Merge pull request optuna#5515 from virendrapatil24/fix-http-links-un…

…derscore

fixed hyperlinks to use double trailing underscores

optuna/_hypervolume/hssp.py

@@ -132,7 +132,7 @@ def _solve_hssp(
     paper:
 
     - `Greedy Hypervolume Subset Selection in Low Dimensions
-       <https://doi.org/10.1162/EVCO_a_00188>`_
+       <https://doi.org/10.1162/EVCO_a_00188>`__
     """
     if subset_size == rank_i_indices.size:
         return rank_i_indices

optuna/importance/__init__.py

@@ -68,7 +68,7 @@ def get_param_importances(
             .. note::
                 :class:`~optuna.importance.FanovaImportanceEvaluator` takes over 1 minute
                 when given a study that contains 1000+ trials. We published
-                `optuna-fast-fanova <https://github.com/optuna/optuna-fast-fanova>`_ library,
+                `optuna-fast-fanova <https://github.com/optuna/optuna-fast-fanova>`__ library,
                 that is a Cython accelerated fANOVA implementation.
                 By using it, you can get hyperparameter importances within a few seconds.
                 If ``n_trials`` is more than 10000, the Cython implementation takes more than

optuna/importance/_fanova/_evaluator.py

@@ -23,7 +23,7 @@ class FanovaImportanceEvaluator(BaseImportanceEvaluator):
 
     Implements the fANOVA hyperparameter importance evaluation algorithm in
     `An Efficient Approach for Assessing Hyperparameter Importance
-    <http://proceedings.mlr.press/v32/hutter14.html>`_.
+    <http://proceedings.mlr.press/v32/hutter14.html>`__.
 
     fANOVA fits a random forest regression model that predicts the objective values
     of :class:`~optuna.trial.TrialState.COMPLETE` trials given their parameter configurations.
@@ -33,13 +33,13 @@ class FanovaImportanceEvaluator(BaseImportanceEvaluator):
     .. note::
 
         This class takes over 1 minute when given a study that contains 1000+ trials.
-        We published `optuna-fast-fanova <https://github.com/optuna/optuna-fast-fanova>`_ library,
+        We published `optuna-fast-fanova <https://github.com/optuna/optuna-fast-fanova>`__ library,
         that is a Cython accelerated fANOVA implementation. By using it, you can get hyperparameter
         importances within a few seconds.
 
     .. note::
 
-        Requires the `sklearn <https://github.com/scikit-learn/scikit-learn>`_ Python package.
+        Requires the `sklearn <https://github.com/scikit-learn/scikit-learn>`__ Python package.
 
     .. note::
 

optuna/importance/_mean_decrease_impurity.py

@@ -31,9 +31,9 @@ class MeanDecreaseImpurityImportanceEvaluator(BaseImportanceEvaluator):
 
     .. note::
 
-        This evaluator requires the `sklearn <https://scikit-learn.org/stable/>`_ Python package
+        This evaluator requires the `sklearn <https://scikit-learn.org/stable/>`__ Python package
         and is based on `sklearn.ensemble.RandomForestClassifier.feature_importances_
-        <https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier.feature_importances_>`_.
+        <https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier.feature_importances_>`__.
 
     Args:
         n_trees:

optuna/importance/_ped_anova/evaluator.py

@@ -72,7 +72,7 @@ class PedAnovaImportanceEvaluator(BaseImportanceEvaluator):
     For further information about PED-ANOVA algorithm, please refer to the following paper:
 
     - `PED-ANOVA: Efficiently Quantifying Hyperparameter Importance in Arbitrary Subspaces
-      <https://arxiv.org/abs/2304.10255>`_
+      <https://arxiv.org/abs/2304.10255>`__
 
     .. note::
 
@@ -81,7 +81,7 @@ class PedAnovaImportanceEvaluator(BaseImportanceEvaluator):
 
     .. note::
 
-        Please refer to `the original work <https://github.com/nabenabe0928/local-anova>`_.
+        Please refer to `the original work <https://github.com/nabenabe0928/local-anova>`__.
 
     Args:
         baseline_quantile:

optuna/pruners/_hyperband.py

@@ -21,15 +21,15 @@ class HyperbandPruner(BasePruner):
     :math:`n` as its hyperparameter.  For a given finite budget :math:`B`,
     all the configurations have the resources of :math:`B \\over n` on average.
     As you can see, there will be a trade-off of :math:`B` and :math:`B \\over n`.
-    `Hyperband <http://www.jmlr.org/papers/volume18/16-558/16-558.pdf>`_ attacks this trade-off
+    `Hyperband <http://www.jmlr.org/papers/volume18/16-558/16-558.pdf>`__ attacks this trade-off
     by trying different :math:`n` values for a fixed budget.
 
