Title: Efficient Bi-Directional Verification of ReLU Networks via Quadratic Programming. Abstract: Neural networks are known to be sensitive to adversarial perturbations. To investigate this undesired behavior we consider the problem of computing the distance to the decision boundary (DtDB) from a given sample for a deep NN classifier. In this work we present an iterative procedure where in each step we solve a convex quadratic programming (QP) task. Solving the single initial QP already results in a lower bound on the DtDB and can be used as a robustness certificate of the classifier around a given sample. In contrast to currently known approaches our method also provides upper bounds used as a measure of quality for the certificate. We show that our approach provides better or competitive results in comparison with a wide range of existing techniques.