From 804fb71ecb2005473af178052d8b847739bd9c51 Mon Sep 17 00:00:00 2001
From: nabenabe0928 <shuhei.watanabe.utokyo@gmail.com>
Date: Wed, 1 Nov 2023 03:04:54 +0100
Subject: [PATCH 01/12] Remove MOTPESampler from the doc because it is
 deprecated

---
 optuna/multi_objective/samplers/_motpe.py | 22 ++++++++++++++++
 optuna/samplers/_tpe/sampler.py           | 31 +++++++++++++++++++++--
 2 files changed, 51 insertions(+), 2 deletions(-)

diff --git a/optuna/multi_objective/samplers/_motpe.py b/optuna/multi_objective/samplers/_motpe.py
index 87b0787e15..1f6cc27dfc 100644
--- a/optuna/multi_objective/samplers/_motpe.py
+++ b/optuna/multi_objective/samplers/_motpe.py
@@ -28,6 +28,28 @@ class MOTPEMultiObjectiveSampler(BaseMultiObjectiveSampler):
 
     This sampler is a multiobjective version of :class:`~optuna.samplers.TPESampler`.
 
+    .. note::
+        For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
+        MOTPEMultiObjectiveSampler is deprecated and :class:`~optuna.samplers.TPESampler` should be
+        used instead. The following code shows how you run TPESampler on a multi-objective task:
+
+        .. testcode::
+
+            import optuna
+
+            def objective(trial):
+                x = trial.suggest_float("x", -100, 100)
+                y = trial.suggest_categorical("y", [-1, 0, 1])
+                f1 = x**2 + y
+                f2 = -((x - 2) ** 2 + y)
+                return f1, f2
+
+
+            # We minimize the first objective and the second objective.
+            sampler = optuna.samplers.TPESampler()
+            study = optuna.create_study(directions=["minimize", "maximize"], sampler=sampler)
+            study.optimize(objective, n_trials=100)
+
     For further information about MOTPE algorithm, please refer to the following paper:
 
     - `Multiobjective tree-structured parzen estimator for computationally expensive optimization
diff --git a/optuna/samplers/_tpe/sampler.py b/optuna/samplers/_tpe/sampler.py
index fe4e1fb596..dd091662ca 100644
--- a/optuna/samplers/_tpe/sampler.py
+++ b/optuna/samplers/_tpe/sampler.py
@@ -74,11 +74,16 @@ class TPESampler(BaseSampler):
       <https://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf>`_
     - `Making a Science of Model Search: Hyperparameter Optimization in Hundreds of
       Dimensions for Vision Architectures <http://proceedings.mlr.press/v28/bergstra13.pdf>`_
-    - `Multiobjective tree-structured parzen estimator for computationally expensive optimization
-      problems <https://dl.acm.org/doi/10.1145/3377930.3389817>`_
+    - `Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for
+      Better Empirical Performance <https://arxiv.org/abs/2304.11127>`_
+
+    For multi-objective TPE (MOTPE), please refer to the following papers:
+    - `Multiobjective Tree-Structured Parzen Estimator for Computationally Expensive Optimization
+      Problems <https://dl.acm.org/doi/10.1145/3377930.3389817>`_
     - `Multiobjective Tree-Structured Parzen Estimator <https://doi.org/10.1613/jair.1.13188>`_
 
     Example:
+        An example of a single-objective optimization is as follows:
 
         .. testcode::
 
@@ -94,6 +99,28 @@ def objective(trial):
             study = optuna.create_study(sampler=TPESampler())
             study.optimize(objective, n_trials=10)
 
+    .. note::
+        For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
+        :class:`~optuna.samplers.MOTPESampler` is deprecated and TPESampler should be used instead.
+        The following code shows how you run TPESampler on a multi-objective task:
+
+        .. testcode::
+
+            import optuna
+
+            def objective(trial):
+                x = trial.suggest_float("x", -100, 100)
+                y = trial.suggest_categorical("y", [-1, 0, 1])
+                f1 = x**2 + y
+                f2 = -((x - 2) ** 2 + y)
+                return f1, f2
+
+
+            # We minimize the first objective and the second objective.
+            sampler = optuna.samplers.TPESampler()
+            study = optuna.create_study(directions=["minimize", "maximize"], sampler=sampler)
+            study.optimize(objective, n_trials=100)
+
     Args:
         consider_prior:
             Enhance the stability of Parzen estimator by imposing a Gaussian prior when

From d63d0cc00dd103d7f79fe18135d463d29979fe0d Mon Sep 17 00:00:00 2001
From: nabenabe0928 <shuhei.watanabe.utokyo@gmail.com>
Date: Wed, 1 Nov 2023 03:18:18 +0100
Subject: [PATCH 02/12] Apply black

---
 optuna/multi_objective/samplers/_motpe.py | 1 +
 optuna/samplers/_tpe/sampler.py           | 1 +
 2 files changed, 2 insertions(+)

diff --git a/optuna/multi_objective/samplers/_motpe.py b/optuna/multi_objective/samplers/_motpe.py
index 1f6cc27dfc..d16f5ab5d5 100644
--- a/optuna/multi_objective/samplers/_motpe.py
+++ b/optuna/multi_objective/samplers/_motpe.py
@@ -37,6 +37,7 @@ class MOTPEMultiObjectiveSampler(BaseMultiObjectiveSampler):
 
             import optuna
 
+
             def objective(trial):
                 x = trial.suggest_float("x", -100, 100)
                 y = trial.suggest_categorical("y", [-1, 0, 1])
diff --git a/optuna/samplers/_tpe/sampler.py b/optuna/samplers/_tpe/sampler.py
index dd091662ca..59a04b4f20 100644
--- a/optuna/samplers/_tpe/sampler.py
+++ b/optuna/samplers/_tpe/sampler.py
@@ -108,6 +108,7 @@ def objective(trial):
 
             import optuna
 
+
             def objective(trial):
                 x = trial.suggest_float("x", -100, 100)
                 y = trial.suggest_categorical("y", [-1, 0, 1])

From 8c1ca930fc496fb13c9eb2e596223a899d521d57 Mon Sep 17 00:00:00 2001
From: nabenabe0928 <shuhei.watanabe.utokyo@gmail.com>
Date: Wed, 1 Nov 2023 05:54:15 +0100
Subject: [PATCH 03/12] [temp] Deactivate tests for quick check

---
 .github/workflows/mac-tests.yml               | 138 ------------------
 .github/workflows/tests-integration.yml       |  78 ----------
 .github/workflows/tests-mpi.yml               |  82 -----------
 .github/workflows/tests-storage.yml           | 130 -----------------
 .../workflows/tests-with-minimum-versions.yml |  92 ------------
 .github/workflows/tests.yml                   |  89 -----------
 .github/workflows/windows-tests.yml           | 135 -----------------
 optuna/multi_objective/samplers/_motpe.py     |   7 +-
 .../samplers/_tpe/multi_objective_sampler.py  |  28 +++-
 optuna/samplers/_tpe/sampler.py               |   5 +-
 10 files changed, 33 insertions(+), 751 deletions(-)

