I was wondering how to implement this kind of loss function since MAE is not continuously twice differentiable. Are there any functions close to the Huber loss?
https://stackoverflow.com/questions/45006341/xgboost-how-to-use-mae-as-objective-function
I'm not familiar with XGBoost but if you're having a problem with differentiability there is a smooth approximation to the Huber Loss
https://en.wikipedia.org/wiki/Huber_loss#Pseudo-Huber_loss_function
This function is (more than twice) continuously differentiable, so try something like f(x) = sqrt(1+(x2) ) -1
Wolfram alpha shows that the curve is what you'd expect from Huber.
http://www.wolframalpha.com/input/?i=sqrt(1%2Bx%5E2)+-1
https://stackoverflow.com/questions/45006341/xgboost-how-to-use-mae-as-objective-function
https://github.com/dmlc/xgboost/issues/2522
https://github.com/dmlc/xgboost/issues/2602
http://codegists.com/code/huber-loss-xgboost/
https://stackoverflow.com/questions/45006341/xgboost-how-to-use-mae-as-objective-function
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