This paper presents a novel regrasp control policy that makes use of tactile sensing to plan local grasp adjustments. Our approach determines regrasp actions by virtually searching for local transformations of tactile measurements that improve the quality of the grasp. First, we construct a tactile-based grasp quality metric using a deep convolutional neural network trained on over 2800 grasps. The quality of each grasp, a continuous value between 0 and 1, is determined experimentally by measuring its resistance to external perturbations. Second, we simulate the tactile imprints associated with robot motions relative to the initial grasp by performing rigid-body transformations of the given tactile measurements. The newly generated tactile imprints are evaluated with the learned grasp quality network and the regrasp action is chosen to maximize the grasp quality. Results show that the grasp quality network can predict the outcome of grasps with an average accuracy of 85% on known objects and 75% on a cross validation set of 12 objects. The regrasp control policy improves the success rate of grasp actions by an average relative increase of 70% on a test set of 8 objects.