The combinations of joint atomic actions, which quickly becomes explosion in the number of discrete actions can intractable when M increases. However, a simple fix be efficiently addressed by a policy with factorized is to represent the joint distribution over discrete actions as distribution across action dimensions. We factorized across dimensions, so that the joint policy is still show that the discrete policy achieves significant tractable. As prior works have applied such discretization performance gains with state-of-the-art on-policy method in practice (OpenAI, 2018; Jaśkowski et al., 2018), optimization algorithms (PPO, TRPO, ACKTR) we aim to carry out a systemic study of such straightforward especially on high-dimensional tasks with complex discretization method in simulated environments, and show dynamics. Additionally, we show that an ordinal how they improve upon on-policy optimization baselines.

Noname manuscript No. (will be inserted by the editor) Abstract Selecting an optimal set of icons is a crucial step in the pipeline of visual design to structure and navigate through content. However, designing the icons sets is usually a difficult task for which expert knowledge isrequired. In this work, to ease the process of icon set selection to the users, we propose a similarity metric which captures the properties of style and visual identity. We train a Siamese Neural Network with an online dataset of icons organized in visually coherent collections that are used to adaptively sample training data and optimize the training process. As the dataset contains noise, we further collect human-rated information onthe perception of icon's similarity which will be used for evaluating and testing the proposed model. We present several results and applications based on searches, kernel visualizations and optimized set proposals thatcan be helpful for designers and non-expert users while exploring large collections of icons. Keywords Iconography · Illustration · Visualization · Appearance Similarity · Machine Learning 1 Introduction Visual communication is one of the most important ways to share and transmit information [34,33]. In the same way as words are used for verbal communication, symbols or icons are the elements used to convey information ina universal and ubiquitous language [1, 20]. Icons are key elements to structure visual content and make it more appealing and comprehensible. Style and visual identity are preserved for each collection.

Spatial time series forecasting problems arise in a broad range of applications, such as environmental and transportation problems. These problems are challenging because of the existence of specific spatial, short-term and long-term patterns, and the curse of dimensionality. In this paper, we propose a deep neural network framework for large-scale spatial time series forecasting problems. We explicitly designed the neural network architecture for capturing various types of patterns. In preprocessing, a time series decomposition method is applied to separately feed short-term, long-term and spatial patterns into different components of a neural network. A fuzzy clustering method finds cluster of neighboring time series based on similarity of time series residuals; as they can be meaningful short-term patterns for spatial time series. In neural network architecture, each kernel of a multi-kernel convolution layer is applied to a cluster of time series to extract short-term features in neighboring areas. The output of convolution layer is concatenated by trends and followed by convolution-LSTM layer to capture long-term patterns in larger regional areas. To make a robust prediction when faced with missing data, an unsupervised pretrained denoising autoencoder reconstructs the output of the model in a fine-tuning step. The experimental results illustrate the model outperforms baseline and state of the art models in a traffic flow prediction dataset.

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential equations into the theoretical framework of diffusion approximation, extending the validity of the weak approximation from finite to infinite time horizon. The new techniques developed in this paper enable us to characterize the asymptotic behavior of constant-step-size SGD algorithms for strongly convex objective functions, a goal previously unreachable within the diffusion approximation framework. Our analysis builds upon a truncated formal power expansion of the solution of a stochastic modified equation arising from diffusion approximation, where the main technical ingredient is a uniform-in-time weak error bound controlling the long-term behavior of the expansion coefficient functions near the global minimum. We expect these new techniques to greatly expand the range of applicability of diffusion approximation to cover wider and deeper aspects of stochastic optimization algorithms in data science.

Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions such as unbiased gradient estimates and convex objective function, which significantly limit their applications to sophisticated tasks such as online and reinforcement learning. These restrictions are all essentially relaxed in this work. In particular, we analyze a general SA scheme to minimize a non-convex, smooth objective function. We consider update procedure whose drift term depends on a state-dependent Markov chain and the mean field is not necessarily of gradient type, covering approximate second-order method and allowing asymptotic bias for the one-step updates. We illustrate these settings with the online EM algorithm and the policy-gradient method for average reward maximization in reinforcement learning.

