In principle, it should be possible to build a gradient boosted tree model on a loss function that only has (nonzero) first derivatives. I've found in practice xgboost and lightgbm make heavy use of second-order information in their custom objective function API. However, lightgbm (for that matter sklearn's random forest too) apparently can train on mean absolute error directly... So if I have structured data that I'd like to build a gradient boosted tree model on, what's the best way to train such a model on a loss function that has no second derivatives? Are there any (mainstream) open source tools that would work with this?

If the answer is "no", I'd love any intuition anyone can provide on why the existing packages use Newton-Raphson iterations for gradient boosting trees as opposed to some variant of raw gradient descent (as is so common in deep learning). Maybe that can give me some intuition as to how to appropriately smooth utility functions that have no second derivatives for the purposes of training gradient boosted models.