Calculate base_score based on input labels for mae. (#8107)

Fit an intercept as base score for abs loss.

tests/python/test_with_dask.py

@@ -1537,13 +1537,56 @@ class TestWithDask:
     @pytest.mark.skipif(**tm.no_dask())
     @pytest.mark.gtest
     def test_quantile_same_on_all_workers(self) -> None:
-        self.run_quantile('SameOnAllWorkers')
+        self.run_quantile("SameOnAllWorkers")
+
+    def test_adaptive(self) -> None:
+        def get_score(config: Dict) -> float:
+            return float(config["learner"]["learner_model_param"]["base_score"])
+
+        def local_test(rabit_args: List[bytes], worker_id: int) -> bool:
+            with xgb.dask.RabitContext(rabit_args):
+                if worker_id == 0:
+                    y = np.array([0.0, 0.0, 0.0])
+                    x = np.array([[0.0]] * 3)
+                else:
+                    y = np.array([1000.0])
+                    x = np.array(
+                        [
+                            [0.0],
+                        ]
+                    )
+
+                Xy = xgb.DMatrix(x, y)
+                booster = xgb.train(
+                    {"tree_method": "hist", "objective": "reg:absoluteerror"},
+                    Xy,
+                    num_boost_round=1,
+                )
+                config = json.loads(booster.save_config())
+                base_score = get_score(config)
+                assert base_score == 250.0
+                return True
+
+        with LocalCluster(n_workers=2, dashboard_address=":0") as cluster:
+            with Client(cluster) as client:
+                workers = _get_client_workers(client)
+                rabit_args = client.sync(
+                    xgb.dask._get_rabit_args, len(workers), None, client
+                )
+                futures = []
+                for i, _ in enumerate(workers):
+                    f = client.submit(local_test, rabit_args, i)
+                    futures.append(f)
+
+                results = client.gather(futures)
+                assert all(results)
 
     def test_n_workers(self) -> None:
         with LocalCluster(n_workers=2, dashboard_address=":0") as cluster:
             with Client(cluster) as client:
                 workers = _get_client_workers(client)
                 from sklearn.datasets import load_breast_cancer
+
                 X, y = load_breast_cancer(return_X_y=True)
                 dX = client.submit(da.from_array, X, workers=[workers[0]]).result()
                 dy = client.submit(da.from_array, y, workers=[workers[0]]).result()