State of the art neural networks have been shown to be highly susceptible to error under small deformations (the so-called adversarial examples). This severely limits their applicability to safety critical domains such as autonomous navigation. To alleviate this deficiency, researchers have started to explore the idea of robust deep learning: iteratively finding deformations of training samples that cause an error, augmenting the training data set with the deformed samples, and retraining the network. To operationalize robust deep learning, we design a novel proximal minimization based algorithm for estimating the error causing deformations. Our approach relies only a single hyperparameter, is anytime, and highly parallelizable.