On Acceleration with Noise-Corrupted Gradients

Jelena Diakonikolas; Lorenzo Orecchia; Michael B. Cohen

On Acceleration with Noise-Corrupted Gradients

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arxiv 1805.12591 v3 pith:QLXKQU6Y submitted 2018-05-31 math.OC cs.DS

Michael B. Cohen , Jelena Diakonikolas , Lorenzo Orecchia This is my paper

classification math.OCcs.DS

keywords acceleratedgradientaccelerationagdpalgorithmsmethodnoisenoise-corrupted

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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 AGDP 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 AGDP 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.

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