We develop a mathematical framework for solving multi-task reinforcement learning problems based on a type of decentralized policy gradient method. The goal in multi-task reinforcement learning is to learn a common policy that operates effectively in different environments; these environments have similar (or overlapping) state and action spaces, but have different rewards and dynamics. Agents immersed in each of these environments communicate with other agents by sharing their models (i.e. their policy parameterizations) but not their state/reward paths. Our analysis provides a convergence rate for a consensus-based distributed, entropy-regularized policy gradient method for finding such a policy. We demonstrate the effectiveness of the proposed method using a series of numerical experiments. These experiments range from small-scale "Grid World" problems that readily demonstrate the trade-offs involved in multi-task learning to large-scale problems, where common policies are learned to play multiple Atari games or to navigate an airborne drone in multiple (simulated) environments.

What do data tell us about physics-and what don't they tell us? There has been a surge of interest in using machine learning models to discover governing physical laws such as differential equations from data, but current methods lack uncertainty quantification to communicate their credibility. This work addresses this shortcoming from a Bayesian perspective. We introduce a novel model comprising "leaf" modules that learn to represent distinct experiments' spatiotemporal functional data as neural networks and a single "root" module that expresses a nonparametric distribution over their governing nonlinear differential operator as a Gaussian process. Automatic differentiation is used to compute the required partial derivatives from the leaf functions as inputs to the root. Our approach quantifies the reliability of the learned physics in terms of a posterior distribution over operators and propagates this uncertainty to solutions of novel initial-boundary value problem instances. Numerical experiments demonstrate the method on several nonlinear PDEs.

Deep neural networks are often ignorant about what they do not know and overconfident when they make uninformed predictions. Some recent approaches quantify classification uncertainty directly by training the model to output high uncertainty for the data samples close to class boundaries or from the outside of the training distribution. These approaches use an auxiliary data set during training to represent out-of-distribution samples. However, selection or creation of such an auxiliary data set is non-trivial, especially for high dimensional data such as images. In this work we develop a novel neural network model that is able to express both aleatoric and epistemic uncertainty to distinguish decision boundary and out-of-distribution regions of the feature space. To this end, variational autoencoders and generative adversarial networks are incorporated to automatically generate out-of-distribution exemplars for training. Through extensive analysis, we demonstrate that the proposed approach provides better estimates of uncertainty for in- and out-of-distribution samples, and adversarial examples on well-known data sets against state-of-the-art approaches including recent Bayesian approaches for neural networks and anomaly detection methods.

Mining and learning the shape variability of underlying population has benefited the applications including parametric shape modeling, 3D animation, and image segmentation. The current statistical shape modeling method works well on learning unstructured shape variations without obvious pose changes (relative rotations of the body parts). Studying the pose variations within a shape population involves segmenting the shapes into different articulated parts and learning the transformations of the segmented parts. This paper formulates the pose learning problem as mixtures of factor analyzers. The segmentation is obtained by components posterior probabilities and the rotations in pose variations are learned by the factor loading matrices. To guarantee that the factor loading matrices are composed by rotation matrices, constraints are imposed and the corresponding closed form optimal solution is derived. Based on the proposed method, the pose variations are automatically learned from the given shape populations. The method is applied in motion animation where new poses are generated by interpolating the existing poses in the training set. The obtained results are smooth and realistic.

Graph Convolutional Networks (GCNs) and their variants have received significant attention and achieved start-of-the-art performances on various recommendation tasks. However, many existing GCN models tend to perform recursive aggregations among all related nodes, which arises severe computational burden. Moreover, they favor multi-layer architectures in conjunction with complicated modeling techniques. Though effective, the excessive amount of model parameters largely hinder their applications in real-world recommender systems. To this end, in this paper, we propose the single-layer GCN model which is able to achieve superior performance along with remarkably less complexity compared with existing models. Our main contribution is three-fold. First, we propose a principled similarity metric named distribution-aware similarity (DA similarity), which can guide the neighbor sampling process and evaluate the quality of the input graph explicitly. We also prove that DA similarity has a positive correlation with the final performance, through both theoretical analysis and empirical simulations. Second, we propose a simplified GCN architecture which employs a single GCN layer to aggregate information from the neighbors filtered by DA similarity and then generates the node representations. Moreover, the aggregation step is a parameter-free operation, such that it can be done in a pre-processing manner to further reduce red the training and inference costs. Third, we conduct extensive experiments on four datasets. The results verify that the proposed model outperforms existing GCN models considerably and yields up to a few orders of magnitude speedup in training, in terms of the recommendation performance.

Learning distributions of graphs can be used for automatic drug discovery, molecular design, complex network analysis, and much more. We present an improved framework for learning generative models of graphs based on the idea of deep state machines. To learn state transition decisions we use a set of graph and node embedding techniques as memory of the state machine. Our analysis is based on learning the distribution of random graph generators for which we provide statistical tests to determine which properties can be learned and how well the original distribution of graphs is represented. We show that the design of the state machine favors specific distributions. Models of graphs of size up to 150 vertices are learned. Code and parameters are publicly available to reproduce our results.

Estimated time of arrival (ETA) is one of the most important services in intelligent transportation systems and becomes a challenging spatial-temporal (ST) data mining task in recent years. Nowadays, deep learning based methods, specifically recurrent neural networks (RNN) based ones are adapted to model the ST patterns from massive data for ETA and become the state-of-the-art. However, RNN is suffering from slow training and inference speed, as its structure is unfriendly to parallel computing. To solve this problem, we propose a novel, brief and effective framework mainly based on feed-forward network (FFN) for ETA, FFN with Multi-factor self-Attention (FMA-ETA). The novel Multi-factor self-attention mechanism is proposed to deal with different category features and aggregate the information purposefully. Extensive experimental results on the real-world vehicle travel dataset show FMA-ETA is competitive with state-of-the-art methods in terms of the prediction accuracy with significantly better inference speed.

Considering deep sequence learning for practical application, two representative RNNs - LSTM and GRU may come to mind first. Nevertheless, is there no chance for other RNNs? Will there be a better RNN in the future? In this work, we propose a novel, succinct and promising RNN - Fusion Recurrent Neural Network (Fusion RNN). Fusion RNN is composed of Fusion module and Transport module every time step. Fusion module realizes the multi-round fusion of the input and hidden state vector. Transport module which mainly refers to simple recurrent network calculate the hidden state and prepare to pass it to the next time step. Furthermore, in order to evaluate Fusion RNN's sequence feature extraction capability, we choose a representative data mining task for sequence data, estimated time of arrival (ETA) and present a novel model based on Fusion RNN. We contrast our method and other variants of RNN for ETA under massive vehicle travel data from DiDi Chuxing. The results demonstrate that for ETA, Fusion RNN is comparable to state-of-the-art LSTM and GRU which are more complicated than Fusion RNN.

Gradient Boosting Machine has proven to be one successful function approximator and has been widely used in a variety of areas. However, since the training procedure of each base learner has to take the sequential order, it is infeasible to parallelize the training process among base learners for speed-up. In addition, under online or incremental learning settings, GBMs achieved sub-optimal performance due to the fact that the previously trained base learners can not adapt with the environment once trained. In this work, we propose the soft Gradient Boosting Machine (sGBM) by wiring multiple differentiable base learners together, by injecting both local and global objectives inspired from gradient boosting, all base learners can then be jointly optimized with linear speed-up. When using differentiable soft decision trees as base learner, such device can be regarded as an alternative version of the (hard) gradient boosting decision trees with extra benefits. Experimental results showed that, sGBM enjoys much higher time efficiency with better accuracy, given the same base learner in both on-line and off-line settings.

Gain a Strong Understanding of TensorFlow - Google's Cutting-Edge Deep Learning Framework Build Deep Learning Algorithms from Scratch in Python Using NumPy and TensorFlow Set Yourself Apart with Hands-on Deep and Machine Learning Experience Grasp the Mathematics Behind Deep Learning Algorithms Understand Backpropagation, Stochastic Gradient Descent, Batching, Momentum, and Learning Rate Schedules Know the Ins and Outs of Underfitting, Overfitting, Training, Validation, Testing, Early Stopping, and Initialization Competently Carry Out Pre-Processing, Standardization, Normalization, and One-Hot Encoding Description Gain a Strong Understanding of TensorFlow - Google's Cutting-Edge Deep Learning Framework Build Deep Learning Algorithms from Scratch in Python Using NumPy and TensorFlow Set Yourself Apart with Hands-on Deep and Machine Learning Experience Grasp the Mathematics Behind Deep Learning Algorithms Understand Backpropagation, Stochastic Gradient Descent, Batching, Momentum, and Learning Rate Schedules Know the Ins and Outs of Underfitting, Overfitting, Training, Validation, Testing, Early Stopping, and Initialization Competently Carry Out Pre-Processing, Standardization, Normalization, and One-Hot Encoding Data scientists, machine learning engineers, and AI researchers all have their own skillsets. But what is that one special thing they have in common? They are all masters of deep learning. We often hear about AI, or self-driving cars, or the'algorithmic magic' at Google, Facebook, and Amazon. But it is not magic - it is deep learning. And more specifically, it is usually deep neural networks – the one algorithm to rule them all.