| Name | optuna JSON |
| Version |
3.6.1
JSON |
| download |
| home_page | None |
| Summary | A hyperparameter optimization framework |
| upload_time | 2024-04-01 06:04:18 |
| maintainer | None |
| docs_url | None |
| author | Takuya Akiba |
| requires_python | >=3.7 |
| license | MIT License Copyright (c) 2018 Preferred Networks, Inc. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. == Optuna contains code that is licensed by third-party developers. == SciPy The Optuna contains the codes from SciPy project. Copyright (c) 2001-2002 Enthought, Inc. 2003-2022, SciPy Developers. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. == fdlibm Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. |
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<div align="center"><img src="https://raw.githubusercontent.com/optuna/optuna/master/docs/image/optuna-logo.png" width="800"/></div>
# Optuna: A hyperparameter optimization framework
[](https://www.python.org)
[](https://pypi.python.org/pypi/optuna)
[](https://anaconda.org/conda-forge/optuna)
[](https://github.com/optuna/optuna)
[](https://optuna.readthedocs.io/en/stable/)
[](https://codecov.io/gh/optuna/optuna)
:link: [**Website**](https://optuna.org/)
| :page_with_curl: [**Docs**](https://optuna.readthedocs.io/en/stable/)
| :gear: [**Install Guide**](https://optuna.readthedocs.io/en/stable/installation.html)
| :pencil: [**Tutorial**](https://optuna.readthedocs.io/en/stable/tutorial/index.html)
| :bulb: [**Examples**](https://github.com/optuna/optuna-examples)
*Optuna* is an automatic hyperparameter optimization software framework, particularly designed
for machine learning. It features an imperative, *define-by-run* style user API. Thanks to our
*define-by-run* API, the code written with Optuna enjoys high modularity, and the user of
Optuna can dynamically construct the search spaces for the hyperparameters.
## :fire: Key Features
Optuna has modern functionalities as follows:
- [Lightweight, versatile, and platform agnostic architecture](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/001_first.html)
- Handle a wide variety of tasks with a simple installation that has few requirements.
- [Pythonic search spaces](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/002_configurations.html)
- Define search spaces using familiar Python syntax including conditionals and loops.
- [Efficient optimization algorithms](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/003_efficient_optimization_algorithms.html)
- Adopt state-of-the-art algorithms for sampling hyperparameters and efficiently pruning unpromising trials.
- [Easy parallelization](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/004_distributed.html)
- Scale studies to tens or hundreds of workers with little or no changes to the code.
- [Quick visualization](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/005_visualization.html)
- Inspect optimization histories from a variety of plotting functions.
## Basic Concepts
We use the terms *study* and *trial* as follows:
- Study: optimization based on an objective function
- Trial: a single execution of the objective function
Please refer to the sample code below. The goal of a *study* is to find out the optimal set of
hyperparameter values (e.g., `regressor` and `svr_c`) through multiple *trials* (e.g.,
`n_trials=100`). Optuna is a framework designed for automation and acceleration of
optimization *studies*.
<details open>
<summary>Sample code with scikit-learn</summary>
[](http://colab.research.google.com/github/optuna/optuna-examples/blob/main/quickstart.ipynb)
```python
import ...
# Define an objective function to be minimized.
def objective(trial):
# Invoke suggest methods of a Trial object to generate hyperparameters.
regressor_name = trial.suggest_categorical('regressor', ['SVR', 'RandomForest'])
if regressor_name == 'SVR':
svr_c = trial.suggest_float('svr_c', 1e-10, 1e10, log=True)
regressor_obj = sklearn.svm.SVR(C=svr_c)
else:
rf_max_depth = trial.suggest_int('rf_max_depth', 2, 32)
regressor_obj = sklearn.ensemble.RandomForestRegressor(max_depth=rf_max_depth)
X, y = sklearn.datasets.fetch_california_housing(return_X_y=True)
X_train, X_val, y_train, y_val = sklearn.model_selection.train_test_split(X, y, random_state=0)
regressor_obj.fit(X_train, y_train)
y_pred = regressor_obj.predict(X_val)
error = sklearn.metrics.mean_squared_error(y_val, y_pred)
return error # An objective value linked with the Trial object.
study = optuna.create_study() # Create a new study.
study.optimize(objective, n_trials=100) # Invoke optimization of the objective function.
