diff --git a/ax/core/search_space.py b/ax/core/search_space.py
index 12188ae626e..1268f9bdeef 100644
--- a/ax/core/search_space.py
+++ b/ax/core/search_space.py
@@ -988,9 +988,8 @@ class SearchSpaceDigest:
             task parameters.
         fidelity_features: A list of parameter indices to be considered as
             fidelity parameters.
-        target_fidelities: A dictionary mapping parameter indices (of fidelity
-            parameters) to their respective target fidelity value. Only used
-            when generating candidates.
+        target_values: A dictionary mapping parameter indices of fidelity or
+            task parameters to their respective target value.
         robust_digest: An optional `RobustSearchSpaceDigest` that carries the
             additional attributes if using a `RobustSearchSpace`.
     """
@@ -1002,7 +1001,7 @@ class SearchSpaceDigest:
     discrete_choices: Dict[int, List[Union[int, float]]] = field(default_factory=dict)
     task_features: List[int] = field(default_factory=list)
     fidelity_features: List[int] = field(default_factory=list)
-    target_fidelities: Dict[int, Union[int, float]] = field(default_factory=dict)
+    target_values: Dict[int, Union[int, float]] = field(default_factory=dict)
     robust_digest: Optional[RobustSearchSpaceDigest] = None
 
 
diff --git a/ax/core/tests/test_search_space.py b/ax/core/tests/test_search_space.py
index 2a64b77e44a..89ad246ecf9 100644
--- a/ax/core/tests/test_search_space.py
+++ b/ax/core/tests/test_search_space.py
@@ -399,7 +399,7 @@ def setUp(self) -> None:
             "discrete_choices": {1: [0, 1, 2], 2: [0, 0.25, 4.0]},
             "task_features": [3],
             "fidelity_features": [0],
-            "target_fidelities": {0: 1.0},
+            "target_values": {0: 1.0},
             "robust_digest": None,
         }
 
diff --git a/ax/modelbridge/modelbridge_utils.py b/ax/modelbridge/modelbridge_utils.py
index b590f79a9b7..e98a8be497e 100644
--- a/ax/modelbridge/modelbridge_utils.py
+++ b/ax/modelbridge/modelbridge_utils.py
@@ -195,6 +195,7 @@ def extract_search_space_digest(
     * Otherwise, its index is added to categorical_features.
     * In all cases, the choices are added to discrete_choices.
     * The minimum and maximum value are added to the bounds.
+    * The target_value is added to target_values.
 
     For RangeParameters:
     * They're assumed not to be in the log_scale. The Log transform handles this.
@@ -204,7 +205,7 @@ def extract_search_space_digest(
 
     If a parameter is_fidelity:
     * Its target_value is assumed to be numerical.
-    * The target_value is added to target_fidelities.
+    * The target_value is added to target_values.
     * Its index is added to fidelity_features.
     """
     bounds: List[Tuple[Union[int, float], Union[int, float]]] = []
@@ -213,13 +214,14 @@ def extract_search_space_digest(
     discrete_choices: Dict[int, List[Union[int, float]]] = {}
     task_features: List[int] = []
     fidelity_features: List[int] = []
-    target_fidelities: Dict[int, Union[int, float]] = {}
+    target_values: Dict[int, Union[int, float]] = {}
 
     for i, p_name in enumerate(param_names):
         p = search_space.parameters[p_name]
         if isinstance(p, ChoiceParameter):
             if p.is_task:
                 task_features.append(i)
+                target_values[i] = checked_cast_to_tuple((int, float), p.target_value)
             elif p.is_ordered:
                 ordinal_features.append(i)
             else:
@@ -239,10 +241,8 @@ def extract_search_space_digest(
         else:
             raise ValueError(f"Unknown parameter type {type(p)}")
         if p.is_fidelity:
-            if not isinstance(not_none(p.target_value), (int, float)):
-                raise NotImplementedError("Only numerical target values are supported.")
-            target_fidelities[i] = checked_cast_to_tuple((int, float), p.target_value)
             fidelity_features.append(i)
+            target_values[i] = checked_cast_to_tuple((int, float), p.target_value)
 
