scikit-learn
diff --git a/‎sklearn/feature_selection/_sequential.py
Copy file name to clipboardExpand all lines: sklearn/feature_selection/_sequential.py
+5-2Lines changed: 5 additions & 2 deletions b/‎sklearn/feature_selection/_sequential.py
Copy file name to clipboardExpand all lines: sklearn/feature_selection/_sequential.py
+5-2Lines changed: 5 additions & 2 deletions
diff --git a/‎sklearn/feature_selection/tests/test_sequential.py
Copy file name to clipboardExpand all lines: sklearn/feature_selection/tests/test_sequential.py
+25-4Lines changed: 25 additions & 4 deletions b/‎sklearn/feature_selection/tests/test_sequential.py
Copy file name to clipboardExpand all lines: sklearn/feature_selection/tests/test_sequential.py
+25-4Lines changed: 25 additions & 4 deletions
@@ -257,8 +257,11 @@ def fit(self, X, y=None):
         elif isinstance(self.n_features_to_select, Real):
             self.n_features_to_select_ = int(n_features * self.n_features_to_select)
 
-        if self.tol is not None and self.tol < 0 and self.direction == "forward":
-            raise ValueError("tol must be positive when doing forward selection")
+        if self.tol is not None:
+            if self.tol < 0 and self.direction == "forward":
+                raise ValueError("tol must be positive when doing forward selection")
+            if self.tol > 0 and self.direction == "backward":
+                raise ValueError("tol must be negative when doing backward selection")
 
         cv = check_cv(self.cv, y, classifier=is_classifier(self.estimator))
 
 
@@ -55,6 +55,9 @@ def test_n_features_to_select_auto(direction, max_features_to_select):
     """
     n_features = 10
     tol = 1e-3
+    if direction == "backward":
+        tol *= -1
+
     X, y = make_regression(n_features=n_features, random_state=0)
     sfs = SequentialFeatureSelector(
         LinearRegression(),
@@ -96,6 +99,8 @@ def test_n_features_to_select_stopping_criterion(direction):
     X, y = make_regression(n_features=50, n_informative=10, random_state=0)
 
     tol = 1e-3
+    if direction == "backward":
+        tol *= -1
 
     sfs = SequentialFeatureSelector(
         LinearRegression(),
@@ -131,7 +136,15 @@ def test_n_features_to_select_stopping_criterion(direction):
         assert (sfs_cv_score - added_cv_score) <= tol
         assert (sfs_cv_score - removed_cv_score) >= tol
     else:
-        assert (added_cv_score - sfs_cv_score) <= tol
+        assert sfs_cv_score <= added_cv_score
+        assert sfs_cv_score >= removed_cv_score
+        # The "added" score should be equal or higher than the SFS score
+        # so the difference between them should be >= tol, which is a
+        # negative number.
+        assert (sfs_cv_score - added_cv_score) >= tol
+        # Because tol is negative the delta between scores should be
+        # less than or equal to the tolerance, in absolute terms
+        # the delta is bigger than the tolerance
         assert (removed_cv_score - sfs_cv_score) <= tol
 
 
@@ -282,19 +295,27 @@ def test_no_y_validation_model_fit(y):
         sfs.fit(X, y)
 
 
-def test_forward_neg_tol_error():
-    """Check that we raise an error when tol<0 and direction='forward'"""
+def test_tol_sign_depends_on_direction():
+    """Check that we raise an error when the sign of tol and the direction do not match"""
     X, y = make_regression(n_features=10, random_state=0)
     sfs = SequentialFeatureSelector(
         LinearRegression(),
         n_features_to_select="auto",
         direction="forward",
         tol=-1e-3,
     )
-
     with pytest.raises(ValueError, match="tol must be positive"):
         sfs.fit(X, y)
 
+    sfs = SequentialFeatureSelector(
+        LinearRegression(),
+        n_features_to_select="auto",
+        direction="backward",
+        tol=+1e-3,
+    )
+    with pytest.raises(ValueError, match="tol must be negative"):
+        sfs.fit(X, y)
+
 
 def test_backward_neg_tol():
     """Check that SequentialFeatureSelector works negative tol