A Robust Adaptive Stochastic Gradient Method for Deep Learning

Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of learning rate and the amount of the noise in stochastic estimates of the gradients. In this paper, we propose an adaptive learning rate algorithm, which utilizes stochastic curvature information of the loss function for automatically tuning the learning rates. The information about the element-wise curvature of the loss function is estimated from the local statistics of the stochastic first order gradients. We further propose a new variance reduction technique to speed up the convergence. In our experiments with deep neural networks, we obtained better performance compared to the popular stochastic gradient algorithms.Comment: IJCNN 2017 Accepted Paper, An extension of our paper, "ADASECANT: Robust Adaptive Secant Method for Stochastic Gradient

ADASECANT: Robust Adaptive Secant Method for Stochastic Gradient

Abstract Stochastic gradient algorithms have been the main focus of large-scale learning problems and led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the noise in stochastic estimates of the gradients. In this paper, we propose a new adaptive learning rate algorithm, which utilizes curvature information for automatically tuning the learning rates. The information about the element-wise curvature of the loss function is estimated from the local statistics of the stochastic first order gradients. We further propose a new variance reduction technique to speed up the convergence. In our experiments with deep neural networks, we obtained better performance compared to the popular stochastic gradient algorithms

Noisy Activation Functions

Abstract Common nonlinear activation functions used in neural networks can cause training difficulties due to the saturation behavior of the activation function, which may hide dependencies that are not visible to vanilla-SGD (using first order gradients only). Gating mechanisms that use softly saturating activation functions to emulate the discrete switching of digital logic circuits are good examples of this. We propose to exploit the injection of appropriate noise so that the gradients may flow easily, even if the noiseless application of the activation function would yield zero gradients. Large noise will dominate the noise-free gradient and allow stochastic gradient descent to explore more. By adding noise only to the problematic parts of the activation function, we allow the optimization procedure to explore the boundary between the degenerate (saturating) and the well-behaved parts of the activation function. We also establish connections to simulated annealing, when the amount of noise is annealed down, making it easier to optimize hard objective functions. We find experimentally that replacing such saturating activation functions by noisy variants helps optimization in many contexts, yielding state-of-the-art or competitive results on different datasets and task, especially when training seems to be the most difficult, e.g., when curriculum learning is necessary to obtain good results