diff --git a/ax/core/batch_trial.py b/ax/core/batch_trial.py
index 985e57ca6c7..3b75293400b 100644
--- a/ax/core/batch_trial.py
+++ b/ax/core/batch_trial.py
@@ -482,10 +482,7 @@ def is_factorial(self) -> bool:
         param_levels: DefaultDict[str, Dict[Union[str, float], int]] = defaultdict(dict)
         for arm in self.arms:
             for param_name, param_value in arm.parameters.items():
-                # Expected `Union[float, str]` for 2nd anonymous parameter to call
-                # `dict.__setitem__` but got `Optional[Union[bool, float, str]]`.
-                # pyre-fixme[6]: Expected `Union[float, str]` for 1st param but got `...
-                param_levels[param_name][param_value] = 1
+                param_levels[param_name][not_none(param_value)] = 1
         param_cardinality = 1
         for param_values in param_levels.values():
             param_cardinality *= len(param_values)
diff --git a/ax/core/parameter.py b/ax/core/parameter.py
index 7b1c59422df..94d6104fa78 100644
--- a/ax/core/parameter.py
+++ b/ax/core/parameter.py
@@ -12,13 +12,14 @@
 from copy import deepcopy
 from enum import Enum
 from math import inf
-from typing import Dict, List, Optional, Tuple, Type, Union
+from typing import cast, Dict, List, Optional, Tuple, Type, Union
 from warnings import warn
 
-from ax.core.types import TParamValue, TParamValueList
+from ax.core.types import TNumeric, TParamValue, TParamValueList
 from ax.exceptions.core import AxWarning, UserInputError
 from ax.utils.common.base import SortableBase
 from ax.utils.common.typeutils import not_none
+from pyre_extensions import assert_is_instance
 
 # Tolerance for floating point comparisons. This is relatively permissive,
 # and allows for serializing at rather low numerical precision.
@@ -81,7 +82,7 @@ def _get_parameter_type(python_type: Type) -> ParameterType:
 class Parameter(SortableBase, metaclass=ABCMeta):
     _is_fidelity: bool = False
     _name: str
-    _target_value: Optional[TParamValue] = None
+    _target_value: TParamValue = None
     _parameter_type: ParameterType
 
     def cast(self, value: TParamValue) -> TParamValue:
@@ -125,7 +126,7 @@ def is_hierarchical(self) -> bool:
         )
 
     @property
-    def target_value(self) -> Optional[TParamValue]:
+    def target_value(self) -> TParamValue:
         return self._target_value
 
     @property
@@ -234,7 +235,7 @@ def __init__(
         logit_scale: bool = False,
         digits: Optional[int] = None,
         is_fidelity: bool = False,
-        target_value: Optional[TParamValue] = None,
+        target_value: TParamValue = None,
     ) -> None:
         """Initialize RangeParameter
 
@@ -259,17 +260,16 @@ def __init__(
             )
 
         self._name = name
+        if parameter_type not in (ParameterType.INT, ParameterType.FLOAT):
+            raise UserInputError("RangeParameter type must be int or float.")
         self._parameter_type = parameter_type
         self._digits = digits
-        # pyre-fixme[4]: Attribute must be annotated.
-        self._lower = self.cast(lower)
-        # pyre-fixme[4]: Attribute must be annotated.
-        self._upper = self.cast(upper)
+        self._lower: TNumeric = not_none(self.cast(lower))
+        self._upper: TNumeric = not_none(self.cast(upper))
         self._log_scale = log_scale
         self._logit_scale = logit_scale
         self._is_fidelity = is_fidelity
-        # pyre-fixme[4]: Attribute must be annotated.
-        self._target_value = self.cast(target_value)
+        self._target_value: Optional[TNumeric] = self.cast(target_value)
 
         self._validate_range_param(
             parameter_type=parameter_type,
@@ -279,16 +279,16 @@ def __init__(
             logit_scale=logit_scale,
         )
 
