In order to integrate uncertainty estimates into deep time-series modelling, Kalman Filters (KFs) (Kalman et al., 1960) have been integrated with deep learning models, however, such approaches typically rely on approximate inference tech- niques such as variational inference which makes learning more complex and often less scalable due to approximation errors. We propose a new deep approach to Kalman filtering which can be learned directly in an end-to-end manner using backpropagation without additional approximations. Our approach uses a high-dimensional factorized latent state representation for which the Kalman updates simplify to scalar operations and thus avoids hard to backpropagate, computationally heavy and potentially unstable matrix inversions. Moreover, we use locally linear dynamic models to efficiently propagate the latent state to the next time step. The resulting network architecture, which we call Recurrent Kalman Network (RKN), can be used for any time-series data, similar to a LSTM (Hochreiter & Schmidhuber, 1997) but uses an explicit representation of uncertainty. As shown by our experiments, the RKN obtains much more accurate uncertainty estimates than an LSTM or Gated Recurrent Units (GRUs) (Cho et al., 2014) while also showing a slightly improved prediction performance and outperforms various recent generative models on an image imputation task.

Swarm robotics investigates how a large population of robots with simple actuation and limited sensors can collectively solve complex tasks. One particular interesting application with robot swarms is autonomous object assembly. Such tasks have been solved successfully with robot swarms that are controlled by a human operator using a light source. In this paper, we present a method to solve such assembly tasks autonomously based on policy search methods. We split the assembly process in two subtasks: generating a high-level assembly plan and learning a low-level object movement policy. The assembly policy plans the trajectories for each object and the object movement policy controls the trajectory execution. Learning the object movement policy is challenging as it depends on the complex state of the swarm which consists of an individual state for each agent. To approach this problem, we introduce a representation of the swarm which is based on Hilbert space embeddings of distributions. This representation is invariant to the number of agents in the swarm as well as to the allocation of an agent to its position in the swarm. These invariances make the learned policy robust to changes in the swarm and also reduce the search space for the policy search method significantly. We show that the resulting system is able to solve assembly tasks with varying object shapes in multiple simulation scenarios and evaluate the robustness of our representation to changes in the swarm size. Furthermore, we demonstrate that the policies learned in simulation are robust enough to be transferred to real robots.

Nonparametric inference techniques provide promising tools for probabilistic reasoning in high-dimensional nonlinear systems.Most of these techniques embed distributions into reproducing kernel Hilbert spaces (RKHS) and rely on the kernel Bayes' rule (KBR) to manipulate the embeddings. However, the computational demands of the KBR scale poorly with the number of samples and the KBR often suffers from numerical instabilities. In this paper, we present the kernel Kalman rule (KKR) as an alternative to the KBR.The derivation of the KKR is based on recursive least squares, inspired by the derivation of the Kalman innovation update.We apply the KKR to filtering tasks where we use RKHS embeddings to represent the belief state, resulting in the kernel Kalman filter (KKF).We show on a nonlinear state estimation task with high dimensional observations that our approach provides a significantly improved estimation accuracy while the computational demands are significantly decreased.