Pseudo-huber loss metric added (#5647)

- Add pseudo huber loss objective.
- Add pseudo huber loss metric.

Co-authored-by: Reetz <s02reetz@iavgroup.local>

doc/parameter.rst

@@ -342,6 +342,7 @@ Specify the learning task and the corresponding learning objective. The objectiv
   - ``reg:squarederror``: regression with squared loss.
   - ``reg:squaredlogerror``: regression with squared log loss :math:`\frac{1}{2}[log(pred + 1) - log(label + 1)]^2`.  All input labels are required to be greater than -1.  Also, see metric ``rmsle`` for possible issue  with this objective.
   - ``reg:logistic``: logistic regression
+  - ``reg:pseudohubererror``: regression with Pseudo Huber loss, a twice differentiable alternative to absolute loss.
   - ``binary:logistic``: logistic regression for binary classification, output probability
   - ``binary:logitraw``: logistic regression for binary classification, output score before logistic transformation
   - ``binary:hinge``: hinge loss for binary classification. This makes predictions of 0 or 1, rather than producing probabilities.
@@ -376,6 +377,7 @@ Specify the learning task and the corresponding learning objective. The objectiv
     - ``rmse``: `root mean square error <http://en.wikipedia.org/wiki/Root_mean_square_error>`_
     - ``rmsle``: root mean square log error: :math:`\sqrt{\frac{1}{N}[log(pred + 1) - log(label + 1)]^2}`. Default metric of ``reg:squaredlogerror`` objective. This metric reduces errors generated by outliers in dataset.  But because ``log`` function is employed, ``rmsle`` might output ``nan`` when prediction value is less than -1.  See ``reg:squaredlogerror`` for other requirements.
     - ``mae``: `mean absolute error <https://en.wikipedia.org/wiki/Mean_absolute_error>`_
+    - ``mphe``: `mean Pseudo Huber error <https://en.wikipedia.org/wiki/Huber_loss>`_. Default metric of ``reg:pseudohubererror`` objective.
     - ``logloss``: `negative log-likelihood <http://en.wikipedia.org/wiki/Log-likelihood>`_
     - ``error``: Binary classification error rate. It is calculated as ``#(wrong cases)/#(all cases)``. For the predictions, the evaluation will regard the instances with prediction value larger than 0.5 as positive instances, and the others as negative instances.
     - ``error@t``: a different than 0.5 binary classification threshold value could be specified by providing a numerical value through 't'.