-    def cardinality(self) -> float:
+    def cardinality(self) -> TNumeric:
         if self.parameter_type == ParameterType.FLOAT:
             return inf
 
-        return self.upper - self.lower + 1
+        return int(self.upper) - int(self.lower) + 1
 
     def _validate_range_param(
         self,
-        lower: TParamValue,
-        upper: TParamValue,
+        lower: TNumeric,
+        upper: TNumeric,
         log_scale: bool,
         logit_scale: bool,
         parameter_type: Optional[ParameterType] = None,
@@ -298,15 +298,13 @@ def _validate_range_param(
             ParameterType.FLOAT,
         ):
             raise UserInputError("RangeParameter type must be int or float.")
-        # pyre-fixme[58]: `>=` is not supported for operand types `Union[None, bool,
-        #  float, int, str]` and `Union[None, bool, float, int, str]`.
+
+        upper = float(upper)
         if lower >= upper:
             raise UserInputError(
                 f"Upper bound of {self.name} must be strictly larger than lower."
                 f"Got: ({lower}, {upper})."
             )
-        # pyre-fixme[58]: `-` is not supported for operand types `Union[None, bool,
-        #  float, int, str]` and `Union[None, bool, float, int, str]`.
         width: float = upper - lower
         if width < 100 * EPS:
             raise UserInputError(
@@ -316,12 +314,8 @@ def _validate_range_param(
             )
         if log_scale and logit_scale:
             raise UserInputError("Can't use both log and logit.")
-        # pyre-fixme[58]: `<=` is not supported for operand types `Union[None, bool,
-        #  float, int, str]` and `int`.
         if log_scale and lower <= 0:
             raise UserInputError("Cannot take log when min <= 0.")
-        # pyre-fixme[58]: `<=` is not supported for operand types `Union[None, bool,
-        #  float, int, str]` and `int`.
         if logit_scale and (lower <= 0 or upper >= 1):
             raise UserInputError("Logit requires lower > 0 and upper < 1")
         if not (self.is_valid_type(lower)) or not (self.is_valid_type(upper)):
@@ -330,7 +324,7 @@ def _validate_range_param(
             )
 
     @property
-    def upper(self) -> float:
+    def upper(self) -> TNumeric:
         """Upper bound of the parameter range.
 
         Value is cast to parameter type upon set and also validated
@@ -338,8 +332,18 @@ def upper(self) -> float:
         """
         return self._upper
 
+    @upper.setter
+    def upper(self, value: TNumeric) -> None:
+        self._validate_range_param(
+            lower=self.lower,
+            upper=value,
+            log_scale=self.log_scale,
+            logit_scale=self.logit_scale,
+        )
+        self._upper = not_none(self.cast(value))
+
     @property
-    def lower(self) -> float:
+    def lower(self) -> TNumeric:
         """Lower bound of the parameter range.
 
         Value is cast to parameter type upon set and also validated
@@ -347,6 +351,16 @@ def lower(self) -> float:
         """
         return self._lower
 
+    @lower.setter
+    def lower(self, value: TNumeric) -> None:
+        self._validate_range_param(
+            lower=value,
+            upper=self.upper,
+            log_scale=self.log_scale,
+            logit_scale=self.logit_scale,
+        )
+        self._lower = not_none(self.cast(value))
+
     @property
     def digits(self) -> Optional[int]:
         """Number of digits to round values to for float type.
@@ -381,8 +395,8 @@ def update_range(
         if upper is None:
             upper = self._upper
 
-        cast_lower = self.cast(lower)
-        cast_upper = self.cast(upper)
+        cast_lower = not_none(self.cast(lower))
+        cast_upper = not_none(self.cast(upper))
         self._validate_range_param(
             lower=cast_lower,
             upper=cast_upper,
@@ -397,10 +411,8 @@ def set_digits(self, digits: int) -> RangeParameter:
         self._digits = digits
 
