No More Pesky Learning Rates

The performance of stochastic gradient descent (SGD) depends critically on how learning rates are tuned and decreased over time. We propose a method to automatically adjust multiple learning rates so as to minimize the expected error at any one time. The method relies on local gradient variations across samples. In our approach, learning rates can increase as well as decrease, making it suitable for non-stationary problems. Using a number of convex and non-convex learning tasks, we show that the resulting algorithm matches the performance of SGD or other adaptive approaches with their best settings obtained through systematic search, and effectively removes the need for learning rate tuning

Large space structures testing

There is considerable interest in the development of testing concepts and facilities that accurately simulate the pathologies believed to exist in future spacecraft. Both the Government and Industry have participated in the development of facilites over the past several years. The progress and problems associated with the development of the Large Space Structure Test Facility at the Marshall Flight Center are presented. This facility was in existence for a number of years and its utilization has run the gamut from total in-house involvement, third party contractor testing, to the mutual participation of other Government Agencies in joint endeavors

Adaptive learning rates and parallelization for stochastic, sparse, non-smooth gradients

Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on stationary problems, and permitting learning rates to grow appropriately in non-stationary tasks. Here, we extend the idea in three directions, addressing proper minibatch parallelization, including reweighted updates for sparse or orthogonal gradients, improving robustness on non-smooth loss functions, in the process replacing the diagonal Hessian estimation procedure that may not always be available by a robust finite-difference approximation. The final algorithm integrates all these components, has linear complexity and is hyper-parameter free.Comment: Published at the First International Conference on Learning Representations (ICLR-2013). Public reviews are available at http://openreview.net/document/c14f2204-fd66-4d91-bed4-153523694041#c14f2204-fd66-4d91-bed4-15352369404

Mimicking Word Embeddings using Subword RNNs

Word embeddings improve generalization over lexical features by placing each word in a lower-dimensional space, using distributional information obtained from unlabeled data. However, the effectiveness of word embeddings for downstream NLP tasks is limited by out-of-vocabulary (OOV) words, for which embeddings do not exist. In this paper, we present MIMICK, an approach to generating OOV word embeddings compositionally, by learning a function from spellings to distributional embeddings. Unlike prior work, MIMICK does not require re-training on the original word embedding corpus; instead, learning is performed at the type level. Intrinsic and extrinsic evaluations demonstrate the power of this simple approach. On 23 languages, MIMICK improves performance over a word-based baseline for tagging part-of-speech and morphosyntactic attributes. It is competitive with (and complementary to) a supervised character-based model in low-resource settings.Comment: EMNLP 201

ADADELTA: An Adaptive Learning Rate Method

We present a novel per-dimension learning rate method for gradient descent called ADADELTA. The method dynamically adapts over time using only first order information and has minimal computational overhead beyond vanilla stochastic gradient descent. The method requires no manual tuning of a learning rate and appears robust to noisy gradient information, different model architecture choices, various data modalities and selection of hyperparameters. We show promising results compared to other methods on the MNIST digit classification task using a single machine and on a large scale voice dataset in a distributed cluster environment.Comment: 6 page

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