Title: Triplet Similarity Learning on Concordance Constraint. Abstract: Triplet-based loss functions have been the paradigm of choice for robust deep metric learning (DML). However, conventional triplet-based losses require carefully tuning a decision boundary, i.e., violation margin. When performing online triplet mining on each mini-batch, choosing a good global and constant prior value for violation margin is challenging and irrational. To circumvent this issue, we propose a novel yet efficient concordance-induced triplet (CIT) loss as an objective function to train DML models. We formulate the similarity of triplet samples as a concordance constraint problem, then directly optimize concordance during DML model learning. Triplet concordance refers to the predicted ordering of intra-class and inter-class similarities being correct, which is invariant to any monotone transformation of the decision boundary of triplet samples. Hence, our CIT loss is free from the plague of adopting the violation margin as a prior constraint. In addition, due to the high training complexity of triplet-based losses, we introduce a partial likelihood term for CIT loss to impose additional penalties on hard triplet samples, thus enforcing fast convergence. We extensively experiment on a variety of DML tasks to demonstrate the elegance and simplicity of our CIT loss against its counterparts. In particular, on face recognition, person re-identification, as well as image retrieval datasets, our method can achieve comparable performances with state-of-the-arts without tuning any hyper-parameters laboriously.