diff --git a/ax/benchmark/benchmark_test_functions/synthetic.py b/ax/benchmark/benchmark_test_functions/synthetic.py
new file mode 100644
index 00000000000..2ec86a5f299
--- /dev/null
+++ b/ax/benchmark/benchmark_test_functions/synthetic.py
@@ -0,0 +1,36 @@
+#!/usr/bin/env python3
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
+
+# pyre-strict
+
+from collections.abc import Mapping, Sequence
+from dataclasses import dataclass, field
+
+import torch
+from ax.benchmark.benchmark_test_function import BenchmarkTestFunction
+
+
+@dataclass(kw_only=True)
+class IdentityTestFunction(BenchmarkTestFunction):
+    """
+    Test function that returns the value of parameter "x0", ignoring any others.
+    """
+
+    outcome_names: Sequence[str] = field(default_factory=lambda: ["objective"])
+    n_steps: int = 1
+
+    # pyre-fixme[14]: Inconsistent override
+    def evaluate_true(self, params: Mapping[str, float]) -> torch.Tensor:
+        """
+        Return params["x0"] for each outcome for each time step.
+
+        Args:
+            params: A dictionary with key "x0".
+        """
+        value = params["x0"]
+        return torch.full(
+            (len(self.outcome_names), self.n_steps), value, dtype=torch.float64
+        )
diff --git a/ax/benchmark/problems/registry.py b/ax/benchmark/problems/registry.py
index 6b0913e70e7..51f6c6e009b 100644
--- a/ax/benchmark/problems/registry.py
+++ b/ax/benchmark/problems/registry.py
@@ -16,6 +16,7 @@
     get_pytorch_cnn_torchvision_benchmark_problem,
 )
 from ax.benchmark.problems.runtime_funcs import int_from_params
+from ax.benchmark.problems.synthetic.bandit import get_bandit_problem
 from ax.benchmark.problems.synthetic.discretized.mixed_integer import (
     get_discrete_ackley,
     get_discrete_hartmann,
@@ -55,6 +56,9 @@ class BenchmarkProblemRegistryEntry:
             "name": "ackley4_async_noisy",
         },
     ),
+    "Bandit": BenchmarkProblemRegistryEntry(
+        factory_fn=get_bandit_problem, factory_kwargs={}
+    ),
     "branin": BenchmarkProblemRegistryEntry(
         factory_fn=create_problem_from_botorch,
         factory_kwargs={
diff --git a/ax/benchmark/problems/synthetic/bandit.py b/ax/benchmark/problems/synthetic/bandit.py
new file mode 100644
index 00000000000..a12419fdc40
--- /dev/null
+++ b/ax/benchmark/problems/synthetic/bandit.py
@@ -0,0 +1,78 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
+
+# pyre-strict
+
+from warnings import warn
+
+import numpy as np
+
+from ax.benchmark.benchmark_problem import BenchmarkProblem, get_soo_opt_config
+from ax.benchmark.benchmark_test_functions.synthetic import IdentityTestFunction
+from ax.core.parameter import ChoiceParameter, ParameterType
+from ax.core.search_space import SearchSpace
+
+
+def get_baseline(num_choices: int, n_sims: int = 100000000) -> float:
+    """
+    Compute the baseline value.
+
+    The baseline for this problem takes into account noise, because it uses the
+    inference trace, and the bandit structure, which allows for running all arms
+    in one noisy batch:
+
+    Run a BatchTrial with every arm, with equal size.  Choose the arm with the
+    best observed value and take its true value.  Take the expectation of the
+    outcome of this process.
+    """
+    noise_per_arm = num_choices**0.5
+    sim_observed_effects = (
+        np.random.normal(0, noise_per_arm, (n_sims, num_choices))
+        + np.arange(num_choices)[None, :]
