diff --git a/optuna/integration/sklearn.py b/optuna/integration/sklearn.py
index 4824c27857..f5a4b7a329 100644
--- a/optuna/integration/sklearn.py
+++ b/optuna/integration/sklearn.py
@@ -48,11 +48,11 @@
 if not _imports.is_successful():
     BaseEstimator = object  # NOQA
 
-ArrayLikeType = Union[List, np.ndarray, "pd.Series", spmatrix]
+ArrayLikeType = Union[List, np.ndarray, "pd.Series", "spmatrix"]
 OneDimArrayLikeType = Union[List[float], np.ndarray, "pd.Series"]
-TwoDimArrayLikeType = Union[List[List[float]], np.ndarray, "pd.DataFrame", spmatrix]
-IterableType = Union[List, "pd.DataFrame", np.ndarray, "pd.Series", spmatrix, None]
-IndexableType = Union[Iterable, None]
+TwoDimArrayLikeType = Union[List[List[float]], np.ndarray, "pd.DataFrame", "spmatrix"]
+IterableType = Union[List, "pd.DataFrame", np.ndarray, "pd.Series", "spmatrix", None]
+IndexableType = Optional[Iterable]
 
 _logger = logging.get_logger(__name__)