diff --git a/aepsych/strategy.py b/aepsych/strategy.py
index 704dd09fd..9ed40e196 100644
--- a/aepsych/strategy.py
+++ b/aepsych/strategy.py
@@ -139,8 +139,8 @@ def __init__(
                 lb=self.lb, ub=self.ub, size=self._n_eval_points
             )
 
-        self.x = None
-        self.y = None
+        self.x: Optional[torch.Tensor] = None
+        self.y: Optional[torch.Tensor] = None
         self.n = 0
         self.min_asks = min_asks
         self._count = 0
@@ -170,38 +170,41 @@ def __init__(
 
         self.name = name
 
-    def normalize_inputs(self, x, y):
+    def normalize_inputs(self, x:torch.Tensor, y:torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor, int]:
         """converts inputs into normalized format for this strategy
 
         Args:
-            x (np.ndarray): training inputs
-            y (np.ndarray): training outputs
+            x (torch.Tensor): training inputs
+            y (torch.Tensor): training outputs
 
         Returns:
-            x (np.ndarray): training inputs, normalized
-            y (np.ndarray): training outputs, normalized
+            x (torch.Tensor): training inputs, normalized
+            y (torch.Tensor): training outputs, normalized
             n (int): number of observations
         """
         assert (
             x.shape == self.event_shape or x.shape[1:] == self.event_shape
         ), f"x shape should be {self.event_shape} or batch x {self.event_shape}, instead got {x.shape}"
-
+        
+        # Handle scalar y values
+        if y.ndim == 0:
+            y = y.unsqueeze(0)
+        
         if x.shape == self.event_shape:
             x = x[None, :]
 
-        if self.x is None:
-            x = np.r_[x]
-        else:
-            x = np.r_[self.x, x]
+        if self.x is not None:
+            x = torch.cat((self.x, x), dim=0)
 
-        if self.y is None:
-            y = np.r_[y]
-        else:
-            y = np.r_[self.y, y]
+        if self.y is not None:
+            y = torch.cat((self.y, y), dim=0)
 
+        # Ensure the correct dtype
+        x = x.to(torch.float64)
+        y = y.to(torch.float64)
         n = y.shape[0]
 
-        return torch.Tensor(x), torch.Tensor(y), n
+        return x, y, n
 
     # TODO: allow user to pass in generator options
     @ensure_model_is_fresh
@@ -306,7 +309,21 @@ def n_trials(self):
         )
         return self.min_asks
 
-    def add_data(self, x, y):
+    def add_data(self, x: Union[np.ndarray, torch.Tensor], y: Union[np.ndarray, torch.Tensor]):
+        """
+        Adds new data points to the strategy, and normalizes the inputs.
+
+        Args:
+            x (torch.Tensor, np.ndarray): The input data points. Can be a PyTorch tensor or NumPy array.
+            y (torch.Tensor, np.ndarray): The output data points. Can be a PyTorch tensor or NumPy array.
+
+        """
+        # Necessary as sometimes the data is passed in as numpy arrays or torch tensors.
+        if not isinstance(y, torch.Tensor):
+            y = torch.tensor(y, dtype=torch.float64)
+        if not isinstance(x, torch.Tensor):
+            x = torch.tensor(x, dtype=torch.float64)
+
         self.x, self.y, self.n = self.normalize_inputs(x, y)
         self._model_is_fresh = False