SUPER-ADAM: Faster and Universal Framework of Adaptive Gradients

• URL: http://arxiv.org/abs/2106.08208v1
• Date: Tue, 15 Jun 2021 15:16:28 GMT
• Title: SUPER-ADAM: Faster and Universal Framework of Adaptive Gradients
• Authors: Feihu Huang, Junyi Li and Heng Huang
• Abstract summary: It is desired to design a universal framework for adaptive algorithms to solve general problems. In particular, our novel framework provides adaptive methods under non convergence support for setting.
• Score: 99.13839450032408
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Adaptive gradient methods have shown excellent performance for solving many machine learning problems. Although multiple adaptive methods were recently studied, they mainly focus on either empirical or theoretical aspects and also only work for specific problems by using specific adaptive learning rates. It is desired to design a universal framework for practical algorithms of adaptive gradients with theoretical guarantee to solve general problems. To fill this gap, we propose a faster and universal framework of adaptive gradients (i.e., SUPER-ADAM) by introducing a universal adaptive matrix that includes most existing adaptive gradient forms. Moreover, our framework can flexibly integrates the momentum and variance reduced techniques. In particular, our novel framework provides the convergence analysis support for adaptive gradient methods under the nonconvex setting. In theoretical analysis, we prove that our new algorithm can achieve the best known complexity of $\tilde{O}(\epsilon^{-3})$ for finding an $\epsilon$-stationary point of nonconvex optimization, which matches the lower bound for stochastic smooth nonconvex optimization. In numerical experiments, we employ various deep learning tasks to validate that our algorithm consistently outperforms the existing adaptive algorithms.

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