Congealing is a flexible nonparametric data-driven framework for the joint alignment of data. It has been successfully applied to the joint alignment of binary images of digits, binary images of object silhouettes, grayscale MRI images, color images of cars and faces, and 3D brain volumes. This research enhances congealing to practically and effectively apply it to curve data. We develop a parameterized set of nonlinear transformations that allow us to apply congealing to this type of data. We present positive results on aligning synthetic and real curve data sets and conclude with a discussion on extending this work to simultaneous alignment and clustering.

Generalization error (also known as the out-of-sample error) measures how well the hypothesis obtained from the training data can generalize to previously unseen data. Obtaining tight generalization error bounds is central to statistical learning theory. In this paper, we study the generalization error bound in learning general non-convex objectives, which has attracted significant attention in recent years. In particular, we study the (algorithm-dependent) generalization bounds of various iterative gradient based methods. (1) We present a very simple and elementary proof of a recent result for stochastic gradient Langevin dynamics (SGLD), due to Mou et al. (2018). Our proof can be easily extended to obtain similar generalization bounds for several other variants of SGLD (e.g., with postprocessing, momentum, mini-batch, acceleration, and more general noises), and improves upon the recent results in Pensia et al. (2018). (2) By incorporating ideas from the PAC-Bayesian theory into the stability framework, we obtain tighter distribution-dependent (or data-dependent) generalization bounds. Our bounds provide an intuitive explanation for the phenomenon reported in Zhang et al. (2017a). (3) We also study the setting where the total loss is the sum of a bounded loss and an additional `l2 regularization term. We obtain new generalization bounds for the continuous Langevin dynamic in this setting by leveraging the tool of Log-Sobolev inequality. Our new bounds are more desirable when the noisy level of the process is not small, and do not grow when T approaches to infinity.

Minmax optimization, especially in its general nonconvex-nonconcave formulation, has found extensive applications in modern machine learning frameworks such as generative adversarial networks (GAN), adversarial training and multi-agent reinforcement learning. Gradient-based algorithms, in particular gradient descent ascent (GDA), are widely used in practice to solve these problems. Despite the practical popularity of GDA, however, its theoretical behavior has been considered highly undesirable. Indeed, apart from possiblity of non-convergence, recent results (Daskalakis and Panageas, 2018; Mazumdar and Ratliff, 2018; Adolphs et al., 2018) show that even when GDA converges, its stable limit points can be points that are not local Nash equilibria, thus not game-theoretically meaningful. In this paper, we initiate a discussion on the proper optimality measures for minmax optimization, and introduce a new notion of local optimality---local minmax---as a more suitable alternative to the notion of local Nash equilibrium. We establish favorable properties of local minmax points, and show, most importantly, that as the ratio of the ascent step size to the descent step size goes to infinity, stable limit points of GDA are exactly local minmax points up to degenerate points, demonstrating that all stable limit points of GDA have a game-theoretic meaning for minmax problems.

Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a generative model that can capture specific syntactic relations between words. Under our model, we prove that the correlations between three words (measured by their PMI) form a tensor that has an approximate low rank Tucker decomposition. The result of the Tucker decomposition gives the word embeddings as well as a core tensor, which can be used to produce better compositions of the word embeddings. We also complement our theoretical results with experiments that verify our assumptions, and demonstrate the effectiveness of the new composition method.

Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for learning graphical models with least amount of data remains an active research topic. Reconstruction of graphical models that describe the statistics of discrete variables is a particularly challenging problem, for which the maximum likelihood approach is intractable. In this work, we provide the first sample-efficient method based on the Interaction Screening framework that allows one to provably learn fully general discrete factor models with node-specific discrete alphabets and multi-body interactions, specified in an arbitrary basis. We identify a single condition related to model parametrization that leads to rigorous guarantees on the recovery of model structure and parameters in any error norm, and is readily verifiable for a large class of models. Importantly, our bounds make explicit distinction between parameters that are proper to the model and priors used as an input to the algorithm. Finally, we show that the Interaction Screening framework includes all models previously considered in the literature as special cases, and for which our analysis shows a systematic improvement in sample complexity.