We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
Fix `Test` warnings from `BoTorch`
### Motivation

Resolve following warnings from test:
```
tests/terminator_tests/improvement_tests/gp_tests/test_botorch.py: 4 warnings
tests/visualization_tests/test_terminator_improvement.py: 46 warnings
  /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/botorch/fit.py:139: DeprecationWarning:
  
  `fit_gpytorch_model` is marked for deprecation, consider using `fit_gpytorch_mll` instead.
```

### Suggestion

Look for the proper way to fix this warning (Hopefully, just replacing `fit_gpytorch_model` with `fit_gpytorch_mll`).

### Additional context (optional)

_No response_

--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `optuna/terminator/improvement/gp/botorch.py`
Content:
```
1 from __future__ import annotations
2 
3 from typing import Optional
4 
5 import numpy as np
6 
7 from optuna._imports import try_import
8 from optuna.distributions import _is_distribution_log
9 from optuna.distributions import CategoricalDistribution
10 from optuna.distributions import FloatDistribution
11 from optuna.distributions import IntDistribution
12 from optuna.search_space import intersection_search_space
13 from optuna.terminator.improvement.gp.base import BaseGaussianProcess
14 from optuna.trial._frozen import FrozenTrial
15 from optuna.trial._state import TrialState
16 
17 
18 with try_import() as _imports:
19     from botorch.fit import fit_gpytorch_model
20     from botorch.models import SingleTaskGP
21     from botorch.models.transforms import Normalize
22     from botorch.models.transforms import Standardize
23     import gpytorch
24     import torch
25 
26 __all__ = [
27     "fit_gpytorch_model",
28     "SingleTaskGP",
29     "Normalize",
30     "Standardize",
31     "gpytorch",
32     "torch",
33 ]
34 
35 
36 class _BoTorchGaussianProcess(BaseGaussianProcess):
37     def __init__(self) -> None:
38         _imports.check()
39 
40         self._gp: Optional[SingleTaskGP] = None
41 
42     def fit(
43         self,
44         trials: list[FrozenTrial],
45     ) -> None:
46         self._trials = trials
47 
48         x, bounds = _convert_trials_to_tensors(trials)
49 
50         n_params = x.shape[1]
51 
52         y = torch.tensor([trial.value for trial in trials], dtype=torch.float64)
53         y = torch.unsqueeze(y, 1)
54 
55         self._gp = SingleTaskGP(
56             x,
57             y,
58             input_transform=Normalize(d=n_params, bounds=bounds),
59             outcome_transform=Standardize(m=1),
60         )
61 
62         mll = gpytorch.mlls.ExactMarginalLogLikelihood(self._gp.likelihood, self._gp)
63 
64         fit_gpytorch_model(mll)
65 
66     def predict_mean_std(
67         self,
68         trials: list[FrozenTrial],
69     ) -> tuple[np.ndarray, np.ndarray]:
70         assert self._gp is not None
71 
72         x, _ = _convert_trials_to_tensors(trials)
73 
74         with torch.no_grad(), gpytorch.settings.fast_pred_var():
75             posterior = self._gp.posterior(x)
76             mean = posterior.mean
77             variance = posterior.variance
78             std = variance.sqrt()
79 
80         return mean.detach().numpy(), std.detach().numpy()
81 
82 
83 def _convert_trials_to_tensors(trials: list[FrozenTrial]) -> tuple[torch.Tensor, torch.Tensor]:
84     """Convert a list of FrozenTrial objects to tensors inputs and bounds.
85 
86     This function assumes the following condition for input trials:
87     - any categorical param is converted to a float or int one;
88     - log is unscaled for any float/int distribution;
89     - the state is COMPLETE for any trial;
90     - direction is MINIMIZE for any trial.