         # Re-scale min and max to new digits definition
-        cast_lower = self.cast(self._lower)
-        cast_upper = self.cast(self._upper)
-        # pyre-fixme[58]: `>=` is not supported for operand types `Union[None, bool,
-        #  float, int, str]` and `Union[None, bool, float, int, str]`.
+        cast_lower = not_none(self.cast(self._lower))
+        cast_upper = not_none(self.cast(self._upper))
         if cast_lower >= cast_upper:
             raise UserInputError(
                 f"Lower bound {cast_lower} is >= upper bound {cast_upper}."
@@ -451,9 +463,7 @@ def is_valid_type(self, value: TParamValue) -> bool:
 
         # This might have issues with ints > 2^24
         if self.parameter_type is ParameterType.INT:
-            # pyre-fixme[6]: Expected `Union[_SupportsIndex, bytearray, bytes, str,
-            #  typing.SupportsFloat]` for 1st param but got `Union[None, float, str]`.
-            return isinstance(value, int) or float(value).is_integer()
+            return isinstance(value, int) or float(not_none(value)).is_integer()
         return True
 
     def clone(self) -> RangeParameter:
@@ -469,13 +479,12 @@ def clone(self) -> RangeParameter:
             target_value=self._target_value,
         )
 
-    def cast(self, value: TParamValue) -> TParamValue:
+    def cast(self, value: TParamValue) -> Optional[TNumeric]:
         if value is None:
             return None
         if self.parameter_type is ParameterType.FLOAT and self._digits is not None:
-            # pyre-fixme[6]: Expected `None` for 2nd param but got `Optional[int]`.
-            return round(float(value), self._digits)
-        return self.python_type(value)
+            return round(float(value), not_none(self._digits))
+        return assert_is_instance(self.python_type(value), TNumeric)
 
     def __repr__(self) -> str:
         ret_val = self._base_repr()
@@ -526,7 +535,7 @@ def __init__(
         is_ordered: Optional[bool] = None,
         is_task: bool = False,
         is_fidelity: bool = False,
-        target_value: Optional[TParamValue] = None,
+        target_value: TParamValue = None,
         sort_values: Optional[bool] = None,
         dependents: Optional[Dict[TParamValue, List[str]]] = None,
     ) -> None:
@@ -561,9 +570,8 @@ def __init__(
                 stacklevel=2,
             )
             values = list(dict_values)
-        self._values: List[TParamValue] = self._cast_values(values)
-        # pyre-fixme[4]: Attribute must be annotated.
-        self._is_ordered = (
+
+        self._is_ordered: bool = (
             is_ordered
             if is_ordered is not None
             else self._get_default_bool_and_warn(param_string="is_ordered")
@@ -575,11 +583,9 @@ def __init__(
             else self._get_default_bool_and_warn(param_string="sort_values")
         )
         if self.sort_values:
-            # pyre-ignore[6]: values/self._values expects List[Union[None, bool, float,
-            # int, str]] but sorted() takes/returns
-            # List[Variable[_typeshed.SupportsLessThanT (bound to
-            # _typeshed.SupportsLessThan)]]
-            self._values = self._cast_values(sorted(values))
+            values = cast(List[TParamValue], sorted([not_none(v) for v in values]))
+        self._values: List[TParamValue] = self._cast_values(values)
+
         if dependents:
             for value in dependents:
                 if value not in self.values:
@@ -714,7 +720,7 @@ def __init__(
         parameter_type: ParameterType,
         value: TParamValue,
         is_fidelity: bool = False,
-        target_value: Optional[TParamValue] = None,
+        target_value: TParamValue = None,
         dependents: Optional[Dict[TParamValue, List[str]]] = None,
     ) -> None:
         """Initialize FixedParameter
@@ -737,11 +743,9 @@ def __init__(
 