diff --git a/.github/workflows/mac-tests.yml b/.github/workflows/mac-tests.yml
index 526d6795d4..e69de29bb2 100644
--- a/.github/workflows/mac-tests.yml
+++ b/.github/workflows/mac-tests.yml
@@ -1,138 +0,0 @@
-# Run tests and integration tests on Mac, which are triggered by each master push.
-# Currently, Python3.8 is only used as an environment.
-# This is mainly for the sake of speed.
-name: mac-tests
-
-on:
-  push:
-    branches:
-      - master
-  pull_request: {}
-  schedule:
-    - cron: '0 23 * * SUN-THU'
-  workflow_dispatch:
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
-  cancel-in-progress: true
-
-jobs:
-  tests-mac:
-    runs-on: macos-latest
-
-    # Scheduled Tests are disabled for forks.
-    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v3
-
-    - name: Setup Python3.8
-      uses: actions/setup-python@v4
-      with:
-        python-version: 3.8
-
-    - name: Setup cache
-      uses: actions/cache@v3
-      env:
-        cache-name: test
-      with:
-        path: ~/Library/Caches/pip
-        key: ${{ runner.os }}-3.8-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
-        restore-keys: |
-          ${{ runner.os }}-3.8-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
-
-    - name: Install
-      run: |
-        python -m pip install --upgrade pip
-        pip install --progress-bar off -U setuptools
-        # Install minimal dependencies and confirm that `import optuna` is successful.
-        pip install --progress-bar off .
-        python -c 'import optuna'
-        optuna --version
-        pip install --progress-bar off .[test]
-        pip install --progress-bar off .[optional]
-
-    - name: Output installed packages
-      run: |
-        pip freeze --all
-    - name: Output dependency tree
-      run: |
-        pip install pipdeptree
-        pipdeptree
-
-
-    - name: Scheduled tests
-      if:  ${{ github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' }}
-      run: |
-        pytest tests -m "not integration"
-    - name: Tests
-      if:  ${{ github.event_name != 'schedule' && github.event_name != 'workflow_dispatch' }}
-      run: |
-        pytest tests -m "not integration and not slow"
-
-
-  tests-integration-mac:
-    runs-on: macos-latest
-
-    # Scheduled Tests are disabled for forks.
-    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v3
-
-    - name: Setup Python3.8
-      uses: actions/setup-python@v4
-      with:
-        python-version: 3.8
-
-    - name: Setup cache
-      uses: actions/cache@v3
-      env:
-        cache-name: test-integration
-      with:
-        path: ~/Library/Caches/pip
-        key: ${{ runner.os }}-3.8-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
-        restore-keys: |
-          ${{ runner.os }}-3.8-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
-
-    - name: Setup mac environment
-      run: |
-        brew install libomp
-        brew install open-mpi
-        brew install openblas
-
-    - name: Install
-      run: |
-        python -m pip install --upgrade pip
-
-        # Install minimal dependencies and confirm that `import optuna` is successful.
-        pip install --progress-bar off .
-        python -c 'import optuna'
-        optuna --version
-
-        pip install --progress-bar off .[test]
-        pip install --progress-bar off .[optional]
-        pip install --progress-bar off .[integration]
-
-    - name: Output installed packages
-      run: |
-        pip freeze --all
-    - name: Output dependency tree
-      run: |
-        pip install pipdeptree
-        pipdeptree
-
-
-    - name: Tests
-      run: |
-        pytest tests -m "integration"
-
-      env:
-        OMP_NUM_THREADS: 1
-
-    - name: Tests MPI
-      run: |
-        export OMPI_MCA_rmaps_base_oversubscribe=yes
-        mpirun -n 2 -- pytest tests/integration_tests/test_pytorch_distributed.py
-      env:
-        OMP_NUM_THREADS: 1
diff --git a/.github/workflows/tests-integration.yml b/.github/workflows/tests-integration.yml
index 2255fc11cc..e69de29bb2 100644
--- a/.github/workflows/tests-integration.yml
+++ b/.github/workflows/tests-integration.yml
@@ -1,78 +0,0 @@
-name: Tests (Integration)
-
-on:
-  push:
-    branches:
-      - master
-  pull_request: {}
-  schedule:
-    - cron: '0 23 * * SUN-THU'
-  workflow_dispatch:
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
-  cancel-in-progress: true
-
-jobs:
-  tests-integration:
-    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
-    runs-on: ubuntu-latest
-
-    strategy:
-      matrix:
-        python-version: ['3.8', '3.9', '3.10', '3.11']
-
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v3
-
-    - name: Setup Python${{ matrix.python-version }}
-      uses: actions/setup-python@v4
-      with:
-        python-version: ${{ matrix.python-version }}
-
-    - name: Setup cache
-      uses: actions/cache@v3
-      env:
-        cache-name: test-integration
-      with:
-        path: ~/.cache/pip
-        key: ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
-        restore-keys: |
-          ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
-
-    - name: Setup environment
-      run: |
-        sudo apt-get update
-        sudo apt-get -y install openmpi-bin libopenmpi-dev libopenblas-dev
-
-    - name: Install
-      run: |
-        python -m pip install --upgrade pip
-
-        # Install minimal dependencies and confirm that `import optuna` is successful.
-        pip install --progress-bar off .
-        python -c 'import optuna'
-        optuna --version
-
-        pip install --progress-bar off .[test]
-        pip install --progress-bar off .[optional] --extra-index-url https://download.pytorch.org/whl/cpu
-        pip install --progress-bar off .[integration] --extra-index-url https://download.pytorch.org/whl/cpu
-
-    - name: Output installed packages
-      run: |
-        pip freeze --all
-    - name: Output dependency tree
-      run: |
-        pip install pipdeptree
-        pipdeptree
-
-    - name: Scheduled tests
-      if:  ${{ github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' }}
-      run: |
-        pytest tests -m "integration"
-        
-    - name: Tests
-      if:  ${{ github.event_name != 'schedule' && github.event_name != 'workflow_dispatch' }}
-      run: |
-        pytest tests -m "integration and not slow"
diff --git a/.github/workflows/tests-mpi.yml b/.github/workflows/tests-mpi.yml
index 3ea1f1f46f..e69de29bb2 100644
--- a/.github/workflows/tests-mpi.yml
+++ b/.github/workflows/tests-mpi.yml
@@ -1,82 +0,0 @@
-name: Tests (MPI)
-
-on:
-  push:
-    branches:
-      - master
-  pull_request: {}
-  schedule:
-    - cron: '0 23 * * SUN-THU'
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
-  cancel-in-progress: true
-
-jobs:
-  tests-mpi:
-    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
-    runs-on: ubuntu-latest
-
-    strategy:
-      matrix:
-        python-version: ['3.8', '3.9', '3.10', '3.11']
-
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v3
-
-    - name: Setup Python${{ matrix.python-version }}
-      uses: actions/setup-python@v4
-      with:
-        python-version: ${{ matrix.python-version }}
-
-    - name: Setup cache
-      uses: actions/cache@v3
-      env:
-        cache-name: test-mpi
-      with:
-        path: ~/.cache/pip
-        key: ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
-        restore-keys: |
-          ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
-
-    - name: Setup environment
-      run: |
-        sudo apt-get update
-        sudo apt-get -y install openmpi-bin libopenmpi-dev
-
-    - name: Install
-      run: |
-        python -m pip install --upgrade pip
-
-        # Install minimal dependencies and confirm that `import optuna` is successful.
-        pip install --progress-bar off .
-        python -c 'import optuna'
-        optuna --version
-
-        pip install --progress-bar off .[test]
-        pip install --progress-bar off .[optional] --extra-index-url https://download.pytorch.org/whl/cpu
-
-        # TODO(not522): Remove this line when torchmetrics can be installed with extra-index-url
-        pip install --progress-bar off torchmetrics
-
-        pip install --progress-bar off .[integration] --extra-index-url https://download.pytorch.org/whl/cpu
-
-    - name: Output installed packages
-      run: |
-        pip freeze --all
-    - name: Output dependency tree
-      run: |
-        pip install pipdeptree
-        pipdeptree
-
-    - name: Tests
-      run: |
-        export OMPI_MCA_rmaps_base_oversubscribe=yes
-
-        if [ ${{ matrix.python-version }} != 3.11 ]; then
-          mpirun -n 2 -- pytest tests/integration_tests/test_pytorch_distributed.py
-        fi
-
-      env:
-        OMP_NUM_THREADS: 1
diff --git a/.github/workflows/tests-storage.yml b/.github/workflows/tests-storage.yml
index bf45161d2c..e69de29bb2 100644
--- a/.github/workflows/tests-storage.yml
+++ b/.github/workflows/tests-storage.yml
@@ -1,130 +0,0 @@
-name: Tests (Storage with server)
-
-on:
-  push:
-    branches:
-      - master
-  pull_request: {}
-  schedule:
-    - cron: '0 23 * * SUN-THU'
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
-  cancel-in-progress: true
-
-jobs:
-  # TODO(masap): Modify job name to "tests-storage-with-server" because this test is not only for
-  # RDB. Since current name "tests-rdbstorage" is required in the Branch protection rules, you
-  # need to modify the Branch protection rules as well.
-  tests-rdbstorage:
-    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
-    runs-on: ubuntu-latest
-
-    strategy:
-      matrix:
-        python-version: ['3.7', '3.8', '3.9', '3.10', '3.11']
-
-    services:
-      mysql:
-        image: mysql:5.7
-        ports:
-          - 3306:3306
-        env:
-          MYSQL_ROOT_PASSWORD: mandatory_arguments
-          MYSQL_DATABASE: optunatest
-          MYSQL_USER: user
-          MYSQL_PASSWORD: test
-        options: >-
-          --health-cmd "mysqladmin ping -h localhost"
-          --health-interval 10s
-          --health-timeout 5s
-          --health-retries 5
-      postgres:
-        image: postgres:10.1-alpine
-        ports:
-          - 5432:5432
-        env:
-          POSTGRES_DB: optunatest
-          POSTGRES_USER: user
-          POSTGRES_PASSWORD: test
-        options: >-
-          --health-cmd pg_isready
-          --health-interval 10s
-          --health-timeout 5s
-          --health-retries 5
-      redis:
-        image: redis
-        ports:
-          - 6379:6379
-
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v3
-
-    - name: Setup Python${{ matrix.python-version }}
-      uses: actions/setup-python@v4
-      with:
-        python-version: ${{ matrix.python-version }}
-
-    - name: Setup cache
-      uses: actions/cache@v3
-      env:
-        cache-name: test-storage-with-server
-      with:
-        path: ~/.cache/pip
-        key: ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
-        restore-keys: |
-          ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
-
-    - name: Setup environment
-      run: |
-        sudo apt-get update
-        sudo apt-get -y install openmpi-bin libopenmpi-dev
-
-    - name: Install
-      run: |
-        python -m pip install --upgrade pip
-        pip install --progress-bar off -U setuptools