+    )
+    identified_best_arm = sim_observed_effects.argmin(axis=1)
+    # because of the use of IdentityTestFunction
+    baseline = identified_best_arm.mean()
+    return baseline
+
+
+def get_bandit_problem(num_choices: int = 30, num_trials: int = 3) -> BenchmarkProblem:
+    parameter = ChoiceParameter(
+        name="x0",
+        parameter_type=ParameterType.INT,
+        values=list(range(num_choices)),
+        is_ordered=False,
+        sort_values=False,
+    )
+    search_space = SearchSpace(parameters=[parameter])
+    test_function = IdentityTestFunction()
+    optimization_config = get_soo_opt_config(
+        outcome_names=test_function.outcome_names, observe_noise_sd=True
+    )
+    baselines = {
+        10: 1.40736478,
+        30: 2.4716703,
+        100: 4.403284,
+    }
+    if num_choices not in baselines:
+        warn(
+            f"Baseline value is not available for num_choices={num_choices}. Use "
+            "`get_baseline` to compute the baseline and add it to `baselines`."
+        )
+        baseline_value = baselines[30]
+    else:
+        baseline_value = baselines[num_choices]
+    return BenchmarkProblem(
+        name="Bandit",
+        num_trials=num_trials,
+        search_space=search_space,
+        optimization_config=optimization_config,
+        optimal_value=0,
+        baseline_value=baseline_value,
+        test_function=test_function,
+        report_inference_value_as_trace=True,
+        noise_std=1.0,
+        status_quo_params={"x0": num_choices // 2},
+    )
diff --git a/ax/benchmark/tests/problems/synthetic/test_bandit.py b/ax/benchmark/tests/problems/synthetic/test_bandit.py
new file mode 100644
index 00000000000..cb49345470a
--- /dev/null
+++ b/ax/benchmark/tests/problems/synthetic/test_bandit.py
@@ -0,0 +1,36 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
+
+# pyre-strict
+
+from ax.benchmark.problems.synthetic.bandit import get_bandit_problem, get_baseline
+from ax.utils.common.testutils import TestCase
+
+
+class TestProblems(TestCase):
+    def test_get_baseline(self) -> None:
+        num_choices = 5
+        baseline = get_baseline(num_choices=num_choices, n_sims=100)
+        self.assertGreater(baseline, 0)
+        # Worst = num_choices - 1; random guessing = (num_choices - 1) / 2
+        self.assertLess(baseline, (num_choices - 1) / 2)
+
+    def test_get_bandit_problem(self) -> None:
+        problem = get_bandit_problem()
+        self.assertEqual(problem.name, "Bandit")
+        self.assertEqual(problem.num_trials, 3)
+        self.assertTrue(problem.report_inference_value_as_trace)
+
+        problem = get_bandit_problem(num_choices=26, num_trials=4)
+        self.assertEqual(problem.num_trials, 4)
+        self.assertEqual(problem.status_quo_params, {"x0": 26 // 2})
+
+    def test_baseline_exception(self) -> None:
+        with self.assertWarnsRegex(
+            Warning, expected_regex="Baseline value is not available for num_choices=17"
+        ):
+            problem = get_bandit_problem(num_choices=17)
+
+        self.assertEqual(problem.baseline_value, get_bandit_problem().baseline_value)
diff --git a/ax/benchmark/tests/problems/test_problems.py b/ax/benchmark/tests/problems/test_problems.py
index e43b2055d4e..9a7971ef2e0 100644
--- a/ax/benchmark/tests/problems/test_problems.py
+++ b/ax/benchmark/tests/problems/test_problems.py
@@ -24,6 +24,7 @@ def test_load_problems(self) -> None:
 
