  Our goal is to learn control policies for robots that provably generalize
well to novel environments given a dataset of example environments. The key
technical idea behind our approach is to leverage tools from generalization
theory in machine learning by exploiting a precise analogy (which we present in
the form of a reduction) between generalization of control policies to novel
environments and generalization of hypotheses in the supervised learning
setting. In particular, we utilize the Probably Approximately Correct
(PAC)-Bayes framework, which allows us to obtain upper bounds that hold with
high probability on the expected cost of (stochastic) control policies across
novel environments. We propose policy learning algorithms that explicitly seek
to minimize this upper bound. The corresponding optimization problem can be
solved using convex optimization (Relative Entropy Programming in particular)
in the setting where we are optimizing over a finite policy space. In the more
general setting of continuously parameterized policies (e.g., neural network
policies), we minimize this upper bound using stochastic gradient descent. We
present simulated results of our approach applied to learning (1) reactive
obstacle avoidance policies and (2) neural network-based grasping policies. We
also present hardware results for the Parrot Swing drone navigating through
different obstacle environments. Our examples demonstrate the potential of our
approach to provide strong generalization guarantees for robotic systems with
continuous state and action spaces, complicated (e.g., nonlinear) dynamics,
rich sensory inputs (e.g., depth images), and neural network-based policies.
