It has been reported repeatedly that discriminative learning of distance metric boosts the pattern recognition performance. Although the ITML (Information Theoretic Metric Learning)-based methods enjoy an advantage that the Bregman projection framework can be applied for optimization of distance metric, a weak point of ITML-based methods is that the distance threshold for similarity/dissimilarity constraints must be determined manually, onto which the generalization performance is sensitive. In this paper, we present a new formulation of metric learning algorithm in which the distance threshold is optimized together. Since the optimization is still in the Bregman projection framework, the Dykstra algorithm can be applied for optimization. A nonlinear equation has to be solved to project the solution onto a half-space in each iteration. We have developed an efficient technique for projection onto a half-space. We empirically show that although the distance threshold is automatically tuned for the proposed metric learning algorithm, the accuracy of pattern recognition for the proposed algorithm is comparable, if not better, to the existing metric learning methods.