91     """
92     search_space = intersection_search_space(trials)
93     sorted_params = sorted(search_space.keys())
94 
95     x = []
96     for trial in trials:
97         assert trial.state == TrialState.COMPLETE
98         x_row = []
99         for param in sorted_params:
100             distribution = search_space[param]
101 
102             assert not _is_distribution_log(distribution)
103             assert not isinstance(distribution, CategoricalDistribution)
104 
105             param_value = float(trial.params[param])
106             x_row.append(param_value)
107 
108         x.append(x_row)
109 
110     min_bounds = []
111     max_bounds = []
112     for param, distribution in search_space.items():
113         assert isinstance(distribution, (FloatDistribution, IntDistribution))
114         min_bounds.append(distribution.low)
115         max_bounds.append(distribution.high)
116     bounds = [min_bounds, max_bounds]
117 
118     return torch.tensor(x, dtype=torch.float64), torch.tensor(bounds, dtype=torch.float64)
119
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/optuna/terminator/improvement/gp/botorch.py b/optuna/terminator/improvement/gp/botorch.py
--- a/optuna/terminator/improvement/gp/botorch.py
+++ b/optuna/terminator/improvement/gp/botorch.py
@@ -3,6 +3,7 @@
 from typing import Optional
 
 import numpy as np
+from packaging import version
 
 from optuna._imports import try_import
 from optuna.distributions import _is_distribution_log
@@ -16,15 +17,20 @@
 
 
 with try_import() as _imports:
-    from botorch.fit import fit_gpytorch_model
+    import botorch
     from botorch.models import SingleTaskGP
     from botorch.models.transforms import Normalize
     from botorch.models.transforms import Standardize
     import gpytorch
     import torch
 
+    if version.parse(botorch.version.version) < version.parse("0.8.0"):
+        from botorch.fit import fit_gpytorch_model as fit_gpytorch_mll
+    else:
+        from botorch.fit import fit_gpytorch_mll
+
 __all__ = [
-    "fit_gpytorch_model",
+    "fit_gpytorch_mll",
     "SingleTaskGP",
     "Normalize",
     "Standardize",
@@ -61,7 +67,7 @@
 
         mll = gpytorch.mlls.ExactMarginalLogLikelihood(self._gp.likelihood, self._gp)
 
-        fit_gpytorch_model(mll)
+        fit_gpytorch_mll(mll)
 
     def predict_mean_std(
         self,

{"golden_diff": "diff --git a/optuna/terminator/improvement/gp/botorch.py b/optuna/terminator/improvement/gp/botorch.py\n--- a/optuna/terminator/improvement/gp/botorch.py\n+++ b/optuna/terminator/improvement/gp/botorch.py\n@@ -3,6 +3,7 @@\n from typing import Optional\n \n import numpy as np\n+from packaging import version\n \n from optuna._imports import try_import\n from optuna.distributions import _is_distribution_log\n@@ -16,15 +17,20 @@\n \n \n with try_import() as _imports:\n-    from botorch.fit import fit_gpytorch_model\n+    import botorch\n     from botorch.models import SingleTaskGP\n     from botorch.models.transforms import Normalize\n     from botorch.models.transforms import Standardize\n     import gpytorch\n     import torch\n \n+    if version.parse(botorch.version.version) < version.parse(\"0.8.0\"):\n+        from botorch.fit import fit_gpytorch_model as fit_gpytorch_mll\n+    else:\n+        from botorch.fit import fit_gpytorch_mll\n+\n __all__ = [\n-    \"fit_gpytorch_model\",\n+    \"fit_gpytorch_mll\",\n     \"SingleTaskGP\",\n     \"Normalize\",\n     \"Standardize\",\n@@ -61,7 +67,7 @@\n \n         mll = gpytorch.mlls.ExactMarginalLogLikelihood(self._gp.likelihood, self._gp)\n \n-        fit_gpytorch_model(mll)\n+        fit_gpytorch_mll(mll)\n \n     def predict_mean_std(\n         self,\n", "issue": "Fix `Test` warnings from `BoTorch`\n### Motivation\n\nResolve following warnings from test:\r\n```\r\ntests/terminator_tests/improvement_tests/gp_tests/test_botorch.py: 4 warnings\r\ntests/visualization_tests/test_terminator_improvement.py: 46 warnings\r\n  /opt/hostedtoolcache/Python/3.9.18/x64/lib/python3.9/site-packages/botorch/fit.py:139: DeprecationWarning:\r\n  \r\n  `fit_gpytorch_model` is marked for deprecation, consider using `fit_gpytorch_mll` instead.