         self._name = name
         self._parameter_type = parameter_type
-        # pyre-fixme[4]: Attribute must be annotated.
-        self._value = self.cast(value)
+        self._value: TParamValue = self.cast(value)
         self._is_fidelity = is_fidelity
-        # pyre-fixme[4]: Attribute must be annotated.
-        self._target_value = self.cast(target_value)
+        self._target_value: TParamValue = self.cast(target_value)
         # NOTE: We don't need to check that dependent parameters actually exist as
         # that is done in `HierarchicalSearchSpace` constructor.
         if dependents:
diff --git a/ax/core/parameter_constraint.py b/ax/core/parameter_constraint.py
index f22a739db44..1c5f3f0f82f 100644
--- a/ax/core/parameter_constraint.py
+++ b/ax/core/parameter_constraint.py
@@ -21,11 +21,10 @@ class ParameterConstraint(SortableBase):
     Constraints are expressed using a map from parameter name to weight
     followed by a bound.
 
-    The constraint is satisfied if w * v <= b where:
+    The constraint is satisfied if sum_i(w_i * v_i) <= b where:
         w is the vector of parameter weights.
         v is a vector of parameter values.
         b is the specified bound.
-        * is the dot product operator.
     """
 
     def __init__(self, constraint_dict: Dict[str, float], bound: float) -> None:
diff --git a/ax/core/search_space.py b/ax/core/search_space.py
index 99d67602a8c..be4d9cc72e6 100644
--- a/ax/core/search_space.py
+++ b/ax/core/search_space.py
@@ -238,8 +238,7 @@ def check_membership(
 
         # parameter constraints only accept numeric parameters
         numerical_param_dict = {
-            # pyre-fixme[6]: Expected `typing.Union[...oat]` but got `unknown`.
-            name: float(value)
+            name: float(not_none(value))
             for name, value in parameterization.items()
             if self.parameters[name].is_numeric
         }
@@ -544,7 +543,8 @@ def flatten_observation_features(
         # that behavior was requested via the opt-in flag.
         warnings.warn(
             f"Cannot flatten observation features {obs_feats} as full "
-            "parameterization is not recorded in metadata."
+            "parameterization is not recorded in metadata.",
+            stacklevel=2,
         )
         return obs_feats
 
diff --git a/ax/core/tests/test_parameter.py b/ax/core/tests/test_parameter.py
index 2cae278ad89..d9ea6227f12 100644
--- a/ax/core/tests/test_parameter.py
+++ b/ax/core/tests/test_parameter.py
@@ -6,6 +6,8 @@
 
 # pyre-strict
 
+from typing import cast, List
+
 from ax.core.parameter import (
     _get_parameter_type,
     ChoiceParameter,
@@ -299,7 +301,7 @@ def test_Properties(self) -> None:
         )
         self.assertTrue(int_param.is_ordered)
         self.assertListEqual(
-            int_param.values, sorted(int_param.values)  # pyre-fixme[6]
+            int_param.values, sorted(cast(List[int], int_param.values))
         )
         float_param = ChoiceParameter(
             name="x", parameter_type=ParameterType.FLOAT, values=[1.5, 2.5, 3.5]
diff --git a/ax/modelbridge/dispatch_utils.py b/ax/modelbridge/dispatch_utils.py
index 548c5ae552f..21a6cb06f7f 100644
--- a/ax/modelbridge/dispatch_utils.py
+++ b/ax/modelbridge/dispatch_utils.py
@@ -189,7 +189,7 @@ def _suggest_gp_model(
             if parameter.parameter_type == ParameterType.FLOAT:
                 all_range_parameters_are_discrete = False
             else:
-                num_param_discrete_values = int(parameter.upper - parameter.lower) + 1
+                num_param_discrete_values = parameter.cardinality()
                 num_possible_points *= num_param_discrete_values
 
         if should_enumerate_param:
diff --git a/ax/modelbridge/transforms/int_range_to_choice.py b/ax/modelbridge/transforms/int_range_to_choice.py
index c94b152e79d..04d07ac80d4 100644
--- a/ax/modelbridge/transforms/int_range_to_choice.py
+++ b/ax/modelbridge/transforms/int_range_to_choice.py
@@ -6,7 +6,8 @@
 
