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Learning Rate Annealing Can Provably Help Generalization, Even for Convex Problems

2020-05-15 · Preetum Nakkiran

Learning rate schedule can significantly affect generalization performance in modern neural networks, but the reasons for this are not yet understood. Li-Wei-Ma (2019) recently proved this behavior can exist in a simplified non-convex neural-network setting. In this note, we show that this phenomenon can exist even for convex learning problems -- in particular, linear regression in 2 dimensions. We give a toy convex problem where learning rate annealing (large initial learning rate, followed by small learning rate) can lead gradient descent to minima with provably better generalization than using a small learning rate throughout. In our case, this occurs due to a combination of the mismatch between the test and train loss landscapes, and early-stopping.

📄 PDF Abstract BibTeX arXiv:2005.07360

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regression

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Linear Regression Linear Regression is a method for modelling a relationship between a dependent variable and independent variables. These models can be fit with numerous approaches. The most…

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