```
</details>
> [!NOTE]
> More examples can be found in [optuna/optuna-examples](https://github.com/optuna/optuna-examples).
>
> The examples cover diverse problem setups such as multi-objective optimization, constrained optimization, pruning, and distributed optimization.
## Installation
Optuna is available at [the Python Package Index](https://pypi.org/project/optuna/) and on [Anaconda Cloud](https://anaconda.org/conda-forge/optuna).
```bash
# PyPI
$ pip install optuna
```
```bash
# Anaconda Cloud
$ conda install -c conda-forge optuna
```
> [!IMPORTANT]
> Optuna supports Python 3.7 or newer.
>
> Also, we provide Optuna docker images on [DockerHub](https://hub.docker.com/r/optuna/optuna).
## Integrations
Optuna has integration features with various third-party libraries. Integrations can be found in [optuna/optuna-integration](https://github.com/optuna/optuna-integration) and the document is available [here](https://optuna-integration.readthedocs.io/en/stable/index.html).
<details>
<summary>Supported integration libraries</summary>
* [Catalyst](https://github.com/optuna/optuna-examples/tree/main/pytorch/catalyst_simple.py)
* [Catboost](https://github.com/optuna/optuna-examples/tree/main/catboost/catboost_pruning.py)
* [Dask](https://github.com/optuna/optuna-examples/tree/main/dask/dask_simple.py)
* [fastai (v2)](https://github.com/optuna/optuna-examples/tree/main/fastai/fastaiv2_simple.py)
* [Keras](https://github.com/optuna/optuna-examples/tree/main/keras/keras_integration.py)
* [LightGBM](https://github.com/optuna/optuna-examples/tree/main/lightgbm/lightgbm_integration.py)
* [MLflow](https://github.com/optuna/optuna-examples/tree/main/mlflow/keras_mlflow.py)
* [MXNet](https://github.com/optuna/optuna-examples/tree/main/mxnet/mxnet_integration.py)
* [PyTorch](https://github.com/optuna/optuna-examples/tree/main/pytorch/pytorch_simple.py)
* [PyTorch Ignite](https://github.com/optuna/optuna-examples/tree/main/pytorch/pytorch_ignite_simple.py)
* [PyTorch Lightning](https://github.com/optuna/optuna-examples/tree/main/pytorch/pytorch_lightning_simple.py)
* [TensorBoard](https://github.com/optuna/optuna-examples/tree/main/tensorboard/tensorboard_simple.py)
* [TensorFlow](https://github.com/optuna/optuna-examples/tree/main/tensorflow/tensorflow_estimator_integration.py)
* [tf.keras](https://github.com/optuna/optuna-examples/tree/main/tfkeras/tfkeras_integration.py)
* [Weights & Biases](https://github.com/optuna/optuna-examples/tree/main/wandb/wandb_integration.py)
* [XGBoost](https://github.com/optuna/optuna-examples/tree/main/xgboost/xgboost_integration.py)
</details>
## Web Dashboard
[Optuna Dashboard](https://github.com/optuna/optuna-dashboard) is a real-time web dashboard for Optuna.
You can check the optimization history, hyperparameter importance, etc. in graphs and tables.
You don't need to create a Python script to call [Optuna's visualization](https://optuna.readthedocs.io/en/stable/reference/visualization/index.html) functions.
Feature requests and bug reports are welcome!
`optuna-dashboard` can be installed via pip:
```shell
$ pip install optuna-dashboard
```
> [!TIP]
> Please check out the convenience of Optuna Dashboard using the sample code below.
<details>
<summary>Sample code to launch Optuna Dashboard</summary>
Save the following code as `optimize_toy.py`.
```python
import optuna
def objective(trial):
x1 = trial.suggest_float("x1", -100, 100)
x2 = trial.suggest_float("x2", -100, 100)
return x1 ** 2 + 0.01 * x2 ** 2
study = optuna.create_study(storage="sqlite:///db.sqlite3") # Create a new study with database.
study.optimize(objective, n_trials=100)
```
Then try the commands below:
```shell
# Run the study specified above
$ python optimize_toy.py
# Launch the dashboard based on the storage `sqlite:///db.sqlite3`
$ optuna-dashboard sqlite:///db.sqlite3
...
