XGBoost did not allow to use absolute error as objective function in the past since it is a non-differentiable function and its Hessian is equal to 0. However, it does allow to use it now (https://xgboost.readthedocs.io/en/stable/parameter.html).
How does it do it and how can I define non-differentiable custom objective functions?
I've tried to implement it as simply:
def absolute_error(predt, dtrain):
y_true = dtrain.get_label()
errors = y_true - predt
grad = -1.0 * np.sign(errors) # Gradient (negative of the sign of the error)
hess = np.zeros_like(y_true) # Hessian (constant, 0, in this case)
return grad, hess
But it obviously does not work
