Support min_delta in early stopping. (#7137)

* Support `min_delta` in early stopping.

* Remove abs_tol.

python-package/xgboost/callback.py

@@ -485,8 +485,8 @@ class EarlyStopping(TrainingCallback):
         Whether to maximize evaluation metric.  None means auto (discouraged).
     save_best
         Whether training should return the best model or the last model.
-    abs_tol
-        Absolute tolerance for early stopping condition.
+    min_delta
+        Minimum absolute change in score to be qualified as an improvement.
 
         .. versionadded:: 1.5.0
 
@@ -505,22 +505,24 @@ class EarlyStopping(TrainingCallback):
             X, y = load_digits(return_X_y=True)
             clf.fit(X, y, eval_set=[(X, y)], callbacks=[es])
     """
-    def __init__(self,
+    def __init__(
+        self,
         rounds: int,
         metric_name: Optional[str] = None,
         data_name: Optional[str] = None,
         maximize: Optional[bool] = None,
         save_best: Optional[bool] = False,
-                 abs_tol: float = 0) -> None:
+        min_delta: float = 0.0
+    ) -> None:
         self.data = data_name
         self.metric_name = metric_name
         self.rounds = rounds
         self.save_best = save_best
         self.maximize = maximize
         self.stopping_history: CallbackContainer.EvalsLog = {}
-        self._tol = abs_tol
-        if self._tol < 0:
-            raise ValueError("tolerance must be greater or equal to 0.")
+        self._min_delta = min_delta
+        if self._min_delta < 0:
+            raise ValueError("min_delta must be greater or equal to 0.")
 
         self.improve_op = None
 
@@ -539,10 +541,12 @@ class EarlyStopping(TrainingCallback):
             return x[0] if isinstance(x, tuple) else x
 
         def maximize(new, best):
-            return numpy.greater(get_s(new) + self._tol, get_s(best))
+            """New score should be greater than the old one."""
+            return numpy.greater(get_s(new) - self._min_delta, get_s(best))
 
         def minimize(new, best):
-            return numpy.greater(get_s(best) + self._tol, get_s(new))
+            """New score should be smaller than the old one."""
+            return numpy.greater(get_s(best) - self._min_delta, get_s(new))
 
         if self.maximize is None:
             # Just to be compatibility with old behavior before 1.3.  We should let

tests/python/test_callback.py

@@ -126,26 +126,30 @@ class TestCallbacks:
         assert len(dump) - booster.best_iteration == early_stopping_rounds + 1
         assert len(early_stop.stopping_history['Train']['CustomErr']) == len(dump)
 
-        # test tolerance, early stop won't occur with high tolerance.
-        tol = 10
         rounds = 100
         early_stop = xgb.callback.EarlyStopping(
             rounds=early_stopping_rounds,
             metric_name='CustomErr',
             data_name='Train',
-            abs_tol=tol
+            min_delta=100,
+            save_best=True,
         )
         booster = xgb.train(
-            {'objective': 'binary:logistic',
+            {
+                'objective': 'binary:logistic',
                 'eval_metric': ['error', 'rmse'],
-             'tree_method': 'hist'}, D_train,
+                'tree_method': 'hist'
+            },
+            D_train,
             evals=[(D_train, 'Train'), (D_valid, 'Valid')],
             feval=tm.eval_error_metric,
             num_boost_round=rounds,
             callbacks=[early_stop],
-            verbose_eval=False)
-        # 0 based index
-        assert booster.best_iteration == rounds - 1
+            verbose_eval=False
+        )
+        # No iteration can be made with min_delta == 100
+        assert booster.best_iteration == 0
+        assert booster.num_boosted_rounds() == 1
 
     def test_early_stopping_skl(self):
         from sklearn.datasets import load_breast_cancer