Add tests for pickling with custom obj and metric. (#9943)

python-package/xgboost/sklearn.py

@@ -192,11 +192,16 @@ __model_doc = f"""
         Boosting learning rate (xgb's "eta")
     verbosity : Optional[int]
         The degree of verbosity. Valid values are 0 (silent) - 3 (debug).
+
     objective : {SklObjective}
-        Specify the learning task and the corresponding learning objective or
-        a custom objective function to be used (see note below).
+
+        Specify the learning task and the corresponding learning objective or a custom
+        objective function to be used. For custom objective, see
+        :doc:`/tutorials/custom_metric_obj` and :ref:`custom-obj-metric` for more
+        information.
+
     booster: Optional[str]
-        Specify which booster to use: gbtree, gblinear or dart.
+        Specify which booster to use: `gbtree`, `gblinear` or `dart`.
     tree_method: Optional[str]
         Specify which tree method to use.  Default to auto.  If this parameter is set to
         default, XGBoost will choose the most conservative option available.  It's
@@ -328,21 +333,21 @@ __model_doc = f"""
 
         Metric used for monitoring the training result and early stopping.  It can be a
         string or list of strings as names of predefined metric in XGBoost (See
-        doc/parameter.rst), one of the metrics in :py:mod:`sklearn.metrics`, or any other
-        user defined metric that looks like `sklearn.metrics`.
+        doc/parameter.rst), one of the metrics in :py:mod:`sklearn.metrics`, or any
+        other user defined metric that looks like `sklearn.metrics`.
 
         If custom objective is also provided, then custom metric should implement the
         corresponding reverse link function.
 
         Unlike the `scoring` parameter commonly used in scikit-learn, when a callable
-        object is provided, it's assumed to be a cost function and by default XGBoost will
-        minimize the result during early stopping.
+        object is provided, it's assumed to be a cost function and by default XGBoost
+        will minimize the result during early stopping.
 
-        For advanced usage on Early stopping like directly choosing to maximize instead of
-        minimize, see :py:obj:`xgboost.callback.EarlyStopping`.
+        For advanced usage on Early stopping like directly choosing to maximize instead
+        of minimize, see :py:obj:`xgboost.callback.EarlyStopping`.
 
-        See :doc:`Custom Objective and Evaluation Metric </tutorials/custom_metric_obj>`
-        for more.
+        See :doc:`/tutorials/custom_metric_obj` and :ref:`custom-obj-metric` for more
+        information.
 
         .. note::
 

python-package/xgboost/testing/__init__.py

@@ -815,6 +815,13 @@ def softprob_obj(
     return objective
 
 
+def ls_obj(y_true: np.ndarray, y_pred: np.ndarray) -> Tuple[np.ndarray, np.ndarray]:
+    """Least squared error."""
+    grad = y_pred - y_true
+    hess = np.ones(len(y_true))
+    return grad, hess
+
+
 class DirectoryExcursion:
     """Change directory.  Change back and optionally cleaning up the directory when
     exit.