Stochastic Average Gradient Descent (SAGD)
We develop and analyze a new algorithm for empirical risk minimization, which is the key paradigm for training supervised machine learning models. Our method—SAGD—is based on a probabilistic interpolation of SAGA and gradient descent (GD). In particular, in each iteration we take a gradient step with probability $q$ and a SAGA step with probability $1-q$. We show that, surprisingly, the total expected complexity of the method (which is obtained by multiplying the number of iterations by the expected number of gradients computed in each iteration) is minimized for a non-trivial probability $q$. For example, for a well conditioned problem the choice $q=1/(n-1)^2$, where $n$ is the number of data samples, gives a method with an overall complexity which is better than both the complexity of GD and SAGA. We further generalize the results to a probabilistic interpolation of SAGA and minibatch SAGA, which allows us to compute both the optimal probability and the optimal minibatch size. While the theoretical improvement may not be large, the practical improvement is robustly present across all synthetic and real data we tested for, and can be substantial. Our theoretical results suggest that for this optimal minibatch size our method achieves linear speedup in minibatch size, which is of key practical importance as minibatch implementations are used to train machine learning models in practice. This is the first time linear speedup in minibatch size is obtained for a variance reduced gradient-type method by directly solving the primal empirical risk minimization problem. …

Bayesian Generative Active Deep Learning
Deep learning models have demonstrated outstanding performance in several problems, but their training process tends to require immense amounts of computational and human resources for training and labeling, constraining the types of problems that can be tackled. Therefore, the design of effective training methods that require small labeled training sets is an important research direction that will allow a more effective use of resources. Among current approaches designed to address this issue, two are particularly interesting: data augmentation and active learning. Data augmentation achieves this goal by artificially generating new training points, while active learning relies on the selection of the ‘most informative’ subset of unlabeled training samples to be labelled by an oracle. Although successful in practice, data augmentation can waste computational resources because it indiscriminately generates samples that are not guaranteed to be informative, and active learning selects a small subset of informative samples (from a large un-annotated set) that may be insufficient for the training process. In this paper, we propose a Bayesian generative active deep learning approach that combines active learning with data augmentation — we provide theoretical and empirical evidence (MNIST, CIFAR-${10,100}$, and SVHN) that our approach has more efficient training and better classification results than data augmentation and active learning. …

GeneRAting TIme Series (GRATIS)
The explosion of time series data in recent years has brought a flourish of new time series analysis methods, for forecasting, clustering, classification and other tasks. The evaluation of these new methods requires a diverse collection of time series benchmarking data to enable reliable comparisons against alternative approaches. We propose GeneRAting TIme Series with diverse and controllable characteristics, named GRATIS, with the use of mixture autoregressive (MAR) models. We generate sets of time series using MAR models and investigate the diversity and coverage of the generated time series in a time series feature space. By tuning the parameters of the MAR models, GRATIS is also able to efficiently generate new time series with controllable features. In general, as a costless surrogate to the traditional data collection approach, GRATIS can be used as an evaluation tool for tasks such as time series forecasting and classification. We illustrate the usefulness of our time series generation process through a time series forecasting application. …

Quality Diversity
While evolutionary computation and evolutionary robotics take inspiration from nature, they have long focused mainly on problems of performance optimization. Yet evolution in nature can be interpreted as more nuanced than a process of simple optimization. In particular, natural evolution is a divergent search that optimizes locally within each niche as it simultaneously diversifies. This tendency to discover both quality and diversity at the same time differs from many of the conventional algorithms of machine learning, and also thereby suggests a different foundation for inferring the approach of greatest potential for evolutionary algorithms. In fact, several recent evolutionary algorithms called quality diversity (QD) algorithms(e.g. novelty search with local competition and MAP-Elites) have drawn inspiration from this more nuanced view, aiming to fill a space of possibilities with the best possible example of each type of achievable behavior. The result is a new class of algorithms that return an archive of diverse, high-quality behaviors in a single run. The aim in this paper is to study the application of QD algorithms in challenging environments (in particular complex mazes) to establish their best practices for ambitious domains in the future. In addition to providing insight into cases when QD succeeds and fails, a new approach is investigated that hybridizes multiple views of behaviors (called behavior characterizations) in the same run, which succeeds in overcoming some of the challenges associated with searching for QD with respect to a behavior characterization that is not necessarily sufficient for generating both quality and diversity at the same time. …