I have an impression of your description more like hinge loss for triplet.
What I was referring to does not have to worry about pairs; apologize if I didn’t make clear.
Particularly, I used MarginRankingLoss() as hinge loss for binary classification as answered here. So I am wondering how to make equal the formula in the OP (eq. 1, I believe that it is y E {-1, 1} not t) and the one from the doc (eq. 2):
max(0, 1 - t * y) where t E {-1, 1} (1)
max(0, -y * (x1 - x2) + 1) (2)
so I make x1 and x2 as y_est[:,0] and y_est[:,1], respectively. I also tried to set x2 to zeros but I am not sure about it.