     .. note::
         * In the Hyperband paper, the counterpart of :class:`~optuna.samplers.RandomSampler`
           is used.
         * Optuna uses :class:`~optuna.samplers.TPESampler` by default.
         * `The benchmark result
-          <https://github.com/optuna/optuna/pull/828#issuecomment-575457360>`_
+          <https://github.com/optuna/optuna/pull/828#issuecomment-575457360>`__
           shows that :class:`optuna.pruners.HyperbandPruner` supports both samplers.
 
     .. note::
@@ -58,7 +58,7 @@ class HyperbandPruner(BasePruner):
         (\\frac{\\texttt{max}\\_\\texttt{resource}}{\\texttt{min}\\_\\texttt{resource}})) + 1`.
         Please set ``reduction_factor`` so that the number of brackets is not too large (about 4 –
         6 in most use cases). Please see Section 3.6 of the `original paper
-        <http://www.jmlr.org/papers/volume18/16-558/16-558.pdf>`_ for the detail.
+        <http://www.jmlr.org/papers/volume18/16-558/16-558.pdf>`__ for the detail.
 
     Example:
 
@@ -235,7 +235,7 @@ def _get_bracket_id(
         """Compute the index of bracket for a trial of ``trial_number``.
 
         The index of a bracket is noted as :math:`s` in
-        `Hyperband paper <http://www.jmlr.org/papers/volume18/16-558/16-558.pdf>`_.
+        `Hyperband paper <http://www.jmlr.org/papers/volume18/16-558/16-558.pdf>`__.
         """
 
         if len(self._pruners) == 0:

optuna/pruners/_successive_halving.py

@@ -11,18 +11,18 @@
 class SuccessiveHalvingPruner(BasePruner):
     """Pruner using Asynchronous Successive Halving Algorithm.
 
-    `Successive Halving <https://proceedings.mlr.press/v51/jamieson16.html>`_ is a bandit-based
+    `Successive Halving <https://proceedings.mlr.press/v51/jamieson16.html>`__ is a bandit-based
     algorithm to identify the best one among multiple configurations. This class implements an
     asynchronous version of Successive Halving. Please refer to the paper of
     `Asynchronous Successive Halving <https://proceedings.mlsys.org/paper_files/paper/2020/file/
-    a06f20b349c6cf09a6b171c71b88bbfc-Paper.pdf>`_ for detailed descriptions.
+    a06f20b349c6cf09a6b171c71b88bbfc-Paper.pdf>`__ for detailed descriptions.
 
     Note that, this class does not take care of the parameter for the maximum
     resource, referred to as :math:`R` in the paper. The maximum resource allocated to a trial is
     typically limited inside the objective function (e.g., ``step`` number in `simple_pruning.py
-    <https://github.com/optuna/optuna-examples/blob/main/simple_pruning.py>`_,
+    <https://github.com/optuna/optuna-examples/blob/main/simple_pruning.py>`__,
     ``EPOCH`` number in `chainer_integration.py
-    <https://github.com/optuna/optuna-examples/tree/main/chainer/chainer_integration.py#L73>`_).
+    <https://github.com/optuna/optuna-examples/tree/main/chainer/chainer_integration.py#L73>`__).
 
     .. seealso::
         Please refer to :meth:`~optuna.trial.Trial.report`.
@@ -71,7 +71,7 @@ def objective(trial):
         min_resource:
             A parameter for specifying the minimum resource allocated to a trial
             (in the `paper <https://proceedings.mlsys.org/paper_files/paper/2020/file/
-            a06f20b349c6cf09a6b171c71b88bbfc-Paper.pdf>`_ this parameter is referred to as
+            a06f20b349c6cf09a6b171c71b88bbfc-Paper.pdf>`__ this parameter is referred to as
             :math:`r`).
             This parameter defaults to 'auto' where the value is determined based on a heuristic
             that looks at the number of required steps for the first trial to complete.
@@ -98,14 +98,14 @@ def objective(trial):
         reduction_factor:
             A parameter for specifying reduction factor of promotable trials
             (in the `paper <https://proceedings.mlsys.org/paper_files/paper/2020/file/
-            a06f20b349c6cf09a6b171c71b88bbfc-Paper.pdf>`_ this parameter is
+            a06f20b349c6cf09a6b171c71b88bbfc-Paper.pdf>`__ this parameter is
             referred to as :math:`\\eta`).  At the completion point of each rung,
             about :math:`{1 \\over \\mathsf{reduction}\\_\\mathsf{factor}}`
             trials will be promoted.
         min_early_stopping_rate:
             A parameter for specifying the minimum early-stopping rate
             (in the `paper <https://proceedings.mlsys.org/paper_files/paper/2020/file/
-            a06f20b349c6cf09a6b171c71b88bbfc-Paper.pdf>`_ this parameter is
+            a06f20b349c6cf09a6b171c71b88bbfc-Paper.pdf>`__ this parameter is
             referred to as :math:`s`).
         bootstrap_count:
             Minimum number of trials that need to complete a rung before any trial

optuna/pruners/_wilcoxon.py

@@ -22,7 +22,7 @@
 
 @experimental_class("3.6.0")
 class WilcoxonPruner(BasePruner):
-    """Pruner based on the `Wilcoxon signed-rank test <https://en.wikipedia.org/w/index.php?title=Wilcoxon_signed-rank_test&oldid=1195011212>`_.
+    """Pruner based on the `Wilcoxon signed-rank test <https://en.wikipedia.org/w/index.php?title=Wilcoxon_signed-rank_test&oldid=1195011212>`__.
 