     return SearchSpaceDigest(
         feature_names=param_names,
@@ -252,7 +252,7 @@ def extract_search_space_digest(
         discrete_choices=discrete_choices,
         task_features=task_features,
         fidelity_features=fidelity_features,
-        target_fidelities=target_fidelities,
+        target_values=target_values,
         robust_digest=extract_robust_digest(
             search_space=search_space, param_names=param_names
         ),
diff --git a/ax/modelbridge/tests/test_torch_modelbridge.py b/ax/modelbridge/tests/test_torch_modelbridge.py
index 880abd46db3..dd5e1fccec5 100644
--- a/ax/modelbridge/tests/test_torch_modelbridge.py
+++ b/ax/modelbridge/tests/test_torch_modelbridge.py
@@ -254,7 +254,7 @@ def test_TorchModelBridge(self, mock_init, dtype=None, device=None) -> None:
         self.assertEqual(gen_opt_config.model_gen_options, {"option": "yes"})
         self.assertIs(gen_opt_config.rounding_func, torch.round)
         self.assertFalse(gen_opt_config.is_moo)
-        self.assertEqual(gen_args["search_space_digest"].target_fidelities, {})
+        self.assertEqual(gen_args["search_space_digest"].target_values, {})
         self.assertEqual(len(gen_run.arms), 1)
         self.assertEqual(gen_run.arms[0].parameters, {"x1": 1.0, "x2": 2.0, "x3": 3.0})
         self.assertEqual(gen_run.weights, [1.0])
diff --git a/ax/models/tests/test_botorch_kg.py b/ax/models/tests/test_botorch_kg.py
index 3a1937ba729..0e01c3ce77b 100644
--- a/ax/models/tests/test_botorch_kg.py
+++ b/ax/models/tests/test_botorch_kg.py
@@ -203,7 +203,7 @@ def test_KnowledgeGradient_multifidelity(self) -> None:
             feature_names=self.feature_names,
             bounds=self.bounds,
             fidelity_features=[2],
-            target_fidelities={2: 5.0},
+            target_values={2: 5.0},
         )
         model = KnowledgeGradient()
         model.fit(
@@ -234,7 +234,7 @@ def test_KnowledgeGradient_multifidelity(self) -> None:
             model.best_point(
                 search_space_digest=dataclasses.replace(
                     search_space_digest,
-                    target_fidelities={},
+                    target_values={},
                 ),
                 torch_opt_config=torch_opt_config,
             )
diff --git a/ax/models/tests/test_botorch_mes.py b/ax/models/tests/test_botorch_mes.py
index 6a12824e21a..3eb579fa9ad 100644
--- a/ax/models/tests/test_botorch_mes.py
+++ b/ax/models/tests/test_botorch_mes.py
@@ -129,7 +129,9 @@ def test_MaxValueEntropySearch(self) -> None:
         with self.assertRaises(RuntimeError):
             model.best_point(
                 search_space_digest=dataclasses.replace(
-                    self.search_space_digest, target_fidelities={2: 1.0}
+                    self.search_space_digest,
+                    fidelity_features=[2],
+                    target_values={2: 1.0},
                 ),
                 torch_opt_config=torch_opt_config,
             )
@@ -175,7 +177,8 @@ def test_MaxValueEntropySearch_MultiFidelity(self) -> None:
         xbest = model.best_point(
             search_space_digest=dataclasses.replace(
                 search_space_digest,
-                target_fidelities={2: 5.0},
+                fidelity_features=[2],
+                target_values={2: 5.0},
             ),
             torch_opt_config=torch_opt_config,
         )
@@ -196,7 +199,7 @@ def test_MaxValueEntropySearch_MultiFidelity(self) -> None:
             model.best_point(
                 search_space_digest=dataclasses.replace(
                     search_space_digest,
-                    target_fidelities={2: 1.0},
+                    target_values={2: 1.0},
                 ),
                 torch_opt_config=dataclasses.replace(
                     torch_opt_config,
@@ -210,7 +213,7 @@ def test_MaxValueEntropySearch_MultiFidelity(self) -> None:
             n=n,
             search_space_digest=dataclasses.replace(
                 search_space_digest,
-                target_fidelities={2: 1.0},
+                target_values={2: 1.0},
             ),
             torch_opt_config=dataclasses.replace(
                 torch_opt_config,
diff --git a/ax/models/tests/test_botorch_model.py b/ax/models/tests/test_botorch_model.py
index 6dd0fc815fb..7b0a30af18d 100644
--- a/ax/models/tests/test_botorch_model.py
+++ b/ax/models/tests/test_botorch_model.py
@@ -468,7 +468,8 @@ def test_BotorchModel(
                     n=n,
                     search_space_digest=dataclasses.replace(
                         search_space_digest,
-                        target_fidelities={0: 3.0},
+                        fidelity_features=[0],
+                        target_values={0: 3.0},
                     ),
                     torch_opt_config=torch_opt_config,
                 )
@@ -500,7 +501,8 @@ def test_BotorchModel(
                 xbest = model.best_point(
                     search_space_digest=dataclasses.replace(
                         search_space_digest,
-                        target_fidelities={0: 3.0},
+                        fidelity_features=[0],
+                        target_values={0: 3.0},
                     ),
                     torch_opt_config=torch_opt_config,
                 )
diff --git a/ax/models/torch/botorch.py b/ax/models/torch/botorch.py
index d482ed86d9c..9b22845d656 100644
--- a/ax/models/torch/botorch.py
+++ b/ax/models/torch/botorch.py
@@ -330,9 +330,9 @@ def gen(
         acf_options = options.get(Keys.ACQF_KWARGS, {})
         optimizer_options = options.get(Keys.OPTIMIZER_KWARGS, {})
 
-        if search_space_digest.target_fidelities:
+        if search_space_digest.fidelity_features:
             raise NotImplementedError(
-                "target_fidelities not implemented for base BotorchModel"
+                "Base BotorchModel does not support fidelity_features."
             )
         X_pending, X_observed = _get_X_pending_and_observed(
             Xs=self.Xs,
@@ -437,6 +437,11 @@ def best_point(
             raise NotImplementedError(
                 "Best observed point is incompatible with MOO problems."
             )
+        target_fidelities = {
+            k: v
+            for k, v in search_space_digest.target_values.items()
+            if k in search_space_digest.fidelity_features
+        }
         return self.best_point_recommender(  # pyre-ignore [28]
             model=self,
             bounds=search_space_digest.bounds,
@@ -445,7 +450,7 @@ def best_point(
             linear_constraints=torch_opt_config.linear_constraints,
             fixed_features=torch_opt_config.fixed_features,
             model_gen_options=torch_opt_config.model_gen_options,
-            target_fidelities=search_space_digest.target_fidelities,
+            target_fidelities=target_fidelities,
         )
 
     @copy_doc(TorchModel.cross_validate)
diff --git a/ax/models/torch/botorch_kg.py b/ax/models/torch/botorch_kg.py
index 02ded019a6c..4209c335e52 100644
--- a/ax/models/torch/botorch_kg.py
+++ b/ax/models/torch/botorch_kg.py
@@ -164,6 +164,11 @@ def gen(
         )
         bounds_ = bounds_.transpose(0, 1)
 