Listening on http://localhost:8080/
Hit Ctrl-C to quit.
```
</details>
## Communication
- [GitHub Discussions] for questions.
- [GitHub Issues] for bug reports and feature requests.
[GitHub Discussions]: https://github.com/optuna/optuna/discussions
[GitHub issues]: https://github.com/optuna/optuna/issues
## Contribution
Any contributions to Optuna are more than welcome!
If you are new to Optuna, please check the [good first issues](https://github.com/optuna/optuna/labels/good%20first%20issue). They are relatively simple, well-defined, and often good starting points for you to get familiar with the contribution workflow and other developers.
If you already have contributed to Optuna, we recommend the other [contribution-welcome issues](https://github.com/optuna/optuna/labels/contribution-welcome).
For general guidelines on how to contribute to the project, take a look at [CONTRIBUTING.md](./CONTRIBUTING.md).
## Reference
If you use Optuna in one of your research projects, please cite [our KDD paper](https://doi.org/10.1145/3292500.3330701) "Optuna: A Next-generation Hyperparameter Optimization Framework":
<details open>
<summary>BibTeX</summary>
```bibtex
@inproceedings{akiba2019optuna,
title={{O}ptuna: A Next-Generation Hyperparameter Optimization Framework},
author={Akiba, Takuya and Sano, Shotaro and Yanase, Toshihiko and Ohta, Takeru and Koyama, Masanori},
booktitle={The 25th ACM SIGKDD International Conference on Knowledge Discovery \& Data Mining},
pages={2623--2631},
year={2019}
}
```
</details>
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"description": "<div align=\"center\"><img src=\"https://raw.githubusercontent.com/optuna/optuna/master/docs/image/optuna-logo.png\" width=\"800\"/></div>\n\n# Optuna: A hyperparameter optimization framework\n\n[](https://www.python.org)\n[](https://pypi.python.org/pypi/optuna)\n[](https://anaconda.org/conda-forge/optuna)\n[](https://github.com/optuna/optuna)\n[](https://optuna.readthedocs.io/en/stable/)\n[](https://codecov.io/gh/optuna/optuna)\n\n:link: [**Website**](https://optuna.org/)\n| :page_with_curl: [**Docs**](https://optuna.readthedocs.io/en/stable/)\n| :gear: [**Install Guide**](https://optuna.readthedocs.io/en/stable/installation.html)\n| :pencil: [**Tutorial**](https://optuna.readthedocs.io/en/stable/tutorial/index.html)\n| :bulb: [**Examples**](https://github.com/optuna/optuna-examples)\n\n*Optuna* is an automatic hyperparameter optimization software framework, particularly designed\nfor machine learning. It features an imperative, *define-by-run* style user API. Thanks to our\n*define-by-run* API, the code written with Optuna enjoys high modularity, and the user of\nOptuna can dynamically construct the search spaces for the hyperparameters.\n\n## :fire: Key Features\n\nOptuna has modern functionalities as follows:\n\n- [Lightweight, versatile, and platform agnostic architecture](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/001_first.html)\n - Handle a wide variety of tasks with a simple installation that has few requirements.\n- [Pythonic search spaces](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/002_configurations.html)\n - Define search spaces using familiar Python syntax including conditionals and loops.\n- [Efficient optimization algorithms](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/003_efficient_optimization_algorithms.html)\n - Adopt state-of-the-art algorithms for sampling hyperparameters and efficiently pruning unpromising trials.\n- [Easy parallelization](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/004_distributed.html)\n - Scale studies to tens or hundreds of workers with little or no changes to the code.\n- [Quick visualization](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/005_visualization.html)\n - Inspect optimization histories from a variety of plotting functions.