-
-        # Install minimal dependencies and confirm that `import optuna` is successful.
-        pip install --progress-bar off .
-        python -c 'import optuna'
-        optuna --version
-
-        pip install --progress-bar off .[test]
-        pip install --progress-bar off .[optional] --extra-index-url https://download.pytorch.org/whl/cpu
-
-    - name: Install DB bindings
-      run: |
-        pip install --progress-bar off PyMySQL cryptography psycopg2-binary redis
-
-    - name: Output installed packages
-      run: |
-        pip freeze --all
-    - name: Output dependency tree
-      run: |
-        pip install pipdeptree
-        pipdeptree
-
-    - name: Tests MySQL
-      run: |
-        pytest tests/storages_tests/test_with_server.py
-      env:
-        SQLALCHEMY_WARN_20: 1
-        OMP_NUM_THREADS: 1
-        TEST_DB_URL: mysql+pymysql://user:test@127.0.0.1/optunatest
-
-    - name: Tests PostgreSQL
-      run: |
-        pytest tests/storages_tests/test_with_server.py
-      env:
-        OMP_NUM_THREADS: 1
-        TEST_DB_URL: postgresql+psycopg2://user:test@127.0.0.1/optunatest
-
-    - name: Tests Journal Redis
-      run: |
-        pytest tests/storages_tests/test_with_server.py
-      env:
-        OMP_NUM_THREADS: 1
-        TEST_DB_URL: redis://localhost:6379
-        TEST_DB_MODE: journal-redis
diff --git a/.github/workflows/tests-with-minimum-versions.yml b/.github/workflows/tests-with-minimum-versions.yml
index 679d9ef7e6..e69de29bb2 100644
--- a/.github/workflows/tests-with-minimum-versions.yml
+++ b/.github/workflows/tests-with-minimum-versions.yml
@@ -1,92 +0,0 @@
-name: Tests with minimum versions
-
-on:
-  push:
-    branches:
-      - master
-  pull_request: {}
-  schedule:
-    - cron: '0 23 * * SUN-THU'
-  workflow_dispatch:
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
-  cancel-in-progress: true
-
-jobs:
-  tests-with-minimum-versions:
-    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
-    runs-on: ubuntu-latest
-
-    strategy:
-      matrix:
-        python-version: ['3.7', '3.8', '3.9']
-
-    services:
-      redis:
-        image: redis
-        options: >-
-          --health-cmd "redis-cli ping"
-          --health-interval 10s
-          --health-timeout 5s
-          --health-retries 5
-
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v3
-
-    - name: Setup Python${{ matrix.python-version }}
-      uses: actions/setup-python@v4
-      with:
-        python-version: ${{ matrix.python-version }}
-
-    - name: Setup cache
-      uses: actions/cache@v3
-      env:
-        cache-name: test-with-minimum-versions
-      with:
-        path: ~/.cache/pip
-        key: ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/setup.py') }}-v1
-        restore-keys: |
-          ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/setup.py') }}
-
-
-    - name: Setup pip
-      run: |
-        python -m pip install --upgrade pip
-        pip install --progress-bar off -U setuptools
-
-    - name: Install
-      run: |
-        # Install minimal dependencies and confirm that `import optuna` is successful.
-        pip install --progress-bar off .
-        python -c 'import optuna'
-        optuna --version
-
-        pip install --progress-bar off .[test]
-        pip install --progress-bar off .[optional] --extra-index-url https://download.pytorch.org/whl/cpu
-
-    - name: Install dependencies with minimum versions
-      run: |
-        # Install dependencies with minimum versions.
-        pip uninstall -y alembic cmaes packaging sqlalchemy plotly scikit-learn
-        pip install alembic==1.5.0 cmaes==0.10.0 packaging==20.0 sqlalchemy==1.3.0 numpy==1.20.3 tqdm==4.27.0 colorlog==0.3 PyYAML==5.1
-        pip install plotly==5.0.0 scikit-learn==0.24.2  # optional extras
-
-    - name: Output installed packages
-      run: |
-        pip freeze --all
-    - name: Output dependency tree
-      run: |
-        pip install pipdeptree
-        pipdeptree
-
-    - name: Scheduled tests
-      if:  ${{ github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' }}
-      run: |
-        pytest tests -m "not integration"
-
-    - name: Tests
-      if:  ${{ github.event_name != 'schedule' && github.event_name != 'workflow_dispatch' }}
-      run: |
-        pytest tests -m "not integration and not slow"
diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 4c8d172139..e69de29bb2 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -1,89 +0,0 @@
-name: Tests
-
-on:
-  push:
-    branches:
-      - master
-  pull_request: {}
-  schedule:
-    - cron: '0 23 * * SUN-THU'
-  workflow_dispatch:
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
-  cancel-in-progress: true
-
-jobs:
-  tests:
-    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
-    runs-on: ubuntu-latest
-
-    strategy:
-      matrix:
-        python-version: ['3.7', '3.8', '3.9', '3.10', '3.11']
-
-    services:
-      redis:
-        image: redis
-        options: >-
-          --health-cmd "redis-cli ping"
-          --health-interval 10s
-          --health-timeout 5s
-          --health-retries 5
-
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v3
-
-    - name: Setup Python${{ matrix.python-version }}
-      uses: actions/setup-python@v4
-      with:
-        python-version: ${{ matrix.python-version }}
-
-    - name: Setup cache
-      uses: actions/cache@v3
-      env:
-        cache-name: test
-      with:
-        path: ~/.cache/pip
-        key: ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
-        restore-keys: |
-          ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
-
-
-    - name: Setup pip
-      run: |
-        python -m pip install --upgrade pip
-        pip install --progress-bar off -U setuptools
-
-    - name: Install
-      run: |
-        # Install minimal dependencies and confirm that `import optuna` is successful.
-        pip install --progress-bar off .
-        python -c 'import optuna'
-        optuna --version
-
-        pip install --progress-bar off .[test]
-        pip install --progress-bar off .[optional] --extra-index-url https://download.pytorch.org/whl/cpu
-
-    - name: Output installed packages
-      run: |
-        pip freeze --all
-    - name: Output dependency tree
-      run: |
-        pip install pipdeptree
-        pipdeptree
-
-    - name: Scheduled tests
-      if:  ${{ github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' }}
-      run: |
-        pytest tests -m "not integration"
-      env:
-        SQLALCHEMY_WARN_20: 1
-
-    - name: Tests
-      if:  ${{ github.event_name != 'schedule' && github.event_name != 'workflow_dispatch' }}
-      run: |
-        pytest tests -m "not integration and not slow"
-      env:
-        SQLALCHEMY_WARN_20: 1
diff --git a/.github/workflows/windows-tests.yml b/.github/workflows/windows-tests.yml
index 7b46856277..e69de29bb2 100644
--- a/.github/workflows/windows-tests.yml
+++ b/.github/workflows/windows-tests.yml
@@ -1,135 +0,0 @@
-# Run tests and integration tests on Windows, which are triggered by each master push.
-# Currently, Python3.9 is only used as an environment.
-# This is mainly for the sake of speed.
-name: windows-tests
-
-on:
-  push:
-    branches:
-      - master
-  pull_request: {}
-  schedule:
-    - cron: '0 23 * * SUN-THU'
-  workflow_dispatch:
-
-concurrency:
-  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
-  cancel-in-progress: true
-
-jobs:
-  tests-windows:
-    runs-on: windows-latest
-
-    # Not intended for forks.
-    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v3
-
-    - name: Setup Python3.9
-      uses: actions/setup-python@v4
-      with:
-        python-version: "3.9"
-
-    - name: Setup cache
-      uses: actions/cache@v3
-      env:
-        cache-name: windows-test
-      with:
-        path: ~\\AppData\\Local\\pip\\Cache
-        key: ${{ runner.os }}-3.9-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
-        restore-keys: |
-          ${{ runner.os }}-3.9-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
-
-    - name: Install
-      run: |
-        python -m pip install --upgrade pip
-        pip install --progress-bar off -U setuptools
-        # Install minimal dependencies and confirm that `import optuna` is successful.
-        pip install --progress-bar off .
-        python -c 'import optuna'
-        optuna --version
-        pip install --progress-bar off .[test]
-        pip install --progress-bar off .[optional]
-        pip install PyQt6 # Install PyQT for using QtAgg as matplotlib backend.
-
-    - name: Output installed packages
-      run: |
-        pip freeze --all
-    - name: Output dependency tree
-      run: |
-        pip install pipdeptree
-        pipdeptree
-
-    - name: Scheduled tests
-      if:  ${{ github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' }}
-      run: |
-        pytest -m "not integration"
-      env:
-        SQLALCHEMY_WARN_20: 1
-        MPLBACKEND: "QtAgg" # Use QtAgg as matplotlib backend.
-
-    - name: Tests
-      if:  ${{ github.event_name != 'schedule' && github.event_name != 'workflow_dispatch' }}
-      run: |
-        pytest -m "not integration and not slow"
-      env:
-        MPLBACKEND: "QtAgg" # Use QtAgg as matplotlib backend.
-
-  tests-integration-windows:
-    runs-on: windows-latest
-
-    # Not intended for forks.
-    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v3
-
-    - name: Setup Python3.9
-      uses: actions/setup-python@v4
-      with:
-        python-version: "3.9"
-
-    - name: Setup cache
-      uses: actions/cache@v3
-      env:
-        cache-name: windows-test-integration
-      with:
-        path: ~\\AppData\\Local\\pip\\Cache
-        key: ${{ runner.os }}-3.9-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
-        restore-keys: |
-          ${{ runner.os }}-3.9-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
-
-    - name: Setup MPI
-      uses: mpi4py/setup-mpi@v1
-      with:
-        mpi: "msmpi"
-
-    - name: Install
-      run: |
-        python -m pip install --upgrade pip
-        pip install --progress-bar off -U setuptools
-        # Install minimal dependencies and confirm that `import optuna` is successful.
-        pip install --progress-bar off .
-        python -c 'import optuna'
-        optuna --version
-        pip install --progress-bar off .[test]
-        pip install --progress-bar off .[optional]
-        pip install --progress-bar off .[integration]
-        pip install "distributed<2023.3.2"
-
-    - name: Output installed packages
-      run: |
-        pip freeze --all
-    - name: Output dependency tree
-      run: |
-        pip install pipdeptree
-        pipdeptree
-
-    - name: Tests
-      # Skip allennlp tests since it's not supported on Windows.
-      run: |
-        pytest tests -m "integration" `
-          --ignore tests/integration_tests/allennlp_tests/test_allennlp.py `
-      env:
-        OMP_NUM_THREADS: 1
diff --git a/optuna/multi_objective/samplers/_motpe.py b/optuna/multi_objective/samplers/_motpe.py
index d16f5ab5d5..85831d9b66 100644
--- a/optuna/multi_objective/samplers/_motpe.py
+++ b/optuna/multi_objective/samplers/_motpe.py
@@ -26,12 +26,13 @@
 class MOTPEMultiObjectiveSampler(BaseMultiObjectiveSampler):
     """Multi-objective sampler using the MOTPE algorithm.
 