     def test_name(self) -> None:
         expected_names = [
+            ("Bandit", "Bandit"),
             ("branin", "Branin"),
             ("hartmann3", "Hartmann_3d"),
             ("hartmann6", "Hartmann_6d"),
diff --git a/ax/benchmark/tests/test_benchmark.py b/ax/benchmark/tests/test_benchmark.py
index 46972341026..29be755ec5a 100644
--- a/ax/benchmark/tests/test_benchmark.py
+++ b/ax/benchmark/tests/test_benchmark.py
@@ -31,6 +31,7 @@
 )
 from ax.benchmark.benchmark_result import BenchmarkResult
 from ax.benchmark.benchmark_runner import BenchmarkRunner
+from ax.benchmark.benchmark_test_functions.synthetic import IdentityTestFunction
 from ax.benchmark.methods.modular_botorch import (
     get_sobol_botorch_modular_acquisition,
     get_sobol_mbm_generation_strategy,
@@ -61,7 +62,6 @@
     get_multi_objective_benchmark_problem,
     get_single_objective_benchmark_problem,
     get_soo_surrogate,
-    IdentityTestFunction,
     TestDataset,
 )
 
diff --git a/ax/benchmark/tests/test_benchmark_runner.py b/ax/benchmark/tests/test_benchmark_runner.py
index 0fa9c9a6251..6d2582ee867 100644
--- a/ax/benchmark/tests/test_benchmark_runner.py
+++ b/ax/benchmark/tests/test_benchmark_runner.py
@@ -18,6 +18,8 @@
 from ax.benchmark.benchmark_runner import _add_noise, BenchmarkRunner
 from ax.benchmark.benchmark_test_functions.botorch_test import BoTorchTestFunction
 from ax.benchmark.benchmark_test_functions.surrogate import SurrogateTestFunction
+
+from ax.benchmark.benchmark_test_functions.synthetic import IdentityTestFunction
 from ax.benchmark.problems.synthetic.hss.jenatton import (
     get_jenatton_benchmark_problem,
     Jenatton,
@@ -35,8 +37,8 @@
     DummyTestFunction,
     get_jenatton_trials,
     get_soo_surrogate_test_function,
-    IdentityTestFunction,
 )
+
 from botorch.test_functions.synthetic import Ackley, ConstrainedHartmann, Hartmann
 from botorch.utils.transforms import normalize
 from pandas import DataFrame
diff --git a/ax/modelbridge/tests/test_discrete_modelbridge.py b/ax/modelbridge/tests/test_discrete_modelbridge.py
index d89db4a504d..bb8b5250c5a 100644
--- a/ax/modelbridge/tests/test_discrete_modelbridge.py
+++ b/ax/modelbridge/tests/test_discrete_modelbridge.py
@@ -276,8 +276,6 @@ def test_cross_validate(self, mock_init: Mock) -> None:
     def test_get_parameter_values(self) -> None:
         parameter_values = _get_parameter_values(self.search_space, ["x", "y", "z"])
         self.assertEqual(parameter_values, [[0.0, 1.0], ["foo", "bar"], [True]])
-        # pyre-fixme[6]: For 1st param expected `List[Parameter]` but got
-        #  `List[Union[ChoiceParameter, FixedParameter]]`.
         search_space = SearchSpace(self.parameters)
         search_space._parameters["x"] = RangeParameter(
             "x", ParameterType.FLOAT, 0.1, 0.4
diff --git a/ax/utils/testing/benchmark_stubs.py b/ax/utils/testing/benchmark_stubs.py
index cd42ae70b24..e50dcfa0e3c 100644
--- a/ax/utils/testing/benchmark_stubs.py
+++ b/ax/utils/testing/benchmark_stubs.py
@@ -5,7 +5,6 @@
 # LICENSE file in the root directory of this source tree.
 
 # pyre-strict
-from collections.abc import Mapping, Sequence
 from dataclasses import dataclass, field
 from typing import Any, Iterator
 
@@ -28,6 +27,7 @@
 from ax.benchmark.benchmark_step_runtime_function import TBenchmarkStepRuntimeFunction
 from ax.benchmark.benchmark_test_function import BenchmarkTestFunction
 from ax.benchmark.benchmark_test_functions.surrogate import SurrogateTestFunction
+from ax.benchmark.benchmark_test_functions.synthetic import IdentityTestFunction
 from ax.benchmark.problems.synthetic.hss.jenatton import get_jenatton_search_space
 from ax.core.arm import Arm
 from ax.core.batch_trial import BatchTrial
@@ -301,23 +301,6 @@ def get_next_candidate(
         return {self.param_name: next(self.iterator)}
 
 
-@dataclass(kw_only=True)
-class IdentityTestFunction(BenchmarkTestFunction):
-    outcome_names: Sequence[str] = field(default_factory=lambda: ["objective"])
-    n_steps: int = 1
-
-    # pyre-fixme[14]: Inconsistent override
-    def evaluate_true(self, params: Mapping[str, float]) -> torch.Tensor:
-        """
-        Args:
-            params: A dictionary with key "x0".
-        """
-        value = params["x0"]
-        return torch.full(
-            (len(self.outcome_names), self.n_steps), value, dtype=torch.float64
-        )
-
-
 def get_discrete_search_space(n_values: int = 20) -> SearchSpace:
     return SearchSpace(
         parameters=[
diff --git a/sphinx/source/benchmark.rst b/sphinx/source/benchmark.rst
index 2ad58067b9d..f8f707f79af 100644
--- a/sphinx/source/benchmark.rst
+++ b/sphinx/source/benchmark.rst
@@ -106,6 +106,14 @@ Benchmark Problems Registry
     :undoc-members:
     :show-inheritance:
 
+Benchmark Problems: Bandit
+~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. automodule:: ax.benchmark.problems.synthetic.bandit
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
 Benchmark Problems High Dimensional Embedding
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
@@ -146,6 +154,7 @@ Benchmark Problems PyTorchCNN TorchVision
     :undoc-members:
     :show-inheritance:
 
+
 Benchmark Problems Runtime Functions
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
@@ -169,3 +178,11 @@ Benchmark Test Functions: Surrogate
     :members:
     :undoc-members:
     :show-inheritance:
+
+Benchmark Test Functions: Synthetic
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. automodule:: ax.benchmark.benchmark_test_functions.synthetic
+    :members:
+    :undoc-members:
+    :show-inheritance: