AdaLoss: A computationally-efficient and provably convergent adaptive gradient method

• URL: http://arxiv.org/abs/2109.08282v1
• Date: Fri, 17 Sep 2021 01:45:25 GMT
• Title: AdaLoss: A computationally-efficient and provably convergent adaptive gradient method
• Authors: Xiaoxia Wu and Yuege Xie and Simon Du and Rachel Ward
• Abstract summary: We propose a computationally-friendly learning schedule, "AnomidaLoss", which uses the information of the loss function to adjust rate numerically. We verify the scope of the numerical experiments by applications in LSTM models for text and control problems.
• Score: 7.856998585396422
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a computationally-friendly adaptive learning rate schedule, "AdaLoss", which directly uses the information of the loss function to adjust the stepsize in gradient descent methods. We prove that this schedule enjoys linear convergence in linear regression. Moreover, we provide a linear convergence guarantee over the non-convex regime, in the context of two-layer over-parameterized neural networks. If the width of the first-hidden layer in the two-layer networks is sufficiently large (polynomially), then AdaLoss converges robustly \emph{to the global minimum} in polynomial time. We numerically verify the theoretical results and extend the scope of the numerical experiments by considering applications in LSTM models for text clarification and policy gradients for control problems.

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