-    This sampler is a multiobjective version of :class:`~optuna.samplers.TPESampler`.
+    This sampler is a multi-objective version of :class:`~optuna.samplers.TPESampler`.
 
     .. note::
         For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
-        MOTPEMultiObjectiveSampler is deprecated and :class:`~optuna.samplers.TPESampler` should be
-        used instead. The following code shows how you run TPESampler on a multi-objective task:
+        This sampler is deprecated and :class:`~optuna.samplers.TPESampler` should be
+        used instead. The following code shows how you run :class:`~optuna.samplers.TPESampler` on
+        a multi-objective task:
 
         .. testcode::
 
diff --git a/optuna/samplers/_tpe/multi_objective_sampler.py b/optuna/samplers/_tpe/multi_objective_sampler.py
index ebd35d1352..a32db024a0 100644
--- a/optuna/samplers/_tpe/multi_objective_sampler.py
+++ b/optuna/samplers/_tpe/multi_objective_sampler.py
@@ -22,9 +22,33 @@ def _default_weights_above(x: int) -> np.ndarray:
 class MOTPESampler(TPESampler):
     """Multi-objective sampler using the MOTPE algorithm.
 
-    This sampler is a multiobjective version of :class:`~optuna.samplers.TPESampler`.
+    This sampler is a multi-objective version of :class:`~optuna.samplers.TPESampler`.
 
-    For further information about MOTPE algorithm, please refer to the following paper:
+    .. note::
+        For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
+        This sampler is deprecated and :class:`~optuna.samplers.TPESampler` should be
+        used instead. The following code shows how you run :class:`~optuna.samplers.TPESampler` on
+        a multi-objective task:
+
+        .. testcode::
+
+            import optuna
+
+
+            def objective(trial):
+                x = trial.suggest_float("x", -100, 100)
+                y = trial.suggest_categorical("y", [-1, 0, 1])
+                f1 = x**2 + y
+                f2 = -((x - 2) ** 2 + y)
+                return f1, f2
+
+
+            # We minimize the first objective and the second objective.
+            sampler = optuna.samplers.TPESampler()
+            study = optuna.create_study(directions=["minimize", "maximize"], sampler=sampler)
+            study.optimize(objective, n_trials=100)
+
+    For further information about MOTPE algorithm, please refer to the following papers:
 
     - `Multiobjective tree-structured parzen estimator for computationally expensive optimization
       problems <https://dl.acm.org/doi/abs/10.1145/3377930.3389817>`_
diff --git a/optuna/samplers/_tpe/sampler.py b/optuna/samplers/_tpe/sampler.py
index 59a04b4f20..7a7157af91 100644
--- a/optuna/samplers/_tpe/sampler.py
+++ b/optuna/samplers/_tpe/sampler.py
@@ -78,6 +78,7 @@ class TPESampler(BaseSampler):
       Better Empirical Performance <https://arxiv.org/abs/2304.11127>`_
 
     For multi-objective TPE (MOTPE), please refer to the following papers:
+
     - `Multiobjective Tree-Structured Parzen Estimator for Computationally Expensive Optimization
       Problems <https://dl.acm.org/doi/10.1145/3377930.3389817>`_
     - `Multiobjective Tree-Structured Parzen Estimator <https://doi.org/10.1613/jair.1.13188>`_
@@ -101,8 +102,8 @@ def objective(trial):
 
     .. note::
         For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
-        :class:`~optuna.samplers.MOTPESampler` is deprecated and TPESampler should be used instead.
-        The following code shows how you run TPESampler on a multi-objective task:
+        :class:`~optuna.samplers.MOTPESampler` is deprecated and this sampler should be used
+        instead. The following code shows how you apply this sampler to a multi-objective task:
 
         .. testcode::
 

From 96d3c564e7c1f5a4af0632f3fabc5300f3fef74c Mon Sep 17 00:00:00 2001
From: nabenabe0928 <shuhei.watanabe.utokyo@gmail.com>
Date: Wed, 1 Nov 2023 06:58:24 +0100
Subject: [PATCH 04/12] Revert tests

---
 .github/workflows/mac-tests.yml               | 138 ++++++++++++++++++
 .github/workflows/tests-integration.yml       |  78 ++++++++++
 .github/workflows/tests-mpi.yml               |  82 +++++++++++
 .github/workflows/tests-storage.yml           | 130 +++++++++++++++++
 .../workflows/tests-with-minimum-versions.yml |  92 ++++++++++++
 .github/workflows/tests.yml                   |  89 +++++++++++
 .github/workflows/windows-tests.yml           | 135 +++++++++++++++++
 7 files changed, 744 insertions(+)

diff --git a/.github/workflows/mac-tests.yml b/.github/workflows/mac-tests.yml
index e69de29bb2..526d6795d4 100644
--- a/.github/workflows/mac-tests.yml
+++ b/.github/workflows/mac-tests.yml
@@ -0,0 +1,138 @@
+# Run tests and integration tests on Mac, which are triggered by each master push.
+# Currently, Python3.8 is only used as an environment.
+# This is mainly for the sake of speed.
+name: mac-tests
+
+on:
+  push:
+    branches:
+      - master
+  pull_request: {}
+  schedule:
+    - cron: '0 23 * * SUN-THU'
+  workflow_dispatch:
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  tests-mac:
+    runs-on: macos-latest
+
+    # Scheduled Tests are disabled for forks.
+    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v3
+
+    - name: Setup Python3.8
+      uses: actions/setup-python@v4
+      with:
+        python-version: 3.8
+
+    - name: Setup cache
+      uses: actions/cache@v3
+      env:
+        cache-name: test
+      with:
+        path: ~/Library/Caches/pip
+        key: ${{ runner.os }}-3.8-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
+        restore-keys: |
+          ${{ runner.os }}-3.8-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
+
+    - name: Install
+      run: |
+        python -m pip install --upgrade pip
+        pip install --progress-bar off -U setuptools
+        # Install minimal dependencies and confirm that `import optuna` is successful.
+        pip install --progress-bar off .
+        python -c 'import optuna'
+        optuna --version
+        pip install --progress-bar off .[test]
+        pip install --progress-bar off .[optional]
+
+    - name: Output installed packages
+      run: |
+        pip freeze --all
+    - name: Output dependency tree
+      run: |
+        pip install pipdeptree
+        pipdeptree
+
+
+    - name: Scheduled tests
+      if:  ${{ github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' }}
+      run: |
+        pytest tests -m "not integration"
+    - name: Tests
+      if:  ${{ github.event_name != 'schedule' && github.event_name != 'workflow_dispatch' }}
+      run: |
+        pytest tests -m "not integration and not slow"
+
+
+  tests-integration-mac:
+    runs-on: macos-latest
+
+    # Scheduled Tests are disabled for forks.
+    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v3
+
+    - name: Setup Python3.8
+      uses: actions/setup-python@v4
+      with:
+        python-version: 3.8
+
+    - name: Setup cache
+      uses: actions/cache@v3
+      env:
+        cache-name: test-integration
+      with:
+        path: ~/Library/Caches/pip
+        key: ${{ runner.os }}-3.8-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
+        restore-keys: |
+          ${{ runner.os }}-3.8-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
+
+    - name: Setup mac environment
+      run: |
+        brew install libomp
+        brew install open-mpi
+        brew install openblas
+
+    - name: Install
+      run: |
+        python -m pip install --upgrade pip
+
+        # Install minimal dependencies and confirm that `import optuna` is successful.
+        pip install --progress-bar off .
+        python -c 'import optuna'
+        optuna --version
+
+        pip install --progress-bar off .[test]
+        pip install --progress-bar off .[optional]
+        pip install --progress-bar off .[integration]
+
+    - name: Output installed packages
+      run: |
+        pip freeze --all
+    - name: Output dependency tree
+      run: |
+        pip install pipdeptree
+        pipdeptree
+
+
+    - name: Tests
+      run: |
+        pytest tests -m "integration"
+
+      env:
+        OMP_NUM_THREADS: 1
+
+    - name: Tests MPI
+      run: |
+        export OMPI_MCA_rmaps_base_oversubscribe=yes
+        mpirun -n 2 -- pytest tests/integration_tests/test_pytorch_distributed.py
+      env:
+        OMP_NUM_THREADS: 1
diff --git a/.github/workflows/tests-integration.yml b/.github/workflows/tests-integration.yml
index e69de29bb2..2255fc11cc 100644
--- a/.github/workflows/tests-integration.yml
+++ b/.github/workflows/tests-integration.yml
@@ -0,0 +1,78 @@
+name: Tests (Integration)
+
+on:
+  push:
+    branches:
+      - master
+  pull_request: {}
+  schedule:
+    - cron: '0 23 * * SUN-THU'
+  workflow_dispatch:
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  tests-integration:
+    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
+    runs-on: ubuntu-latest
+
+    strategy:
+      matrix:
+        python-version: ['3.8', '3.9', '3.10', '3.11']
+
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v3
+
+    - name: Setup Python${{ matrix.python-version }}
+      uses: actions/setup-python@v4
+      with:
+        python-version: ${{ matrix.python-version }}
+
+    - name: Setup cache
+      uses: actions/cache@v3
+      env:
+        cache-name: test-integration
+      with:
+        path: ~/.cache/pip
+        key: ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
+        restore-keys: |
+          ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
+
+    - name: Setup environment
+      run: |
+        sudo apt-get update
+        sudo apt-get -y install openmpi-bin libopenmpi-dev libopenblas-dev
+
+    - name: Install
+      run: |
+        python -m pip install --upgrade pip
+
+        # Install minimal dependencies and confirm that `import optuna` is successful.
+        pip install --progress-bar off .
+        python -c 'import optuna'
+        optuna --version
+
+        pip install --progress-bar off .[test]
+        pip install --progress-bar off .[optional] --extra-index-url https://download.pytorch.org/whl/cpu
+        pip install --progress-bar off .[integration] --extra-index-url https://download.pytorch.org/whl/cpu
+
+    - name: Output installed packages
+      run: |
+        pip freeze --all
+    - name: Output dependency tree
+      run: |
+        pip install pipdeptree
+        pipdeptree
+
+    - name: Scheduled tests
+      if:  ${{ github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' }}
+      run: |
+        pytest tests -m "integration"
+        
+    - name: Tests
+      if:  ${{ github.event_name != 'schedule' && github.event_name != 'workflow_dispatch' }}
+      run: |
+        pytest tests -m "integration and not slow"
diff --git a/.github/workflows/tests-mpi.yml b/.github/workflows/tests-mpi.yml
index e69de29bb2..3ea1f1f46f 100644
--- a/.github/workflows/tests-mpi.yml
+++ b/.github/workflows/tests-mpi.yml
@@ -0,0 +1,82 @@
+name: Tests (MPI)
+
+on:
+  push:
+    branches:
+      - master
+  pull_request: {}
+  schedule:
+    - cron: '0 23 * * SUN-THU'
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  tests-mpi:
+    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
+    runs-on: ubuntu-latest
+
+    strategy:
+      matrix:
+        python-version: ['3.8', '3.9', '3.10', '3.11']
+
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v3
+
+    - name: Setup Python${{ matrix.python-version }}
+      uses: actions/setup-python@v4
+      with:
+        python-version: ${{ matrix.python-version }}
+
+    - name: Setup cache
+      uses: actions/cache@v3
+      env:
+        cache-name: test-mpi
+      with:
+        path: ~/.cache/pip
+        key: ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
+        restore-keys: |
+          ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
+
+    - name: Setup environment
+      run: |
+        sudo apt-get update
+        sudo apt-get -y install openmpi-bin libopenmpi-dev
+
+    - name: Install
+      run: |
+        python -m pip install --upgrade pip
+
+        # Install minimal dependencies and confirm that `import optuna` is successful.
+        pip install --progress-bar off .
+        python -c 'import optuna'
+        optuna --version
+
+        pip install --progress-bar off .[test]
+        pip install --progress-bar off .[optional] --extra-index-url https://download.pytorch.org/whl/cpu
+
+        # TODO(not522): Remove this line when torchmetrics can be installed with extra-index-url
+        pip install --progress-bar off torchmetrics
+
+        pip install --progress-bar off .[integration] --extra-index-url https://download.pytorch.org/whl/cpu
+
+    - name: Output installed packages
+      run: |
+        pip freeze --all
+    - name: Output dependency tree
+      run: |
+        pip install pipdeptree
+        pipdeptree
+
+    - name: Tests
+      run: |
+        export OMPI_MCA_rmaps_base_oversubscribe=yes
+
+        if [ ${{ matrix.python-version }} != 3.11 ]; then
+          mpirun -n 2 -- pytest tests/integration_tests/test_pytorch_distributed.py
+        fi
+
+      env:
+        OMP_NUM_THREADS: 1
diff --git a/.github/workflows/tests-storage.yml b/.github/workflows/tests-storage.yml
index e69de29bb2..bf45161d2c 100644
--- a/.github/workflows/tests-storage.yml
+++ b/.github/workflows/tests-storage.yml
@@ -0,0 +1,130 @@
+name: Tests (Storage with server)
+
+on:
+  push:
+    branches:
+      - master
+  pull_request: {}
+  schedule:
+    - cron: '0 23 * * SUN-THU'
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  # TODO(masap): Modify job name to "tests-storage-with-server" because this test is not only for
+  # RDB. Since current name "tests-rdbstorage" is required in the Branch protection rules, you
+  # need to modify the Branch protection rules as well.
+  tests-rdbstorage:
+    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
+    runs-on: ubuntu-latest
+
+    strategy:
+      matrix:
+        python-version: ['3.7', '3.8', '3.9', '3.10', '3.11']
+
+    services:
+      mysql:
+        image: mysql:5.7
+        ports:
+          - 3306:3306
+        env:
+          MYSQL_ROOT_PASSWORD: mandatory_arguments
+          MYSQL_DATABASE: optunatest
+          MYSQL_USER: user
+          MYSQL_PASSWORD: test
+        options: >-
+          --health-cmd "mysqladmin ping -h localhost"
+          --health-interval 10s
+          --health-timeout 5s
+          --health-retries 5
+      postgres:
+        image: postgres:10.1-alpine
+        ports:
+          - 5432:5432
+        env:
+          POSTGRES_DB: optunatest
+          POSTGRES_USER: user
+          POSTGRES_PASSWORD: test
+        options: >-
+          --health-cmd pg_isready
+          --health-interval 10s
+          --health-timeout 5s
+          --health-retries 5
+      redis:
+        image: redis
+        ports:
+          - 6379:6379
+
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v3
+
+    - name: Setup Python${{ matrix.python-version }}
+      uses: actions/setup-python@v4
+      with:
+        python-version: ${{ matrix.python-version }}
+
+    - name: Setup cache
+      uses: actions/cache@v3
+      env:
+        cache-name: test-storage-with-server
+      with:
+        path: ~/.cache/pip
+        key: ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
+        restore-keys: |
+          ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
+
+    - name: Setup environment
+      run: |
+        sudo apt-get update
+        sudo apt-get -y install openmpi-bin libopenmpi-dev
+
+    - name: Install
+      run: |
+        python -m pip install --upgrade pip
+        pip install --progress-bar off -U setuptools
+
+        # Install minimal dependencies and confirm that `import optuna` is successful.
+        pip install --progress-bar off .
+        python -c 'import optuna'
+        optuna --version
+
+        pip install --progress-bar off .[test]
+        pip install --progress-bar off .[optional] --extra-index-url https://download.pytorch.org/whl/cpu
+
+    - name: Install DB bindings
+      run: |
+        pip install --progress-bar off PyMySQL cryptography psycopg2-binary redis
+
+    - name: Output installed packages
+      run: |
+        pip freeze --all
+    - name: Output dependency tree
+      run: |
+        pip install pipdeptree
+        pipdeptree
+
+    - name: Tests MySQL
+      run: |
+        pytest tests/storages_tests/test_with_server.py
+      env:
+        SQLALCHEMY_WARN_20: 1
+        OMP_NUM_THREADS: 1
+        TEST_DB_URL: mysql+pymysql://user:test@127.0.0.1/optunatest
+
+    - name: Tests PostgreSQL
+      run: |
+        pytest tests/storages_tests/test_with_server.py
+      env:
+        OMP_NUM_THREADS: 1
+        TEST_DB_URL: postgresql+psycopg2://user:test@127.0.0.1/optunatest
+
+    - name: Tests Journal Redis
+      run: |
+        pytest tests/storages_tests/test_with_server.py
+      env:
+        OMP_NUM_THREADS: 1
+        TEST_DB_URL: redis://localhost:6379
+        TEST_DB_MODE: journal-redis
diff --git a/.github/workflows/tests-with-minimum-versions.yml b/.github/workflows/tests-with-minimum-versions.yml
index e69de29bb2..679d9ef7e6 100644
--- a/.github/workflows/tests-with-minimum-versions.yml
+++ b/.github/workflows/tests-with-minimum-versions.yml
@@ -0,0 +1,92 @@
+name: Tests with minimum versions
+
+on:
+  push:
+    branches:
+      - master
+  pull_request: {}
+  schedule:
+    - cron: '0 23 * * SUN-THU'
+  workflow_dispatch:
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  tests-with-minimum-versions:
+    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
+    runs-on: ubuntu-latest
+
+    strategy:
+      matrix:
+        python-version: ['3.7', '3.8', '3.9']
+
+    services:
+      redis:
+        image: redis
+        options: >-
+          --health-cmd "redis-cli ping"
+          --health-interval 10s
+          --health-timeout 5s
+          --health-retries 5
+
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v3
+
+    - name: Setup Python${{ matrix.python-version }}
+      uses: actions/setup-python@v4
+      with:
+        python-version: ${{ matrix.python-version }}
+
+    - name: Setup cache
+      uses: actions/cache@v3
+      env:
+        cache-name: test-with-minimum-versions
+      with:
+        path: ~/.cache/pip
+        key: ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/setup.py') }}-v1
+        restore-keys: |
+          ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/setup.py') }}
+
+
+    - name: Setup pip
+      run: |
+        python -m pip install --upgrade pip
+        pip install --progress-bar off -U setuptools
+
+    - name: Install
+      run: |
+        # Install minimal dependencies and confirm that `import optuna` is successful.
+        pip install --progress-bar off .
+        python -c 'import optuna'
+        optuna --version
+
+        pip install --progress-bar off .[test]
+        pip install --progress-bar off .[optional] --extra-index-url https://download.pytorch.org/whl/cpu
+
+    - name: Install dependencies with minimum versions
+      run: |
+        # Install dependencies with minimum versions.
+        pip uninstall -y alembic cmaes packaging sqlalchemy plotly scikit-learn
+        pip install alembic==1.5.0 cmaes==0.10.0 packaging==20.0 sqlalchemy==1.3.0 numpy==1.20.3 tqdm==4.27.0 colorlog==0.3 PyYAML==5.1
+        pip install plotly==5.0.0 scikit-learn==0.24.2  # optional extras
+
+    - name: Output installed packages
+      run: |
+        pip freeze --all
+    - name: Output dependency tree
+      run: |
+        pip install pipdeptree
+        pipdeptree
+
+    - name: Scheduled tests
+      if:  ${{ github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' }}
+      run: |
+        pytest tests -m "not integration"
+
+    - name: Tests
+      if:  ${{ github.event_name != 'schedule' && github.event_name != 'workflow_dispatch' }}
+      run: |
+        pytest tests -m "not integration and not slow"
diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index e69de29bb2..4c8d172139 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -0,0 +1,89 @@
+name: Tests
+
+on:
+  push:
+    branches:
+      - master
+  pull_request: {}
+  schedule:
+    - cron: '0 23 * * SUN-THU'
+  workflow_dispatch:
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  tests:
+    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
+    runs-on: ubuntu-latest
+
+    strategy:
+      matrix:
+        python-version: ['3.7', '3.8', '3.9', '3.10', '3.11']
+
+    services:
+      redis:
+        image: redis
+        options: >-
+          --health-cmd "redis-cli ping"
+          --health-interval 10s
+          --health-timeout 5s
+          --health-retries 5
+
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v3
+
+    - name: Setup Python${{ matrix.python-version }}
+      uses: actions/setup-python@v4
+      with:
+        python-version: ${{ matrix.python-version }}
+
+    - name: Setup cache
+      uses: actions/cache@v3
+      env:
+        cache-name: test
+      with:
+        path: ~/.cache/pip
+        key: ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
+        restore-keys: |
+          ${{ runner.os }}-${{ matrix.python-version }}-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
+
+
+    - name: Setup pip
+      run: |
+        python -m pip install --upgrade pip
+        pip install --progress-bar off -U setuptools
+
+    - name: Install
+      run: |
+        # Install minimal dependencies and confirm that `import optuna` is successful.
+        pip install --progress-bar off .
+        python -c 'import optuna'
+        optuna --version
+
+        pip install --progress-bar off .[test]
+        pip install --progress-bar off .[optional] --extra-index-url https://download.pytorch.org/whl/cpu
+
+    - name: Output installed packages
+      run: |
+        pip freeze --all
+    - name: Output dependency tree
+      run: |
+        pip install pipdeptree
+        pipdeptree
+
+    - name: Scheduled tests
+      if:  ${{ github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' }}
+      run: |
+        pytest tests -m "not integration"
+      env:
+        SQLALCHEMY_WARN_20: 1
+
+    - name: Tests
+      if:  ${{ github.event_name != 'schedule' && github.event_name != 'workflow_dispatch' }}
+      run: |
+        pytest tests -m "not integration and not slow"
+      env:
+        SQLALCHEMY_WARN_20: 1
diff --git a/.github/workflows/windows-tests.yml b/.github/workflows/windows-tests.yml
index e69de29bb2..7b46856277 100644
--- a/.github/workflows/windows-tests.yml
+++ b/.github/workflows/windows-tests.yml
@@ -0,0 +1,135 @@
+# Run tests and integration tests on Windows, which are triggered by each master push.
+# Currently, Python3.9 is only used as an environment.
+# This is mainly for the sake of speed.
+name: windows-tests
+
+on:
+  push:
+    branches:
+      - master
+  pull_request: {}
+  schedule:
+    - cron: '0 23 * * SUN-THU'
+  workflow_dispatch:
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref == 'refs/heads/master' && github.run_number || github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  tests-windows:
+    runs-on: windows-latest
+
+    # Not intended for forks.
+    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v3
+
+    - name: Setup Python3.9
+      uses: actions/setup-python@v4
+      with:
+        python-version: "3.9"
+
+    - name: Setup cache
+      uses: actions/cache@v3
+      env:
+        cache-name: windows-test
+      with:
+        path: ~\\AppData\\Local\\pip\\Cache
+        key: ${{ runner.os }}-3.9-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
+        restore-keys: |
+          ${{ runner.os }}-3.9-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
+
+    - name: Install
+      run: |
+        python -m pip install --upgrade pip
+        pip install --progress-bar off -U setuptools
+        # Install minimal dependencies and confirm that `import optuna` is successful.
+        pip install --progress-bar off .
+        python -c 'import optuna'
+        optuna --version
+        pip install --progress-bar off .[test]
+        pip install --progress-bar off .[optional]
+        pip install PyQt6 # Install PyQT for using QtAgg as matplotlib backend.
+
+    - name: Output installed packages
+      run: |
+        pip freeze --all
+    - name: Output dependency tree
+      run: |
+        pip install pipdeptree
+        pipdeptree
+
+    - name: Scheduled tests
+      if:  ${{ github.event_name == 'schedule' || github.event_name == 'workflow_dispatch' }}
+      run: |
+        pytest -m "not integration"
+      env:
+        SQLALCHEMY_WARN_20: 1
+        MPLBACKEND: "QtAgg" # Use QtAgg as matplotlib backend.
+
+    - name: Tests
+      if:  ${{ github.event_name != 'schedule' && github.event_name != 'workflow_dispatch' }}
+      run: |
+        pytest -m "not integration and not slow"
+      env:
+        MPLBACKEND: "QtAgg" # Use QtAgg as matplotlib backend.
+
+  tests-integration-windows:
+    runs-on: windows-latest
+
+    # Not intended for forks.
+    if: (github.event_name == 'schedule' && github.repository == 'optuna/optuna') || (github.event_name != 'schedule')
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v3
+
+    - name: Setup Python3.9
+      uses: actions/setup-python@v4
+      with:
+        python-version: "3.9"
+
+    - name: Setup cache
+      uses: actions/cache@v3
+      env:
+        cache-name: windows-test-integration
+      with:
+        path: ~\\AppData\\Local\\pip\\Cache
+        key: ${{ runner.os }}-3.9-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}-v1
+        restore-keys: |
+          ${{ runner.os }}-3.9-${{ env.cache-name }}-${{ hashFiles('**/pyproject.toml') }}
+
+    - name: Setup MPI
+      uses: mpi4py/setup-mpi@v1
+      with:
+        mpi: "msmpi"
+
+    - name: Install
+      run: |
+        python -m pip install --upgrade pip
+        pip install --progress-bar off -U setuptools
+        # Install minimal dependencies and confirm that `import optuna` is successful.
+        pip install --progress-bar off .
+        python -c 'import optuna'
+        optuna --version
+        pip install --progress-bar off .[test]
+        pip install --progress-bar off .[optional]
+        pip install --progress-bar off .[integration]
+        pip install "distributed<2023.3.2"
+
+    - name: Output installed packages
+      run: |
+        pip freeze --all
+    - name: Output dependency tree
+      run: |
+        pip install pipdeptree
+        pipdeptree
+
+    - name: Tests
+      # Skip allennlp tests since it's not supported on Windows.
+      run: |
+        pytest tests -m "integration" `
+          --ignore tests/integration_tests/allennlp_tests/test_allennlp.py `
+      env:
+        OMP_NUM_THREADS: 1