\r\n```\n\n### Suggestion\n\nLook for the proper way to fix this warning (Hopefully, just replacing `fit_gpytorch_model` with `fit_gpytorch_mll`).\n\n### Additional context (optional)\n\n_No response_\n", "before_files": [{"content": "from __future__ import annotations\n\nfrom typing import Optional\n\nimport numpy as np\n\nfrom optuna._imports import try_import\nfrom optuna.distributions import _is_distribution_log\nfrom optuna.distributions import CategoricalDistribution\nfrom optuna.distributions import FloatDistribution\nfrom optuna.distributions import IntDistribution\nfrom optuna.search_space import intersection_search_space\nfrom optuna.terminator.improvement.gp.base import BaseGaussianProcess\nfrom optuna.trial._frozen import FrozenTrial\nfrom optuna.trial._state import TrialState\n\n\nwith try_import() as _imports:\n    from botorch.fit import fit_gpytorch_model\n    from botorch.models import SingleTaskGP\n    from botorch.models.transforms import Normalize\n    from botorch.models.transforms import Standardize\n    import gpytorch\n    import torch\n\n__all__ = [\n    \"fit_gpytorch_model\",\n    \"SingleTaskGP\",\n    \"Normalize\",\n    \"Standardize\",\n    \"gpytorch\",\n    \"torch\",\n]\n\n\nclass _BoTorchGaussianProcess(BaseGaussianProcess):\n    def __init__(self) -> None:\n        _imports.check()\n\n        self._gp: Optional[SingleTaskGP] = None\n\n    def fit(\n        self,\n        trials: list[FrozenTrial],\n    ) -> None:\n        self._trials = trials\n\n        x, bounds = _convert_trials_to_tensors(trials)\n\n        n_params = x.shape[1]\n\n        y = torch.tensor([trial.value for trial in trials], dtype=torch.float64)\n        y = torch.unsqueeze(y, 1)\n\n        self._gp = SingleTaskGP(\n            x,\n            y,\n            input_transform=Normalize(d=n_params, bounds=bounds),\n            outcome_transform=Standardize(m=1),\n        )\n\n        mll = gpytorch.mlls.ExactMarginalLogLikelihood(self._gp.likelihood, self._gp)\n\n        fit_gpytorch_model(mll)\n\n    def predict_mean_std(\n        self,\n        trials: list[FrozenTrial],\n    ) -> tuple[np.ndarray, np.ndarray]:\n        assert self._gp is not None\n\n        x, _ = _convert_trials_to_tensors(trials)\n\n        with torch.no_grad(), gpytorch.settings.fast_pred_var():\n            posterior = self._gp.posterior(x)\n            mean = posterior.mean\n            variance = posterior.variance\n            std = variance.sqrt()\n\n        return mean.detach().numpy(), std.detach().numpy()\n\n\ndef _convert_trials_to_tensors(trials: list[FrozenTrial]) -> tuple[torch.Tensor, torch.Tensor]:\n    \"\"\"Convert a list of FrozenTrial objects to tensors inputs and bounds.\n\n    This function assumes the following condition for input trials:\n    - any categorical param is converted to a float or int one;\n    - log is unscaled for any float/int distribution;\n    - the state is COMPLETE for any trial;\n    - direction is MINIMIZE for any trial.\n    \"\"\"\n    search_space = intersection_search_space(trials)\n    sorted_params = sorted(search_space.keys())\n\n    x = []\n    for trial in trials:\n        assert trial.state == TrialState.COMPLETE\n        x_row = []\n        for param in sorted_params:\n            distribution = search_space[param]\n\n            assert not _is_distribution_log(distribution)\n            assert not isinstance(distribution, CategoricalDistribution)\n\n            param_value = float(trial.params[param])\n            x_row.append(param_value)\n\n        x.append(x_row)\n\n    min_bounds = []\n    max_bounds = []\n    for param, distribution in search_space.items():\n        assert isinstance(distribution, (FloatDistribution, IntDistribution))\n        min_bounds.append(distribution.low)\n        max_bounds.append(distribution.high)\n    bounds = [min_bounds, max_bounds]\n\n    return torch.tensor(x, dtype=torch.float64), torch.tensor(bounds, dtype=torch.float64)\n", "path": "optuna/terminator/improvement/gp/botorch.py"}], "after_files": [{"content": "from __future__ import annotations\n\nfrom typing import Optional\n\nimport numpy as np\nfrom packaging import version\n\nfrom optuna._imports import try_import\nfrom optuna.distributions import _is_distribution_log\nfrom optuna.distributions import CategoricalDistribution\nfrom optuna.distributions import FloatDistribution\nfrom optuna.distributions import IntDistribution\nfrom optuna.search_space import intersection_search_space\nfrom optuna.terminator.improvement.gp.base import BaseGaussianProcess\nfrom optuna.trial._frozen import FrozenTrial\nfrom optuna.trial._state import TrialState\n\n\nwith try_import() as _imports:\n    import botorch\n    from botorch.models import SingleTaskGP\n    from botorch.models.transforms import Normalize\n    from botorch.models.transforms import Standardize\n    import gpytorch\n    import torch\n\n    if version.parse(botorch.version.version) < version.parse(\"0.8.0\"):\n        from botorch.fit import fit_gpytorch_model as fit_gpytorch_mll\n    else:\n        from botorch.fit import fit_gpytorch_mll\n\n__all__ = [\n    \"fit_gpytorch_mll\",\n    \"SingleTaskGP\",\n    \"Normalize\",\n    \"Standardize\",\n    \"gpytorch\",\n    \"torch\",\n]\n\n\nclass _BoTorchGaussianProcess(BaseGaussianProcess):\n    def __init__(self) -> None:\n        _imports.check()\n\n        self._gp: Optional[SingleTaskGP] = None\n\n    def fit(\n        self,\n        trials: list[FrozenTrial],\n    ) -> None:\n        self._trials = trials\n\n        x, bounds = _convert_trials_to_tensors(trials)\n\n        n_params = x.shape[1]\n\n        y = torch.tensor([trial.value for trial in trials], dtype=torch.float64)\n        y = torch.unsqueeze(y, 1)\n\n        self._gp = SingleTaskGP(\n            x,\n            y,\n            input_transform=Normalize(d=n_params, bounds=bounds),\n            outcome_transform=Standardize(m=1),\n        )\n\n        mll = gpytorch.mlls.ExactMarginalLogLikelihood(self._gp.likelihood, self._gp)\n\n        fit_gpytorch_mll(mll)\n\n    def predict_mean_std(\n        self,\n        trials: list[FrozenTrial],\n    ) -> tuple[np.ndarray, np.ndarray]:\n        assert self._gp is not None\n\n        x, _ = _convert_trials_to_tensors(trials)\n\n        with torch.no_grad(), gpytorch.settings.fast_pred_var():\n            posterior = self._gp.posterior(x)\n            mean = posterior.mean\n            variance = posterior.variance\n            std = variance.sqrt()\n\n        return mean.detach().numpy(), std.detach().numpy()\n\n\ndef _convert_trials_to_tensors(trials: list[FrozenTrial]) -> tuple[torch.Tensor, torch.Tensor]:\n    \"\"\"Convert a list of FrozenTrial objects to tensors inputs and bounds.\n\n    This function assumes the following condition for input trials:\n    - any categorical param is converted to a float or int one;\n    - log is unscaled for any float/int distribution;\n    - the state is COMPLETE for any trial;\n    - direction is MINIMIZE for any trial.\n    \"\"\"\n    search_space = intersection_search_space(trials)\n    sorted_params = sorted(search_space.keys())\n\n    x = []\n    for trial in trials:\n        assert trial.state == TrialState.COMPLETE\n        x_row = []\n        for param in sorted_params:\n            distribution = search_space[param]\n\n            assert not _is_distribution_log(distribution)\n            assert not isinstance(distribution, CategoricalDistribution)\n\n            param_value = float(trial.params[param])\n            x_row.append(param_value)\n\n        x.append(x_row)\n\n    min_bounds = []\n    max_bounds = []\n    for param, distribution in search_space.items():\n        assert isinstance(distribution, (FloatDistribution, IntDistribution))\n        min_bounds.append(distribution.low)\n        max_bounds.append(distribution.high)\n    bounds = [min_bounds, max_bounds]\n\n    return torch.tensor(x, dtype=torch.float64), torch.tensor(bounds, dtype=torch.float64)\n", "path": "optuna/terminator/improvement/gp/botorch.py"}]}