Hello,
I am working this paper : Multi-Label Learning to Rank through Multi-Objective
Optimization
The algorithm is to used an customized gradient “lambda” from multiple cost functions (c_1, c_2, …c_K) in the xgboost training process.
Within the algorithm mentioned in the paper, I need to fit the t-th tree using the data ( see equation (3) below) where the label is constructed with the new gradients “lambda”. 
My question here is:
When I use Pytorch to build a customized cost function as well as its gradient, how can I use xgboost package to
- fit a single tree with the new data (i.e. the set of (feature, residual) pairs )
- update the model by adding the newly fitted tree in xgboost package.
Thank you here for your help.
Best,
Zongjun