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Register a new userA New Adaptive Gradient Method with Gradient Decomposition
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Added by
Zhou Shao
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Adaptive gradient methods, especially Adam-type methods (such as Adam, AMSGrad, and AdaBound), have been proposed to speed up the training process with an element-wise scaling term on learning rates. However, they often generalize poorly compared with stochastic gradient descent (SGD) and its accelerated schemes such as SGD with momentum (SGDM). In this paper, we propose a new adaptive method called DecGD, which simultaneously achieves good generalization like SGDM and obtain rapid convergence like Adam-type methods. In particular, DecGD decomposes the current gradient into the product of two terms including a surrogate gradient and a loss based vector. Our method adjusts the learning rates adaptively according to the current loss based vector instead of the squared gradients used in Adam-type methods. The intuition for adaptive learning rates of DecGD is that a good optimizer, in general cases, needs to decrease the learning rates as the loss decreases, which is similar to the learning rates decay scheduling technique. Therefore, DecGD gets a rapid convergence in the early phases of training and controls the effective learning rates according to the loss based vectors which help lead to a better generalization. Convergence analysis is discussed in both convex and non-convex situations. Finally, empirical results on widely-used tasks and models demonstrate that DecGD shows better generalization performance than SGDM and rapid convergence like Adam-type methods.
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Several variants of stochastic gradient descent (SGD) have been proposed to improve the learning effectiveness and efficiency when training deep neural networks, among which some recent influential attempts would like to adaptively control the parameter-wise learning rate (e.g., Adam and RMSProp). Although they show a large improvement in convergence speed, most adaptive learning rate methods suffer from compromised generalization compared with SGD. In this paper, we proposed an Adaptive Gradient Method with Resilience and Momentum (AdaRem), motivated by the observation that the oscillations of network parameters slow the training, and give a theoretical proof of convergence. For each parameter, AdaRem adjusts the parameter-wise learning rate according to whether the direction of one parameter changes in the past is aligned with the direction of the current gradient, and thus encourages long-term consistent parameter updating with much fewer oscillations. Comprehensive experiments have been conducted to verify the effectiveness of AdaRem when training various models on a large-scale image recognition dataset, e.g., ImageNet, which also demonstrate that our method outperforms previous adaptive learning rate-based algorithms in terms of the training speed and the test error, respectively.
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Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss functions and training nonconvex deep neural networks. The theory assumes that one can easily compute an unbiased gradient estimator, which is usually the case due to the sample average nature of empirical risk minimization. There exist, however, many scenarios (e.g., graphs) where an unbiased estimator may be as expensive to compute as the full gradient because training examples are interconnected. Recently, Chen et al. (2018) proposed using a consistent gradient estimator as an economic alternative. Encouraged by empirical success, we show, in a general setting, that consistent estimators result in the same convergence behavior as do unbiased ones. Our analysis covers strongly convex, convex, and nonconvex objectives. We verify the results with illustrative experiments on synthetic and real-world data. This work opens several new research directions, including the development of more efficient SGD updates with consistent estimators and the design of efficient training algorithms for large-scale graphs.
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