Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks, Binarized Neural Networks, using the well-developed means of Boolean satisfiability. Our main contribution is a construction that creates a representation of a binarized neural network as a Boolean formula. Our encoding is the first exact Boolean representation of a deep neural network. Using this encoding, we leverage the power of modern SAT solvers along with a proposed counterexample-guided search procedure to verify various properties of these networks. A particular focus will be on the critical property of robustness to adversarial perturbations. For this property, our experimental results demonstrate that our approach scales to medium-size deep neural networks used in image classification tasks. To the best of our knowledge, this is the first work on verifying properties of deep neural networks using an exact Boolean encoding of the network.

In many reinforcement learning problems, parameters of the model may vary with its phase while the agent attempts to learn through its interaction with the environment. For example, an autonomous car's reward on selecting a path may depend on traffic conditions at the time of the day or the transition dynamics of a drone may depend on the current wind direction. Many such processes exhibit a cyclic phase-structure and could be represented with a control policy parameterized over a circular or cyclic phase space. Attempting to model such phase variations with a standard data-driven approach (e.g. deep networks) without explicitly modeling the phase of the model can be challenging. Ambiguities may arise as the optimal action for a given state can vary depending on the phase. To better model cyclic environments, we propose phase-parameterized policies and value function approximators that explicitly enforce a cyclic structure to the policy or value space. We apply our phase-parameterized reinforcement learning approach to both feed-forward and recurrent deep networks in the context of trajectory optimization and locomotion problems. Our experiments show that our proposed approach has superior modeling performance than traditional function approximators in cyclic environments.

Robots assisting the disabled or elderly must perform complex manipulation tasks and must adapt to the home environment and preferences of their user. Learning from demonstration is a promising choice, that would allow the non-technical user to teach the robot different tasks. However, collecting demonstrations in the home environment of a disabled user is time consuming, disruptive to the comfort of the user, and presents safety challenges. It would be desirable to perform the demonstrations in a virtual environment. In this paper we describe a solution to the challenging problem of behavior transfer from virtual demonstration to a physical robot. The virtual demonstrations are used to train a deep neural network based controller, which is using a Long Short Term Memory (LSTM) recurrent neural network to generate trajectories. The training process uses a Mixture Density Network (MDN) to calculate an error signal suitable for the multimodal nature of demonstrations. The controller learned in the virtual environment is transferred to a physical robot (a Rethink Robotics Baxter). An off-the-shelf vision component is used to substitute for geometric knowledge available in the simulation and an inverse kinematics module is used to allow the Baxter to enact the trajectory. Our experimental studies validate the three contributions of the paper: (1) the controller learned from virtual demonstrations can be used to successfully perform the manipulation tasks on a physical robot, (2) the LSTM+MDN architectural choice outperforms other choices, such as the use of feedforward networks and mean-squared error based training signals and (3) allowing imperfect demonstrations in the training set also allows the controller to learn how to correct its manipulation mistakes.

Inertial sensors play a pivotal role in indoor localization, which in turn lays the foundation for pervasive personal applications. However, low-cost inertial sensors, as commonly found in smartphones, are plagued by bias and noise, which leads to unbounded growth in error when accelerations are double integrated to obtain displacement. Small errors in state estimation propagate to make odometry virtually unusable in a matter of seconds. We propose to break the cycle of continuous integration, and instead segment inertial data into independent windows. The challenge becomes estimating the latent states of each window, such as velocity and orientation, as these are not directly observable from sensor data. We demonstrate how to formulate this as an optimization problem, and show how deep recurrent neural networks can yield highly accurate trajectories, outperforming state-of-the-art shallow techniques, on a wide range of tests and attachments. In particular, we demonstrate that IONet can generalize to estimate odometry for non-periodic motion, such as a shopping trolley or baby-stroller, an extremely challenging task for existing techniques.

Robust reinforcement learning aims to produce policies that have strong guarantees even in the face of environments/transition models whose parameters have strong uncertainty. Existing work uses value-based methods and the usual primitive action setting. In this paper, we propose robust methods for learning temporally abstract actions, in the framework of options. We present a Robust Options Policy Iteration (ROPI) algorithm with convergence guarantees, which learns options that are robust to model uncertainty. We utilize ROPI to learn robust options with the Robust Options Deep Q Network (RO-DQN) that solves multiple tasks and mitigates model misspecification due to model uncertainty. We present experimental results which suggest that policy iteration with linear features may have an inherent form of robustness when using coarse feature representations. In addition, we present experimental results which demonstrate that robustness helps policy iteration implemented on top of deep neural networks to generalize over a much broader range of dynamics than non-robust policy iteration.