From ef4c60453192e907caf9bf1eee24636655dc464b Mon Sep 17 00:00:00 2001
From: nabenabe0928 <shuhei.watanabe.utokyo@gmail.com>
Date: Wed, 1 Nov 2023 07:00:29 +0100
Subject: [PATCH 05/12] Modify an expression a bit

---
 optuna/multi_objective/samplers/_motpe.py       | 6 +++---
 optuna/samplers/_tpe/multi_objective_sampler.py | 4 ++--
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/optuna/multi_objective/samplers/_motpe.py b/optuna/multi_objective/samplers/_motpe.py
index 85831d9b66..5add0c5e86 100644
--- a/optuna/multi_objective/samplers/_motpe.py
+++ b/optuna/multi_objective/samplers/_motpe.py
@@ -31,8 +31,8 @@ class MOTPEMultiObjectiveSampler(BaseMultiObjectiveSampler):
     .. note::
         For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
         This sampler is deprecated and :class:`~optuna.samplers.TPESampler` should be
-        used instead. The following code shows how you run :class:`~optuna.samplers.TPESampler` on
-        a multi-objective task:
+        used instead. The following code shows how you apply :class:`~optuna.samplers.TPESampler`
+        to a multi-objective task:
 
         .. testcode::
 
@@ -52,7 +52,7 @@ def objective(trial):
             study = optuna.create_study(directions=["minimize", "maximize"], sampler=sampler)
             study.optimize(objective, n_trials=100)
 
-    For further information about MOTPE algorithm, please refer to the following paper:
+    For further information about MOTPE algorithm, please refer to the following papers:
 
     - `Multiobjective tree-structured parzen estimator for computationally expensive optimization
       problems <https://dl.acm.org/doi/abs/10.1145/3377930.3389817>`_
diff --git a/optuna/samplers/_tpe/multi_objective_sampler.py b/optuna/samplers/_tpe/multi_objective_sampler.py
index a32db024a0..cee92163f7 100644
--- a/optuna/samplers/_tpe/multi_objective_sampler.py
+++ b/optuna/samplers/_tpe/multi_objective_sampler.py
@@ -27,8 +27,8 @@ class MOTPESampler(TPESampler):
     .. note::
         For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
         This sampler is deprecated and :class:`~optuna.samplers.TPESampler` should be
-        used instead. The following code shows how you run :class:`~optuna.samplers.TPESampler` on
-        a multi-objective task:
+        used instead. The following code shows how you apply :class:`~optuna.samplers.TPESampler`
+        to a multi-objective task:
 
         .. testcode::
 

From b078625d859d7eb3608cf4e1ca0a824a0d8ad61b Mon Sep 17 00:00:00 2001
From: Shuhei Watanabe <47781922+nabenabe0928@users.noreply.github.com>
Date: Thu, 2 Nov 2023 08:59:18 +0100
Subject: [PATCH 06/12] Add a missing `maximize` in the comment

Co-authored-by: Shinichi Hemmi <50256998+Alnusjaponica@users.noreply.github.com>
---
 optuna/samplers/_tpe/sampler.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/optuna/samplers/_tpe/sampler.py b/optuna/samplers/_tpe/sampler.py
index 7a7157af91..abe403aa30 100644
--- a/optuna/samplers/_tpe/sampler.py
+++ b/optuna/samplers/_tpe/sampler.py
@@ -118,7 +118,7 @@ def objective(trial):
                 return f1, f2
 
 
-            # We minimize the first objective and the second objective.
+            # We minimize the first objective and maximize the second objective.
             sampler = optuna.samplers.TPESampler()
             study = optuna.create_study(directions=["minimize", "maximize"], sampler=sampler)
             study.optimize(objective, n_trials=100)

From ccd49d9f4b92633352e1921696fba9f82f79431a Mon Sep 17 00:00:00 2001
From: Shuhei Watanabe <47781922+nabenabe0928@users.noreply.github.com>
Date: Thu, 2 Nov 2023 09:00:18 +0100
Subject: [PATCH 07/12] Add a missing `maximize` in the comment

