[POC] Experimental support for l1 error. (#7812)

Support adaptive tree, a feature supported by both sklearn and lightgbm.  The tree leaf is recomputed based on residue of labels and predictions after construction.

For l1 error, the optimal value is the median (50 percentile).

This is marked as experimental support for the following reasons:
- The value is not well defined for distributed training, where we might have empty leaves for local workers. Right now I just use the original leaf value for computing the average with other workers, which might cause significant errors.
- Some follow-ups are required, for exact, pruner, and optimization for quantile function. Also, we need to calculate the initial estimation.

doc/model.schema

@@ -400,7 +400,6 @@
                 "reg_loss_param"
               ]
             },
-
             {
               "type": "object",
               "properties": {
@@ -433,6 +432,14 @@
                 "tweedie_regression_param"
               ]
             },
+            {
+              "properties": {
+                "name": {
+                  "const": "reg:absoluteerror"
+                }
+              },
+              "type": "object"
+            },
             {
               "type": "object",
               "properties": {

doc/parameter.rst

@@ -349,6 +349,7 @@ Specify the learning task and the corresponding learning objective. The objectiv
   - ``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.
+  - ``reg:absoluteerror``: Regression with L1 error. When tree model is used, leaf value is refreshed after tree construction.
   - ``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.