This paper presents the Dexterity Network (Dex-Net) 1.0, a dataset of 3D object models and a sampling-based planning algorithm to explore how Cloud Robotics can be used for robust grasp planning. The algorithm uses a Multi- Armed Bandit model with correlated rewards to leverage prior grasps and 3D object models in a growing dataset that currently includes over 10,000 unique 3D object models and 2.5 million parallel-jaw grasps. Each grasp includes an estimate of the probability of force closure under uncertainty in object and gripper pose and friction. Dex-Net 1.0 uses Multi-View Convolutional Neural Networks (MV-CNNs), a new deep learning method for 3D object classification, to provide a similarity metric between objects, and the Google Cloud Platform to simultaneously run up to 1,500 virtual cores, reducing experiment runtime by up to three orders of magnitude. Experiments suggest that correlated bandit techniques can use a cloud-based network of object models to significantly reduce the number of samples required for robust grasp planning. We report on system sensitivity to variations in similarity metrics and in uncertainty in pose and friction. Code and updated information is available at http://berkeleyautomation.github.io/dex-net/.