We introduce a mixed integer program (MIP) for assigning importance scores to each neuron in deep neural network architectures which is guided by the impact of their simultaneous pruning on the main learning task of the network. By carefully devising the objective function of the MIP, we drive the solver to minimize the number of critical neurons (i.e., with high importance score) that need to be kept for maintaining the overall accuracy of the trained neural network. Further, the proposed formulation generalizes the recently considered lottery ticket optimization by identifying multiple "lucky" sub-networks resulting in optimized architecture that not only performs well on a single dataset, but also generalizes across multiple ones upon retraining of network weights. Finally, we present a scalable implementation of our method by decoupling the importance scores across layers using auxiliary networks. We demonstrate the ability of our formulation to prune neural networks with marginal loss in accuracy and generalizability on popular datasets and architectures.