  We consider the exploration problem: an agent equipped with a depth sensor
must map out a previously unknown environment using as few sensor measurements
as possible. We propose an approach based on supervised learning of a greedy
algorithm. We provide a bound on the optimality of the greedy algorithm using
submodularity theory. Using a level set representation, we train a
convolutional neural network to determine vantage points that maximize
visibility. We show that this method drastically reduces the on-line
computational cost and determines a small set of vantage points that solve the
problem. This enables us to efficiently produce highly-resolved and
topologically accurate maps of complex 3D environments. Unlike traditional
next-best-view and frontier-based strategies, the proposed method accounts for
geometric priors while evaluating potential vantage points. While existing deep
learning approaches focus on obstacle avoidance and local navigation, our
method aims at finding near-optimal solutions to the more global exploration
problem. We present realistic simulations on 2D and 3D urban environments.
