  This paper presents an approach for learning vision-based planners that
provably generalize to novel environments (i.e., environments unseen during
training). We leverage the Probably Approximately Correct (PAC)-Bayes framework
to obtain an upper bound on the expected cost of policies across all
environments. Minimizing the PAC-Bayes upper bound thus trains policies that
are accompanied by a certificate of performance on novel environments. The
training pipeline we propose provides strong generalization guarantees for deep
neural network policies by (a) obtaining a good prior distribution on the space
of policies using Evolutionary Strategies (ES) followed by (b) formulating the
PAC-Bayes optimization as an efficiently-solvable parametric convex
optimization problem. We demonstrate the efficacy of our approach for producing
strong generalization guarantees for learned vision-based motion planners
through two simulated examples: (1) an Unmanned Aerial Vehicle (UAV) navigating
obstacle fields with an onboard vision sensor, and (2) a dynamic quadrupedal
robot traversing rough terrains with proprioceptive and exteroceptive sensors.
