Question about the learning rate in rank:pairwise

Hi all,

I am trying to understand where does the learning rate (‘eta’) implemented in the rank:pairwise objective.
When reading the documentation (and the paper) I got the understanding that the learning rate is in the boosting phase, i.e. that the contribution of each tree is shrinked based with ‘eta’. But when I look at the actual outputs I see that the prediction is the sum of all trees, and that the values at the leaves of each tree are not shrinked with each iteration.
Does that mean the learning rate is a part of something else (GD)?
Does the regularization I mentioned exists?

[I run version 0.9 on python]

Thank you very much ahead!