The volatility of the price movements reflects the ubiquitous In this paper, we take a fully data driven approach and determine uncertainty within financial markets. It is critical the configurations with as few exogenous input as that the level of risk (aka, the degree of variation), indicated possible, or even purely from the historical data. We propose by volatility, is taken into consideration before investment a neural network re-formulation of stochastic volatility decisions are made and portfolio are optimised (Hull by leveraging stochastic models and recurrent neural networks 2006); volatility is substantially a key variable in the pricing (RNNs). In inspired by the work from Chung et al. of derivative securities. Hence, estimating and forecasting (Chung et al. 2015) and Fraccaro et al. (Fraccaro et al. 2016), volatility is of great importance in branches of financial studies, the proposed model is rooted in variational inference and including investment, risk management, security valuation equipped with the latest advances of stochastic neural networks.

In this paper, we introduce the Action Schema Network (ASNet): a neural network architecture for learning generalised policies for probabilistic planning problems. By mimicking the relational structure of planning problems, ASNets are able to adopt a weight sharing scheme which allows the network to be applied to any problem from a given planning domain. This allows the cost of training the network to be amortised over all problems in that domain. Further, we propose a training method which balances exploration and supervised training on small problems to produce a policy which remains robust when evaluated on larger problems. In experiments, we show that ASNet's learning capability allows it to significantly outperform traditional non-learning planners in several challenging domains.

In this paper, we introduce a generalized value iteration network (GVIN), which is an end-to-end neural network planning module. GVIN emulates the value iteration algorithm by using a novel graph convolution operator, which enables GVIN to learn and plan on irregular spatial graphs. We propose three novel differentiable kernels as graph convolution operators and show that the embedding-based kernel achieves the best performance. Furthermore, we present episodic Q-learning, an improvement upon traditional n-step Q-learning that stabilizes training for VIN and GVIN. Lastly, we evaluate GVIN on planning problems in 2D mazes, irregular graphs, and real-world street networks, showing that GVIN generalizes well for both arbitrary graphs and unseen graphs of larger scaleand outperforms a naive generalization of VIN (discretizing a spatial graph into a 2D image).

Current domain-independent, classical planners require symbolic models of the problem domain and instance as input, resulting in a knowledge acquisition bottleneck. Meanwhile, although deep learning has achieved significant success in many fields, the knowledge is encoded in a subsymbolic representation which is incompatible with symbolic systems such as planners. We propose LatPlan, an unsupervised architecture combining deep learning and classical planning. Given only an unlabeled set of image pairs showing a subset of transitions allowed in the environment (training inputs), and a pair of images representing the initial and the goal states (planning inputs), LatPlan finds a plan to the goal state in a symbolic latent space and returns a visualized plan execution. The contribution of this paper is twofold: (1) State Autoencoder, which finds a propositional state representation of the environment using a Variational Autoencoder. It generates a discrete latent vector from the images, based on which a PDDL model can be constructed and then solved by an off-the-shelf planner. (2) Action Autoencoder / Discriminator, a neural architecture which jointly finds the action symbols and the implicit action models (preconditions/effects), and provides a successor function for the implicit graph search. We evaluate LatPlan using image-based versions of 3 planning domains: 8-puzzle, Towers of Hanoi and LightsOut.

Knowledge graph (KG) is known to be helpful for the task of question answering (QA), since it provides well-structured relational information between entities, and allows one to further infer indirect facts. However, it is challenging to build QA systems which can learn to reason over knowledge graphs based on question-answer pairs alone. First, when people ask questions, their expressions are noisy (for example, typos in texts, or variations in pronunciations), which is non-trivial for the QA system to match those mentioned entities to the knowledge graph. Second, many questions require multi-hop logic reasoning over the knowledge graph to retrieve the answers. To address these challenges, we propose a novel and unified deep learning architecture, and an end-to-end variational learning algorithm which can handle noise in questions, and learn multi-hop reasoning simultaneously. Our method achieves state-of-the-art performance on a recent benchmark dataset in the literature. We also derive a series of new benchmark datasets, including questions for multi-hop reasoning, questions paraphrased by neural translation model, and questions in human voice. Our method yields very promising results on all these challenging datasets.