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