Abstract This paper presents a discrepancy minimizing model to address the discrete optimization problem in hashing learning. The discrete optimization introduced by binary constraint is an NP-hard mixed integer programming problem. It is usually addressed by relaxing the binary variables into continuous variables to adapt to the gradient based learning of hashing functions, especially the training of deep neural networks. To deal with the objective discrepancy caused by relaxation, we transform the original binary optimization into differentiable optimization problem over hash functions through series expansion. This transformation decouples the binary constraint and the similarity preserving hashing function optimization. The transformed objective is optimized in a tractable alternating optimization framework with gradual discrepancy minimization. Extensive experimental results on three benchmark datasets validate the efficacy of the proposed discrepancy minimizing hashing