Towards Bayesian Deep Learning: A Survey <s> Bayesian Deep Learning for Control <s> Kullback Leibler (KL) control problems allow for efficient computation of optimal control by solving a principal eigenvector problem. However, direct applicability of such framework to continuous state-action systems is limited. In this paper, we propose to embed a KL control problem in a probabilistic graphical model where observed variables correspond to the continuous (possibly high-dimensional) state of the system and latent variables correspond to a discrete (low-dimensional) representation of the state amenable for KL control computation. We present two examples of this approach. The first one uses standard hidden Markov models (HMMs) and computes exact optimal control, but is only applicable to low-dimensional systems. The second one uses factorial HMMs, it is scalable to higher dimensional problems, but control computation is approximate. We illustrate both examples in several robot motor control tasks. <s> BIB001 </s> Towards Bayesian Deep Learning: A Survey <s> Bayesian Deep Learning for Control <s> We introduce Embed to Control (E2C), a method for model learning and control of non-linear dynamical systems from raw pixel images. E2C consists of a deep generative model, belonging to the family of variational autoencoders, that learns to generate image trajectories from a latent space in which the dynamics is constrained to be locally linear. Our model is derived directly from an optimal control formulation in latent space, supports long-term prediction of image sequences and exhibits strong performance on a variety of complex control problems. <s> BIB002
As mentioned in Section 1, Bayesian deep learning can also be applied to the control of nonlinear dynamical systems from raw images. Consider controlling a complex dynamical system according to the live video stream received from a camera. One way of solving this control problem is by iteration between two tasks, perception from raw images and control based on dynamic models. The perception task can be taken care of using multiple layers of simple nonlinear transformation (deep learning) while the control task usually needs more sophisticated models like hidden Markov models and Kalman filters  , BIB001 . To enable an effective iterative process between the perception task and the control task, we need two-way information exchange between them. The perception component would be the basis on which the control component estimates its states and on the other hand, the control component with a dynamic model built in would be able to predict the future trajectory (images) by reversing the perception process BIB002 .