+        target_fidelities = {
+            k: v
+            for k, v in search_space_digest.target_values.items()
+            if k in search_space_digest.fidelity_features
+        }
         # get acquisition function
         acq_function = _instantiate_KG(
             model=model,
@@ -176,7 +181,7 @@ def gen(
             seed_inner=seed_inner,
             seed_outer=acf_options.get("seed_outer", None),
             X_pending=X_pending,
-            target_fidelities=search_space_digest.target_fidelities,
+            target_fidelities=target_fidelities,
             fidelity_weights=options.get("fidelity_weights"),
             current_value=current_value,
             cost_intercept=self.cost_intercept,
@@ -238,6 +243,11 @@ def _get_current_value(
         acquisition function' (typically `PosteriorMean` or `qSimpleRegret`), not of
         the Knowledge Gradient acquisition function.
         """
+        target_fidelities = {
+            k: v
+            for k, v in search_space_digest.target_values.items()
+            if k in search_space_digest.fidelity_features
+        }
         best_point_acqf, non_fixed_idcs = get_out_of_sample_best_point_acqf(
             model=model,
             Xs=self.Xs,
@@ -247,7 +257,7 @@ def _get_current_value(
             seed_inner=seed_inner,
             fixed_features=torch_opt_config.fixed_features,
             fidelity_features=self.fidelity_features,
-            target_fidelities=search_space_digest.target_fidelities,
+            target_fidelities=target_fidelities,
             qmc=qmc,
         )
 
diff --git a/ax/models/torch/botorch_mes.py b/ax/models/torch/botorch_mes.py
index b57a5f99b0e..1431cac75f5 100644
--- a/ax/models/torch/botorch_mes.py
+++ b/ax/models/torch/botorch_mes.py
@@ -130,6 +130,11 @@ def gen(
         candidate_set = torch.rand(candidate_size, bounds_.size(1))
         candidate_set = bounds_[0] + (bounds_[1] - bounds_[0]) * candidate_set
 
+        target_fidelities = {
+            k: v
+            for k, v in search_space_digest.target_values.items()
+            if k in search_space_digest.fidelity_features
+        }
         acq_function = _instantiate_MES(
             model=model,
             candidate_set=candidate_set,
@@ -139,7 +144,7 @@ def gen(
             num_y_samples=num_y_samples,
             X_pending=X_pending,
             maximize=True if objective_weights[0] == 1 else False,
-            target_fidelities=search_space_digest.target_fidelities,
+            target_fidelities=target_fidelities,
             fidelity_weights=options.get("fidelity_weights"),
             cost_intercept=self.cost_intercept,
         )
diff --git a/ax/models/torch/botorch_modular/acquisition.py b/ax/models/torch/botorch_modular/acquisition.py
index 5a077d45f2d..a49388bcdf1 100644
--- a/ax/models/torch/botorch_modular/acquisition.py
+++ b/ax/models/torch/botorch_modular/acquisition.py
@@ -273,7 +273,11 @@ def __init__(
             if len(self.surrogates) > 1
             else {"model": model}
         )
-
+        target_fidelities = {
+            k: v
+            for k, v in search_space_digest.target_values.items()
+            if k in search_space_digest.fidelity_features
+        }
         input_constructor_kwargs = {
             "X_baseline": unique_Xs_observed,
             "X_pending": unique_Xs_pending,
@@ -281,7 +285,7 @@ def __init__(
             "constraints": get_outcome_constraint_transforms(
                 outcome_constraints=outcome_constraints
             ),
-            "target_fidelities": search_space_digest.target_fidelities,
+            "target_fidelities": target_fidelities,
             "bounds": search_space_digest.bounds,
             **acqf_model_kwarg,
             **model_deps,
diff --git a/ax/models/torch/botorch_modular/model.py b/ax/models/torch/botorch_modular/model.py
index 55e28889fcd..926c5c9ad9d 100644
--- a/ax/models/torch/botorch_modular/model.py
+++ b/ax/models/torch/botorch_modular/model.py
@@ -443,11 +443,11 @@ def gen(
             acqf_options=self.acquisition_options,
             model_gen_options=torch_opt_config.model_gen_options,
         )
-        # update bounds / target fidelities
+        # update bounds / target values
         search_space_digest = dataclasses.replace(
             self.search_space_digest,
             bounds=search_space_digest.bounds,
-            target_fidelities=search_space_digest.target_fidelities or {},
+            target_values=search_space_digest.target_values or {},
         )
 
