# Noise and Fluctuation of Finite Learning Rate Stochastic Gradient Descent

@inproceedings{Liu2020NoiseAF, title={Noise and Fluctuation of Finite Learning Rate Stochastic Gradient Descent}, author={Kangqiao Liu and Liu Ziyin and Masakuni Ueda}, booktitle={International Conference on Machine Learning}, year={2020} }

In the vanishing learning rate regime, stochastic gradient descent (SGD) is now relatively well understood. In this work, we propose to study the basic properties of SGD and its variants in the non-vanishing learning rate regime. The focus is on deriving exactly solvable results and discussing their implications. The main contributions of this work are to derive the stationary distribution for discrete-time SGD in a quadratic loss function with and without momentum; in particular, one…

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