\n\n\n## Basic Concepts\n\nWe use the terms *study* and *trial* as follows:\n\n- Study: optimization based on an objective function\n- Trial: a single execution of the objective function\n\nPlease refer to the sample code below. The goal of a *study* is to find out the optimal set of\nhyperparameter values (e.g., `regressor` and `svr_c`) through multiple *trials* (e.g.,\n`n_trials=100`). Optuna is a framework designed for automation and acceleration of\noptimization *studies*.\n\n<details open>\n<summary>Sample code with scikit-learn</summary>\n\n[](http://colab.research.google.com/github/optuna/optuna-examples/blob/main/quickstart.ipynb)\n\n```python\nimport ...\n\n# Define an objective function to be minimized.\ndef objective(trial):\n\n # Invoke suggest methods of a Trial object to generate hyperparameters.\n regressor_name = trial.suggest_categorical('regressor', ['SVR', 'RandomForest'])\n if regressor_name == 'SVR':\n svr_c = trial.suggest_float('svr_c', 1e-10, 1e10, log=True)\n regressor_obj = sklearn.svm.SVR(C=svr_c)\n else:\n rf_max_depth = trial.suggest_int('rf_max_depth', 2, 32)\n regressor_obj = sklearn.ensemble.RandomForestRegressor(max_depth=rf_max_depth)\n\n X, y = sklearn.datasets.fetch_california_housing(return_X_y=True)\n X_train, X_val, y_train, y_val = sklearn.model_selection.train_test_split(X, y, random_state=0)\n\n regressor_obj.fit(X_train, y_train)\n y_pred = regressor_obj.predict(X_val)\n\n error = sklearn.metrics.mean_squared_error(y_val, y_pred)\n\n return error # An objective value linked with the Trial object.\n\nstudy = optuna.create_study() # Create a new study.\nstudy.optimize(objective, n_trials=100) # Invoke optimization of the objective function.\n```\n</details>\n\n> [!NOTE]\n> More examples can be found in [optuna/optuna-examples](https://github.com/optuna/optuna-examples).\n>\n> The examples cover diverse problem setups such as multi-objective optimization, constrained optimization, pruning, and distributed optimization. \n\n## Installation\n\nOptuna is available at [the Python Package Index](https://pypi.org/project/optuna/) and on [Anaconda Cloud](https://anaconda.org/conda-forge/optuna).\n\n```bash\n# PyPI\n$ pip install optuna\n```\n\n```bash\n# Anaconda Cloud\n$ conda install -c conda-forge optuna\n```\n\n> [!IMPORTANT]\n> Optuna supports Python 3.7 or newer.\n>\n> Also, we provide Optuna docker images on [DockerHub](https://hub.docker.com/r/optuna/optuna).\n\n## Integrations\n\nOptuna has integration features with various third-party libraries. Integrations can be found in [optuna/optuna-integration](https://github.com/optuna/optuna-integration) and the document is available [here](https://optuna-integration.readthedocs.io/en/stable/index.html).\n\n<details>\n<summary>Supported integration libraries</summary>\n\n* [Catalyst](https://github.com/optuna/optuna-examples/tree/main/pytorch/catalyst_simple.py)\n* [Catboost](https://github.com/optuna/optuna-examples/tree/main/catboost/catboost_pruning.py)\n* [Dask](https://github.com/optuna/optuna-examples/tree/main/dask/dask_simple.py)\n* [fastai (v2)](https://github.com/optuna/optuna-examples/tree/main/fastai/fastaiv2_simple.py)\n* [Keras](https://github.com/optuna/optuna-examples/tree/main/keras/keras_integration.py)\n* [LightGBM](https://github.com/optuna/optuna-examples/tree/main/lightgbm/lightgbm_integration.py)\n* [MLflow](https://github.com/optuna/optuna-examples/tree/main/mlflow/keras_mlflow.py)\n* [MXNet](https://github.com/optuna/optuna-examples/tree/main/mxnet/mxnet_integration.py)\n* [PyTorch](https://github.com/optuna/optuna-examples/tree/main/pytorch/pytorch_simple.py)\n* [PyTorch Ignite](https://github.com/optuna/optuna-examples/tree/main/pytorch/pytorch_ignite_simple.py)\n* [PyTorch Lightning](https://github.com/optuna/optuna-examples/tree/main/pytorch/pytorch_lightning_simple.py)\n* [TensorBoard](https://github.com/optuna/optuna-examples/tree/main/tensorboard/tensorboard_simple.py)\n* [TensorFlow](https://github.com/optuna/optuna-examples/tree/main/tensorflow/tensorflow_estimator_integration.py)\n* [tf.keras](https://github.com/optuna/optuna-examples/tree/main/tfkeras/tfkeras_integration.py)\n* [Weights & Biases](https://github.com/optuna/optuna-examples/tree/main/wandb/wandb_integration.py)\n* [XGBoost](https://github.com/optuna/optuna-examples/tree/main/xgboost/xgboost_integration.py)\n</details>\n\n## Web Dashboard\n\n[Optuna Dashboard](https://github.com/optuna/optuna-dashboard) is a real-time web dashboard for Optuna.