         acqf = self._instantiate_acquisition(
diff --git a/ax/models/torch/botorch_modular/multi_fidelity.py b/ax/models/torch/botorch_modular/multi_fidelity.py
index 9ebe6d3149f..c532ef35e35 100644
--- a/ax/models/torch/botorch_modular/multi_fidelity.py
+++ b/ax/models/torch/botorch_modular/multi_fidelity.py
@@ -36,7 +36,11 @@ def compute_model_dependencies(
             raise UnsupportedError(
                 f"{self.__class__.__name__} does not support risk measures."
             )
-        target_fidelities = search_space_digest.target_fidelities
+        target_fidelities = {
+            k: v
+            for k, v in search_space_digest.target_values.items()
+            if k in search_space_digest.fidelity_features
+        }
         if not target_fidelities:
             raise ValueError(
                 "Target fidelities are required for {self.__class__.__name__}."
diff --git a/ax/models/torch/botorch_moo.py b/ax/models/torch/botorch_moo.py
index a320aeaa1ba..aaea00a74bd 100644
--- a/ax/models/torch/botorch_moo.py
+++ b/ax/models/torch/botorch_moo.py
@@ -246,9 +246,9 @@ def gen(
         acf_options = options.get("acquisition_function_kwargs", {})
         optimizer_options = options.get("optimizer_kwargs", {})
 
-        if search_space_digest.target_fidelities:  # untested
+        if search_space_digest.fidelity_features:  # untested
             raise NotImplementedError(
-                "target_fidelities not implemented for base BotorchModel"
+                "fidelity_features not implemented for base BotorchModel"
             )
         if (
             torch_opt_config.objective_thresholds is not None
diff --git a/ax/models/torch/tests/test_acquisition.py b/ax/models/torch/tests/test_acquisition.py
index 92ce96ee091..58b6d5db3ce 100644
--- a/ax/models/torch/tests/test_acquisition.py
+++ b/ax/models/torch/tests/test_acquisition.py
@@ -117,7 +117,7 @@ def setUp(self) -> None:
         self.search_space_digest = SearchSpaceDigest(
             feature_names=self.feature_names,
             bounds=[(0.0, 10.0), (0.0, 10.0), (0.0, 10.0)],
-            target_fidelities={2: 1.0},
+            target_values={2: 1.0},
         )
         self.surrogate.construct(
             datasets=self.training_data,
@@ -126,7 +126,7 @@ def setUp(self) -> None:
             search_space_digest=SearchSpaceDigest(
                 feature_names=self.search_space_digest.feature_names[:1],
                 bounds=self.search_space_digest.bounds,
-                target_fidelities=self.search_space_digest.target_fidelities,
+                target_values=self.search_space_digest.target_values,
             ),
         )
 
diff --git a/ax/models/torch/tests/test_input_transform_argparse.py b/ax/models/torch/tests/test_input_transform_argparse.py
index 9e7ddfac027..360484b40ae 100644
--- a/ax/models/torch/tests/test_input_transform_argparse.py
+++ b/ax/models/torch/tests/test_input_transform_argparse.py
@@ -48,7 +48,7 @@ def setUp(self) -> None:
             discrete_choices={1: [0, 1, 2], 2: [0, 0.25, 4.0]},
             task_features=[3],
             fidelity_features=[0],
-            target_fidelities={0: 1.0},
+            target_values={0: 1.0},
             robust_digest=None,
         )
 