 # pyre-strict
 
-from typing import Dict, List, Optional, Set, TYPE_CHECKING
+from numbers import Real
+from typing import cast, Dict, List, Optional, Set, TYPE_CHECKING
 
 from ax.core.observation import Observation
 from ax.core.parameter import ChoiceParameter, Parameter, ParameterType, RangeParameter
@@ -35,14 +36,16 @@ def __init__(
     ) -> None:
         assert search_space is not None, "IntRangeToChoice requires search space"
         config = config or {}
-        self.max_choices: float = config.get("max_choices", float("inf"))  # pyre-ignore
+        self.max_choices: float = float(
+            cast(Real, (config.get("max_choices", float("inf"))))
+        )
         # Identify parameters that should be transformed
         self.transform_parameters: Set[str] = {
             p_name
             for p_name, p in search_space.parameters.items()
             if isinstance(p, RangeParameter)
             and p.parameter_type == ParameterType.INT
-            and p.upper - p.lower + 1 <= self.max_choices
+            and p.cardinality() <= self.max_choices
         }
 
     def _transform_search_space(self, search_space: SearchSpace) -> SearchSpace:
@@ -52,9 +55,9 @@ def _transform_search_space(self, search_space: SearchSpace) -> SearchSpace:
                 p_name in self.transform_parameters
                 and isinstance(p, RangeParameter)
                 and p.parameter_type == ParameterType.INT
-                and p.upper - p.lower + 1 <= self.max_choices
+                and p.cardinality() <= self.max_choices
             ):
-                values = list(range(p.lower, p.upper + 1))  # pyre-ignore
+                values = list(range(int(p.lower), int(p.upper) + 1))
                 target_value = (
                     None
                     if p.target_value is None
diff --git a/ax/modelbridge/transforms/int_to_float.py b/ax/modelbridge/transforms/int_to_float.py
index 9b1bf746581..ccdaadb3c4c 100644
--- a/ax/modelbridge/transforms/int_to_float.py
+++ b/ax/modelbridge/transforms/int_to_float.py
@@ -69,7 +69,7 @@ def __init__(
             for p_name, p in self.search_space.parameters.items()
             if isinstance(p, RangeParameter)
             and p.parameter_type == ParameterType.INT
-            and (p.upper - p.lower + 1 >= self.min_choices or p.log_scale)
+            and ((p.cardinality() >= self.min_choices) or p.log_scale)
         }
         if contains_constrained_integer(self.search_space, self.transform_parameters):
             self.rounding = "randomized"
diff --git a/ax/plot/helper.py b/ax/plot/helper.py
index e8a5cef2a4f..f49b07087ff 100644
--- a/ax/plot/helper.py
+++ b/ax/plot/helper.py
@@ -15,13 +15,7 @@
 import numpy as np
 from ax.core.generator_run import GeneratorRun
 from ax.core.observation import Observation, ObservationFeatures
-from ax.core.parameter import (
-    ChoiceParameter,
-    FixedParameter,
-    Parameter,
-    ParameterType,
-    RangeParameter,
-)
+from ax.core.parameter import ChoiceParameter, FixedParameter, Parameter, RangeParameter
 from ax.core.types import TParameterization
 from ax.modelbridge.base import ModelBridge
 from ax.modelbridge.prediction_utils import (
@@ -444,10 +438,7 @@ def get_range_parameters_from_list(
         parameter
         for parameter in parameters
         if isinstance(parameter, RangeParameter)
-        and (
-            parameter.parameter_type == ParameterType.FLOAT
-            or parameter.upper - parameter.lower + 1 >= min_num_values
-        )
+        and parameter.cardinality() >= min_num_values  # float has inf cardinality
     ]
 
