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Register a new userAn Adaptive Remote Stochastic Gradient Method for Training Neural Networks
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Yushu Chen
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We present the remote stochastic gradient (RSG) method, which computes the gradients at configurable remote observation points, in order to improve the convergence rate and suppress gradient noise at the same time for different curvatures. RSG is further combined with adaptive methods to construct ARSG for acceleration. The method is efficient in computation and memory, and is straightforward to implement. We analyze the convergence properties by modeling the training process as a dynamic system, which provides a guideline to select the configurable observation factor without grid search. ARSG yields $O(1/sqrt{T})$ convergence rate in non-convex settings, that can be further improved to $O(log(T)/T)$ in strongly convex settings. Numerical experiments demonstrate that ARSG achieves both faster convergence and better generalization, compared with popular adaptive methods, such as ADAM, NADAM, AMSGRAD, and RANGER for the tested problems. In particular, for training ResNet-50 on ImageNet, ARSG outperforms ADAM in convergence speed and meanwhile it surpasses SGD in generalization.
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Artificial neural networks (ANNs) are typically highly nonlinear systems which are finely tuned via the optimization of their associated, non-convex loss functions. Typically, the gradient of any such loss function fails to be dissipative making the use of widely-accepted (stochastic) gradient descent methods problematic. We offer a new learning algorithm based on an appropriately constructed variant of the popular stochastic gradient Langevin dynamics (SGLD), which is called tamed unadjusted stochastic Langevin algorithm (TUSLA). We also provide a nonasymptotic analysis of the new algorithms convergence properties in the context of non-convex learning problems with the use of ANNs. Thus, we provide finite-time guarantees for TUSLA to find approximate minimizers of both empirical and population risks. The roots of the TUSLA algorithm are based on the taming technology for diffusion processes with superlinear coefficients as developed in citet{tamed-euler, SabanisAoAP} and for MCMC algorithms in citet{tula}. Numerical experiments are presented which confirm the theoretical findings and illustrate the need for the use of the new algorithm in comparison to vanilla SGLD within the framework of ANNs.
Recurrent Neural Networks (RNNs) are powerful models that achieve exceptional performance on several pattern recognition problems. However, the training of RNNs is a computationally difficult task owing to the well-known vanishing/exploding gradient problem. Algorithms proposed for training RNNs either exploit no (or limited) curvature information and have cheap per-iteration complexity, or attempt to gain significant curvature information at the cost of increased per-iteration cost. The former set includes diagonally-scaled first-order methods such as ADAGRAD and ADAM, while the latter consists of second-order algorithms like Hessian-Free Newton and K-FAC. In this paper, we present adaQN, a stochastic quasi-Newton algorithm for training RNNs. Our approach retains a low per-iteration cost while allowing for non-diagonal scaling through a stochastic L-BFGS updating scheme. The method uses a novel L-BFGS scaling initialization scheme and is judicious in storing and retaining L-BFGS curvature pairs. We present numerical experiments on two language modeling tasks and show that adaQN is competitive with popular RNN training algorithms.
In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of interval sets. Interval-based reachability analysis is then performed for the hidden layer. With the reachability analysis results, a robust optimization training method is developed in the framework of robust least-square problems. Then, the developed robust least-square problem is relaxed to a semidefinite programming problem. It has been shown that the developed robust learning method can provide better robustness against perturbations at the price of loss of training accuracy to some extent. At last, the proposed method is evaluated on a robot arm model learning example.
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.
One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies this surprising phenomenon for two-layer fully connected ReLU activated neural networks. For an $m$ hidden node shallow neural network with ReLU activation and $n$ training data, we show as long as $m$ is large enough and no two inputs are parallel, randomly initialized gradient descent converges to a globally optimal solution at a linear convergence rate for the quadratic loss function. Our analysis relies on the following observation: over-parameterization and random initialization jointly restrict every weight vector to be close to its initialization for all iterations, which allows us to exploit a strong convexity-like property to show that gradient descent converges at a global linear rate to the global optimum. We believe these insights are also useful in analyzing deep models and other first order methods.
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