diff --git a/ax/models/torch/tests/test_model.py b/ax/models/torch/tests/test_model.py
index 8a640cc6562..25aa9d3b6be 100644
--- a/ax/models/torch/tests/test_model.py
+++ b/ax/models/torch/tests/test_model.py
@@ -123,7 +123,7 @@ def setUp(self) -> None:
             bounds=[(0.0, 10.0), (0.0, 10.0), (0.0, 10.0)],
             task_features=[],
             fidelity_features=[2],
-            target_fidelities={1: 1.0},
+            target_values={1: 1.0},
         )
         self.metric_names = ["y"]
         self.metric_names_for_list_surrogate = ["y1", "y2"]
diff --git a/ax/models/torch/tests/test_multi_fidelity.py b/ax/models/torch/tests/test_multi_fidelity.py
index 86dc8bb58b8..1a976e89a5d 100644
--- a/ax/models/torch/tests/test_multi_fidelity.py
+++ b/ax/models/torch/tests/test_multi_fidelity.py
@@ -48,7 +48,7 @@ def setUp(self) -> None:
         self.search_space_digest = SearchSpaceDigest(
             feature_names=self.feature_names,
             bounds=[(0.0, 10.0), (0.0, 10.0), (0.0, 10.0)],
-            target_fidelities={2: 1.0},
+            target_values={2: 1.0},
             fidelity_features=self.fidelity_features,
         )
         self.surrogate.construct(
@@ -120,7 +120,9 @@ def test_compute_model_dependencies(
             mf_acquisition.compute_model_dependencies(
                 surrogates={"regression": self.surrogate},
                 search_space_digest=dataclasses.replace(
-                    self.search_space_digest, target_fidelities={1: 5.0}
+                    self.search_space_digest,
+                    fidelity_features=[1],
+                    target_values={1: 5.0},
                 ),
                 torch_opt_config=self.torch_opt_config,
                 options=self.options,
@@ -129,7 +131,9 @@ def test_compute_model_dependencies(
         mf_acquisition.compute_model_dependencies(
             surrogates={"regression": self.surrogate},
             search_space_digest=dataclasses.replace(
-                self.search_space_digest, target_fidelities={2: 5.0, 3: 5.0}
+                self.search_space_digest,
+                fidelity_features=[2, 3],
+                target_values={2: 5.0, 3: 5.0},
             ),
             torch_opt_config=self.torch_opt_config,
             options={Keys.COST_INTERCEPT: 1.0, Keys.NUM_TRACE_OBSERVATIONS: 0},
@@ -163,12 +167,12 @@ def test_compute_model_dependencies(
         project(torch.tensor([1.0]))
         mock_project.assert_called_with(
             X=torch.tensor([1.0]),
-            target_fidelities=self.search_space_digest.target_fidelities,
+            target_fidelities=self.search_space_digest.target_values,
         )
         expand = dependencies.get(Keys.EXPAND)
         expand(torch.tensor([1.0]))
         mock_expand.assert_called_with(
             X=torch.tensor([1.0]),
-            fidelity_dims=sorted(self.search_space_digest.target_fidelities),
+            fidelity_dims=sorted(self.search_space_digest.target_values),
             num_trace_obs=self.options.get(Keys.NUM_TRACE_OBSERVATIONS),
         )
diff --git a/ax/models/torch/tests/test_sebo.py b/ax/models/torch/tests/test_sebo.py
index 09005e73430..c83fb3bfd77 100644
--- a/ax/models/torch/tests/test_sebo.py
+++ b/ax/models/torch/tests/test_sebo.py
@@ -58,7 +58,7 @@ def setUp(self) -> None:
         self.search_space_digest = SearchSpaceDigest(
             feature_names=["a", "b", "c"],
             bounds=[(0.0, 10.0), (0.0, 10.0), (0.0, 10.0)],
-            target_fidelities={2: 1.0},
+            target_values={2: 1.0},
         )
         self.surrogates.construct(
             datasets=self.training_data,
diff --git a/ax/models/torch/tests/test_surrogate.py b/ax/models/torch/tests/test_surrogate.py
index 4c0d5f0ff05..48fc788c3d6 100644
--- a/ax/models/torch/tests/test_surrogate.py
+++ b/ax/models/torch/tests/test_surrogate.py
@@ -92,7 +92,7 @@ def setUp(self) -> None:
         self.search_space_digest = SearchSpaceDigest(
             feature_names=["x1", "x2"],
             bounds=self.bounds,
-            target_fidelities={1: 1.0},
+            target_values={1: 1.0},
         )
         self.fixed_features = {1: 2.0}
         self.refit = True