diff --git a/botorch/models/transforms/outcome.py b/botorch/models/transforms/outcome.py
index a143dd1c23..9923d75c35 100644
--- a/botorch/models/transforms/outcome.py
+++ b/botorch/models/transforms/outcome.py
@@ -532,7 +532,7 @@ def __init__(
         OutcomeTransform.__init__(self)
         self._stratification_idx = stratification_idx
         task_values = task_values.unique(sorted=True)
-        self.strata_mapping = get_task_value_remapping(task_values, dtype=torch.long)
+        self.strata_mapping = get_task_value_remapping(task_values, dtype=torch.double)
         if self.strata_mapping is None:
             self.strata_mapping = task_values
         n_strata = self.strata_mapping.shape[0]
@@ -576,7 +576,7 @@ def forward(
             strata = X[..., self._stratification_idx].long()
             unique_strata = strata.unique()
             for s in unique_strata:
-                mapped_strata = self.strata_mapping[s]
+                mapped_strata = self.strata_mapping[s].long()
                 mask = strata != s
                 Y_strata = Y.clone()
                 Y_strata[..., mask, :] = float("nan")
@@ -616,7 +616,7 @@ def _get_per_input_means_stdvs(
             - The per-input stdvs squared.
         """
         strata = X[..., self._stratification_idx].long()
-        mapped_strata = self.strata_mapping[strata].unsqueeze(-1)
+        mapped_strata = self.strata_mapping[strata].unsqueeze(-1).long()
         # get means and stdvs for each strata
         n_extra_batch_dims = mapped_strata.ndim - 2 - len(self._batch_shape)
         expand_shape = mapped_strata.shape[:n_extra_batch_dims] + self.means.shape
diff --git a/botorch/models/utils/assorted.py b/botorch/models/utils/assorted.py
index 6cf04a5923..521b355515 100644
--- a/botorch/models/utils/assorted.py
+++ b/botorch/models/utils/assorted.py
@@ -422,6 +422,8 @@ def get_task_value_remapping(task_values: Tensor, dtype: torch.dtype) -> Tensor
         return value will be `None`, when the task values are contiguous
         integers starting from zero.
     """
+    if dtype not in (torch.float, torch.double):
+        raise ValueError(f"dtype must be torch.float or torch.double, but got {dtype}.")
     task_range = torch.arange(
         len(task_values), dtype=task_values.dtype, device=task_values.device
     )
diff --git a/test/models/test_multitask.py b/test/models/test_multitask.py
index b9edc3e073..f36ca4301c 100644
--- a/test/models/test_multitask.py
+++ b/test/models/test_multitask.py
@@ -700,3 +700,12 @@ def test_get_task_value_remapping(self) -> None:
             mapping = get_task_value_remapping(task_values, dtype)
             self.assertTrue(torch.equal(mapping[[1, 3]], expected_mapping_no_nan))
             self.assertTrue(torch.isnan(mapping[[0, 2]]).all())
+
+    def test_get_task_value_remapping_invalid_dtype(self) -> None:
+        task_values = torch.tensor([1, 3])
+        for dtype in (torch.int32, torch.long, torch.bool):
+            with self.assertRaisesRegex(
+                ValueError,
+                f"dtype must be torch.float or torch.double, but got {dtype}.",
+            ):
+                get_task_value_remapping(task_values, dtype)
diff --git a/test/models/transforms/test_outcome.py b/test/models/transforms/test_outcome.py
index 29d31593b9..03a5c1167a 100644
--- a/test/models/transforms/test_outcome.py
+++ b/test/models/transforms/test_outcome.py
@@ -372,16 +372,24 @@ def test_stratified_standardize(self):
         n = 5
         seed = randint(0, 100)
         torch.manual_seed(seed)
-        for dtype, batch_shape in itertools.product(
-            (torch.float, torch.double), (torch.Size([]), torch.Size([3]))
+        for dtype, batch_shape, task_values in itertools.product(
+            (torch.float, torch.double),
+            (torch.Size([]), torch.Size([3])),
+            (
+                torch.tensor([0, 1], dtype=torch.long, device=self.device),
+                torch.tensor([0, 3], dtype=torch.long, device=self.device),
+            ),
         ):
             torch.manual_seed(seed)
+            tval = task_values[1].item()
             X = torch.rand(*batch_shape, n, 2, dtype=dtype, device=self.device)
-            X[..., -1] = torch.tensor([0, 1, 0, 1, 0], dtype=dtype, device=self.device)
+            X[..., -1] = torch.tensor(
+                [0, tval, 0, tval, 0], dtype=dtype, device=self.device
+            )
             Y = torch.randn(*batch_shape, n, 1, dtype=dtype, device=self.device)
             Yvar = torch.rand(*batch_shape, n, 1, dtype=dtype, device=self.device)
             strata_tf = StratifiedStandardize(
-                task_values=torch.tensor([0, 1], dtype=torch.long, device=self.device),
+                task_values=task_values,
                 stratification_idx=-1,
                 batch_shape=batch_shape,
             )
@@ -400,9 +408,11 @@ def test_stratified_standardize(self):
             tf_Y1, tf_Yvar1 = tf1(Y=Y1, Yvar=Yvar1, X=X1)
             # check that stratified means are expected
             self.assertAllClose(strata_tf.means[..., :1, :], tf0.means)
-            self.assertAllClose(strata_tf.means[..., 1:, :], tf1.means)
+            # use remapped task values to index
+            self.assertAllClose(strata_tf.means[..., 1:2, :], tf1.means)
             self.assertAllClose(strata_tf.stdvs[..., :1, :], tf0.stdvs)
-            self.assertAllClose(strata_tf.stdvs[..., 1:, :], tf1.stdvs)
+            # use remapped task values to index
+            self.assertAllClose(strata_tf.stdvs[..., 1:2, :], tf1.stdvs)
             # check the transformed values
             self.assertAllClose(tf_Y0, tf_Y[mask0].view(*batch_shape, -1, 1))
             self.assertAllClose(tf_Y1, tf_Y[mask1].view(*batch_shape, -1, 1))