 
diff --git a/ax/telemetry/experiment.py b/ax/telemetry/experiment.py
index 637e8ff06ab..eaba3902d04 100644
--- a/ax/telemetry/experiment.py
+++ b/ax/telemetry/experiment.py
@@ -181,7 +181,7 @@ def _get_param_counts_from_search_space(
                 isinstance(param, RangeParameter)
                 or (isinstance(param, ChoiceParameter) and param.is_ordered)
             )
-            and (1 < param.cardinality() <= 3)
+            and (1.0 < param.cardinality() <= 3.0)
         )
         num_int_range_parameters_medium = sum(
             1
@@ -190,7 +190,7 @@ def _get_param_counts_from_search_space(
                 isinstance(param, RangeParameter)
                 or (isinstance(param, ChoiceParameter) and param.is_ordered)
             )
-            and (3 < param.cardinality() <= 7)
+            and (3.0 < param.cardinality() <= 7.0)
         )
         num_int_range_parameters_large = sum(
             1
@@ -199,7 +199,7 @@ def _get_param_counts_from_search_space(
                 isinstance(param, RangeParameter)
                 or (isinstance(param, ChoiceParameter) and param.is_ordered)
             )
-            and (7 < param.cardinality() < inf)
+            and (7.0 < param.cardinality() < inf)
         )
         num_log_scale_range_parameters = sum(
             1
diff --git a/ax/utils/testing/core_stubs.py b/ax/utils/testing/core_stubs.py
index 8ce79c9ea33..37343452497 100644
--- a/ax/utils/testing/core_stubs.py
+++ b/ax/utils/testing/core_stubs.py
@@ -1978,8 +1978,8 @@ def get_branin_data(
                 "metric_name": "branin",
                 "arm_name": not_none(checked_cast(Trial, trial).arm).name,
                 "mean": branin(
-                    float(not_none(trial.arm).parameters["x1"]),  # pyre-ignore[6]
-                    float(not_none(trial.arm).parameters["x2"]),  # pyre-ignore[6]
+                    float(not_none(not_none(trial.arm).parameters["x1"])),
+                    float(not_none(not_none(trial.arm).parameters["x2"])),
                 ),
                 "sem": 0.0,
             }
@@ -2007,9 +2007,10 @@ def get_branin_data_batch(batch: BatchTrial) -> Data:
                 "arm_name": [arm.name for arm in batch.arms],
                 "metric_name": "branin",
                 "mean": [
-                    # pyre-ignore[6]: This function can fail if a parameter value
-                    # does not support conversion to float.
-                    branin(float(arm.parameters["x1"]), float(arm.parameters["x2"]))
+                    branin(
+                        float(not_none(arm.parameters["x1"])),
+                        float(not_none(arm.parameters["x2"])),
+                    )
                     for arm in batch.arms
                 ],
                 "sem": 0.1,
diff --git a/ax/utils/testing/modeling_stubs.py b/ax/utils/testing/modeling_stubs.py
index b070ac6876a..89efeb06e48 100644
--- a/ax/utils/testing/modeling_stubs.py
+++ b/ax/utils/testing/modeling_stubs.py
@@ -506,7 +506,8 @@ def transform_search_space(self, search_space: SearchSpace) -> SearchSpace:
         new_ss = search_space.clone()
         for param in new_ss.parameters.values():
             if isinstance(param, FixedParameter):
-                param._value += 1.0
+                if param._value is not None and not isinstance(param._value, str):
+                    param._value += 1.0
             elif isinstance(param, RangeParameter):
                 param._lower += 1.0
                 param._upper += 1.0
@@ -564,7 +565,8 @@ def transform_search_space(self, search_space: SearchSpace) -> SearchSpace:
         new_ss = search_space.clone()
         for param in new_ss.parameters.values():
             if isinstance(param, FixedParameter):
-                param._value *= 2.0
+                if param._value is not None and not isinstance(param._value, str):
+                    param._value *= 2.0
             elif isinstance(param, RangeParameter):
                 param._lower *= 2.0
                 param._upper *= 2.0