications in large-scale optimization, due to their generality and fast convergence. However, their stability in the practical setting of noise-corrupted gradient oracles is not well-understood. This paper provides two main technical contributions: (i) a new accelerated method AGD+ that generalizes Nesterov’s AGD and improves on the recent method AXGD (Diakonikolas & Orecchia, 2018), and (ii) a theoretical study of accelerated algorithms under noisy and inexact gradient oracles, which is supported by numerical experiments. This study leverages the simplicity of AGD+ and its analysis to clarify the interaction between noise and acceleration and to suggest modifications to the algorithm that reduce the mean and variance of the error incurred due to the gradient noise.
RightsCopyright 2018 by the author(s).