\nYou can check the optimization history, hyperparameter importance, etc. in graphs and tables.\nYou don't need to create a Python script to call [Optuna's visualization](https://optuna.readthedocs.io/en/stable/reference/visualization/index.html) functions.\nFeature requests and bug reports are welcome!\n\n\n\n`optuna-dashboard` can be installed via pip:\n\n```shell\n$ pip install optuna-dashboard\n```\n\n> [!TIP]\n> Please check out the convenience of Optuna Dashboard using the sample code below.\n\n<details>\n<summary>Sample code to launch Optuna Dashboard</summary>\n\nSave the following code as `optimize_toy.py`.\n\n```python\nimport optuna\n\n\ndef objective(trial):\n x1 = trial.suggest_float(\"x1\", -100, 100)\n x2 = trial.suggest_float(\"x2\", -100, 100)\n return x1 ** 2 + 0.01 * x2 ** 2\n\n\nstudy = optuna.create_study(storage=\"sqlite:///db.sqlite3\") # Create a new study with database.\nstudy.optimize(objective, n_trials=100)\n```\n\nThen try the commands below:\n\n```shell\n# Run the study specified above\n$ python optimize_toy.py\n\n# Launch the dashboard based on the storage `sqlite:///db.sqlite3`\n$ optuna-dashboard sqlite:///db.sqlite3\n...\nListening on http://localhost:8080/\nHit Ctrl-C to quit.\n```\n\n</details>\n\n\n## Communication\n\n- [GitHub Discussions] for questions.\n- [GitHub Issues] for bug reports and feature requests.\n\n[GitHub Discussions]: https://github.com/optuna/optuna/discussions\n[GitHub issues]: https://github.com/optuna/optuna/issues\n\n\n## Contribution\n\nAny contributions to Optuna are more than welcome!\n\nIf you are new to Optuna, please check the [good first issues](https://github.com/optuna/optuna/labels/good%20first%20issue). They are relatively simple, well-defined, and often good starting points for you to get familiar with the contribution workflow and other developers.\n\nIf you already have contributed to Optuna, we recommend the other [contribution-welcome issues](https://github.com/optuna/optuna/labels/contribution-welcome).\n\nFor general guidelines on how to contribute to the project, take a look at [CONTRIBUTING.md](./CONTRIBUTING.md).\n\n\n## Reference\n\nIf you use Optuna in one of your research projects, please cite [our KDD paper](https://doi.org/10.1145/3292500.3330701) \"Optuna: A Next-generation Hyperparameter Optimization Framework\":\n\n<details open>\n<summary>BibTeX</summary>\n\n```bibtex\n@inproceedings{akiba2019optuna,\n title={{O}ptuna: A Next-Generation Hyperparameter Optimization Framework},\n author={Akiba, Takuya and Sano, Shotaro and Yanase, Toshihiko and Ohta, Takeru and Koyama, Masanori},\n booktitle={The 25th ACM SIGKDD International Conference on Knowledge Discovery \\& Data Mining},\n pages={2623--2631},\n year={2019}\n}\n```\n</details>\n",
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"license": "MIT License Copyright (c) 2018 Preferred Networks, Inc. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"Software\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. == Optuna contains code that is licensed by third-party developers. == SciPy The Optuna contains the codes from SciPy project. Copyright (c) 2001-2002 Enthought, Inc. 2003-2022, SciPy Developers. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. == fdlibm Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. Developed at SunPro, a Sun Microsystems, Inc. business. Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved. ",
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