Co-authored-by: Shinichi Hemmi <50256998+Alnusjaponica@users.noreply.github.com>
---
 optuna/multi_objective/samplers/_motpe.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/optuna/multi_objective/samplers/_motpe.py b/optuna/multi_objective/samplers/_motpe.py
index 5add0c5e86..e116b453d8 100644
--- a/optuna/multi_objective/samplers/_motpe.py
+++ b/optuna/multi_objective/samplers/_motpe.py
@@ -47,7 +47,7 @@ def objective(trial):
                 return f1, f2
 
 
-            # We minimize the first objective and the second objective.
+            # We minimize the first objective and maximize the second objective.
             sampler = optuna.samplers.TPESampler()
             study = optuna.create_study(directions=["minimize", "maximize"], sampler=sampler)
             study.optimize(objective, n_trials=100)

From 5e25b9455e892fd2796fc30f7ec7bad33461e475 Mon Sep 17 00:00:00 2001
From: Shuhei Watanabe <47781922+nabenabe0928@users.noreply.github.com>
Date: Thu, 2 Nov 2023 09:10:23 +0100
Subject: [PATCH 08/12] Add self-referencing of `TPESampler` in _tpe.sampler.py

Co-authored-by: Shinichi Hemmi <50256998+Alnusjaponica@users.noreply.github.com>
---
 optuna/samplers/_tpe/sampler.py | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/optuna/samplers/_tpe/sampler.py b/optuna/samplers/_tpe/sampler.py
index abe403aa30..128a060e5c 100644
--- a/optuna/samplers/_tpe/sampler.py
+++ b/optuna/samplers/_tpe/sampler.py
@@ -102,8 +102,9 @@ def objective(trial):
 
     .. note::
         For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
-        :class:`~optuna.samplers.MOTPESampler` is deprecated and this sampler should be used
-        instead. The following code shows how you apply this sampler to a multi-objective task:
+        :class:`~optuna.samplers.MOTPESampler` is deprecated and
+        :class:`~optuna.samplers.TPESampler` should be used instead. The following code shows
+        how you apply :class:`~optuna.samplers.TPESampler` to a multi-objective task:
 
         .. testcode::
 

From 131bbaad1cbacbc5fdd27955b9246adb3aa9dd36 Mon Sep 17 00:00:00 2001
From: nabenabe0928 <shuhei.watanabe.utokyo@gmail.com>
Date: Thu, 2 Nov 2023 09:19:37 +0100
Subject: [PATCH 09/12] Remove the ref of the TPE paper

---
 optuna/samplers/_tpe/sampler.py | 2 --
 1 file changed, 2 deletions(-)

diff --git a/optuna/samplers/_tpe/sampler.py b/optuna/samplers/_tpe/sampler.py
index 128a060e5c..8ed6f834e9 100644
--- a/optuna/samplers/_tpe/sampler.py
+++ b/optuna/samplers/_tpe/sampler.py
@@ -74,8 +74,6 @@ class TPESampler(BaseSampler):
       <https://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf>`_
     - `Making a Science of Model Search: Hyperparameter Optimization in Hundreds of
       Dimensions for Vision Architectures <http://proceedings.mlr.press/v28/bergstra13.pdf>`_
-    - `Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for
-      Better Empirical Performance <https://arxiv.org/abs/2304.11127>`_
 
     For multi-objective TPE (MOTPE), please refer to the following papers:
 

From ef8cc4b2aa0223d600a3525080c1b09a79fbd8bf Mon Sep 17 00:00:00 2001
From: Shuhei Watanabe <47781922+nabenabe0928@users.noreply.github.com>
Date: Thu, 2 Nov 2023 09:36:43 +0100
Subject: [PATCH 10/12] Add a missing `maximize` in the comment

Co-authored-by: Shinichi Hemmi <50256998+Alnusjaponica@users.noreply.github.com>
---
 optuna/samplers/_tpe/multi_objective_sampler.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/optuna/samplers/_tpe/multi_objective_sampler.py b/optuna/samplers/_tpe/multi_objective_sampler.py
index cee92163f7..83565dacde 100644
--- a/optuna/samplers/_tpe/multi_objective_sampler.py
+++ b/optuna/samplers/_tpe/multi_objective_sampler.py
@@ -43,7 +43,7 @@ def objective(trial):
                 return f1, f2
 
 
-            # We minimize the first objective and the second objective.
+            # We minimize the first objective and maximize the second objective.
             sampler = optuna.samplers.TPESampler()
             study = optuna.create_study(directions=["minimize", "maximize"], sampler=sampler)
             study.optimize(objective, n_trials=100)

From 42eb9ebea2806e862c1f9bd9b28ea495b7078c21 Mon Sep 17 00:00:00 2001
From: nabenabe0928 <shuhei.watanabe.utokyo@gmail.com>
Date: Mon, 6 Nov 2023 09:22:51 +0100
Subject: [PATCH 11/12] Fix the deprecated versions in the doc

---
 optuna/multi_objective/samplers/_motpe.py       | 8 ++++----
 optuna/samplers/_tpe/multi_objective_sampler.py | 6 +++---
 2 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/optuna/multi_objective/samplers/_motpe.py b/optuna/multi_objective/samplers/_motpe.py
index e116b453d8..9f358b798a 100644
--- a/optuna/multi_objective/samplers/_motpe.py
+++ b/optuna/multi_objective/samplers/_motpe.py
@@ -29,10 +29,10 @@ class MOTPEMultiObjectiveSampler(BaseMultiObjectiveSampler):
     This sampler is a multi-objective version of :class:`~optuna.samplers.TPESampler`.
 
     .. note::
-        For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
-        This sampler is deprecated and :class:`~optuna.samplers.TPESampler` should be
-        used instead. The following code shows how you apply :class:`~optuna.samplers.TPESampler`
-        to a multi-objective task:
+        For `v2.4.0 <https://github.com/optuna/optuna/releases/tag/v2.4.0>`_ or later,
+        :class:`~optuna.multi_objective.samplers.MOTPEMultiObjectiveSampler` is deprecated and
+        :class:`~optuna.samplers.TPESampler` should be used instead. The following code shows how
+        you apply :class:`~optuna.samplers.TPESampler` to a multi-objective task:
 
         .. testcode::
 
diff --git a/optuna/samplers/_tpe/multi_objective_sampler.py b/optuna/samplers/_tpe/multi_objective_sampler.py
index 83565dacde..6f9ff9f78e 100644
--- a/optuna/samplers/_tpe/multi_objective_sampler.py
+++ b/optuna/samplers/_tpe/multi_objective_sampler.py
@@ -26,9 +26,9 @@ class MOTPESampler(TPESampler):
 
     .. note::
         For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
-        This sampler is deprecated and :class:`~optuna.samplers.TPESampler` should be
-        used instead. The following code shows how you apply :class:`~optuna.samplers.TPESampler`
-        to a multi-objective task:
+        :class:`~optuna.samplers.MOTPESampler` is deprecated and
+        :class:`~optuna.samplers.TPESampler` should be used instead. The following code shows how
+        you apply :class:`~optuna.samplers.TPESampler` to a multi-objective task:
 
         .. testcode::
 

From 3b0e58ee5fc5401851a381ac964c055ce1c6137e Mon Sep 17 00:00:00 2001
From: nabenabe0928 <shuhei.watanabe.utokyo@gmail.com>
Date: Mon, 6 Nov 2023 09:35:26 +0100
Subject: [PATCH 12/12] Address the comment by knshnb

---
 optuna/samplers/_tpe/sampler.py | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/optuna/samplers/_tpe/sampler.py b/optuna/samplers/_tpe/sampler.py
index 8ed6f834e9..b8a6aaa13d 100644
--- a/optuna/samplers/_tpe/sampler.py
+++ b/optuna/samplers/_tpe/sampler.py
@@ -99,10 +99,8 @@ def objective(trial):
             study.optimize(objective, n_trials=10)
 
     .. note::
-        For `v2.9.0 <https://github.com/optuna/optuna/releases/tag/v2.9.0>`_ or later,
-        :class:`~optuna.samplers.MOTPESampler` is deprecated and
-        :class:`~optuna.samplers.TPESampler` should be used instead. The following code shows
-        how you apply :class:`~optuna.samplers.TPESampler` to a multi-objective task:
+        :class:`~optuna.samplers.TPESampler` can handle a multi-objective task as well and
+        the following shows an example:
 
         .. testcode::