In this paper, we address the challenge of exploring unknown indoor environments using autonomous aerial robots with Size Weight and Power (SWaP) constraints. The SWaP constraints induce limits on mission time requiring efficiency in exploration. We present a novel exploration framework that uses Deep Learning (DL) to predict the most likely indoor map given the previous observations, and Deep Reinforcement Learning (DRL) for exploration, designed to run on modern SWaP constraints neural processors. The DL-based map predictor provides a prediction of the occupancy of the unseen environment while the DRL-based planner determines the best navigation goals that can be safely reached to provide the most information. The two modules are tightly coupled and run onboard allowing the vehicle to safely map an unknown environment. Extensive experimental and simulation results show that our approach surpasses state-of-the-art methods by 50-60% in efficiency, which we measure by the fraction of the explored space as a function of the trajectory length.

Neural networks have recently re-emerged as a powerful hypothesis class, yielding impressive classification accuracy in multiple domains. However, their training is a non convex optimization problem. Here we address this difficulty by turning to "improper learning" of neural nets. In other words, we learn a classifier that is not a neural net but is competitive with the best neural net model given a sufficient number of training examples. Our approach relies on a novel kernel which integrates over the set of possible neural models. It turns out that the corresponding integral can be evaluated in closed form via a simple recursion. The learning problem is then an SVM with this kernel, and a global optimum can thus be found efficiently. We also provide sample complexity results which depend on the stability of the optimal neural net.

Unsupervised learning of graphical models is an important task in many domains. Although maximum likelihood learning is computationally hard, there do exist consistent learning algorithms (e.g., psuedo-likelihood and its variants). However, inference in the learned models is still hard, and thus they are not directly usable. In other words, given a probabilistic query they are not guaranteed to provide an answer that is close to the true one. In the current paper, we provide a learning algorithm that is guaranteed to provide approximately correct probabilistic inference. We focus on a particular class of models, namely high girth graphs in the correlation decay regime. It is well known that approximate inference (e.g, using loopy BP) in such models yields marginals that are close to the true ones. Motivated by this, we propose an algorithm that always returns models of this type, and hence in the models it returns inference is approximately correct. We derive finite sample results guaranteeing that beyond a certain sample size, the resulting models will answer probabilistic queries with a high level of accuracy. Results on synthetic data show that the models we learn indeed outperform those obtained by other algorithms, which do not return high girth graphs.