     This pruner performs the Wilcoxon signed-rank test between the current trial and the current best trial,
     and stops whenever the pruner is sure up to a given p-value that the current trial is worse than the best one.

optuna/samplers/_cmaes.py

@@ -59,7 +59,7 @@ class _CmaEsAttrKeys(NamedTuple):
 
 
 class CmaEsSampler(BaseSampler):
-    """A sampler using `cmaes <https://github.com/CyberAgentAILab/cmaes>`_ as the backend.
+    """A sampler using `cmaes <https://github.com/CyberAgentAILab/cmaes>`__ as the backend.
 
     Example:
 
@@ -95,27 +95,27 @@ def objective(trial):
     For further information about CMA-ES algorithm, please refer to the following papers:
 
     - `N. Hansen, The CMA Evolution Strategy: A Tutorial. arXiv:1604.00772, 2016.
-      <https://arxiv.org/abs/1604.00772>`_
+      <https://arxiv.org/abs/1604.00772>`__
     - `A. Auger and N. Hansen. A restart CMA evolution strategy with increasing population
       size. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2005),
-      pages 1769–1776. IEEE Press, 2005. <https://doi.org/10.1109/CEC.2005.1554902>`_
+      pages 1769–1776. IEEE Press, 2005. <https://doi.org/10.1109/CEC.2005.1554902>`__
     - `N. Hansen. Benchmarking a BI-Population CMA-ES on the BBOB-2009 Function Testbed.
-      GECCO Workshop, 2009. <https://doi.org/10.1145/1570256.1570333>`_
+      GECCO Workshop, 2009. <https://doi.org/10.1145/1570256.1570333>`__
     - `Raymond Ros, Nikolaus Hansen. A Simple Modification in CMA-ES Achieving Linear Time and
       Space Complexity. 10th International Conference on Parallel Problem Solving From Nature,
-      Sep 2008, Dortmund, Germany. inria-00287367. <https://doi.org/10.1007/978-3-540-87700-4_30>`_
+      Sep 2008, Dortmund, Germany. inria-00287367. <https://doi.org/10.1007/978-3-540-87700-4_30>`__
     - `Masahiro Nomura, Shuhei Watanabe, Youhei Akimoto, Yoshihiko Ozaki, Masaki Onishi.
       Warm Starting CMA-ES for Hyperparameter Optimization, AAAI. 2021.
-      <https://doi.org/10.1609/aaai.v35i10.17109>`_
+      <https://doi.org/10.1609/aaai.v35i10.17109>`__
     - `R. Hamano, S. Saito, M. Nomura, S. Shirakawa. CMA-ES with Margin: Lower-Bounding Marginal
       Probability for Mixed-Integer Black-Box Optimization, GECCO. 2022.
-      <https://doi.org/10.1145/3512290.3528827>`_
+      <https://doi.org/10.1145/3512290.3528827>`__
     - `M. Nomura, Y. Akimoto, I. Ono. CMA-ES with Learning Rate Adaptation: Can CMA-ES with
       Default Population Size Solve Multimodal and Noisy Problems?, GECCO. 2023.
-      <https://doi.org/10.1145/3583131.3590358>`_
+      <https://doi.org/10.1145/3583131.3590358>`__
 
     .. seealso::
-        You can also use `optuna_integration.PyCmaSampler <https://optuna-integration.readthedocs.io/en/stable/reference/generated/optuna_integration.PyCmaSampler.html#optuna_integration.PyCmaSampler>`_ which is a sampler using cma
+        You can also use `optuna_integration.PyCmaSampler <https://optuna-integration.readthedocs.io/en/stable/reference/generated/optuna_integration.PyCmaSampler.html#optuna_integration.PyCmaSampler>`__ which is a sampler using cma
         library as the backend.
 
     Args:
@@ -196,7 +196,7 @@ def objective(trial):
                 :class:`~optuna.pruners.MedianPruner` is used. On the other hand, it is suggested
                 to set this flag :obj:`True` when the :class:`~optuna.pruners.HyperbandPruner` is
                 used. Please see `the benchmark result
-                <https://github.com/optuna/optuna/pull/1229>`_ for the details.
+                <https://github.com/optuna/optuna/pull/1229>`__ for the details.
 
         use_separable_cma:
             If this is :obj:`True`, the covariance matrix is constrained to be diagonal.

optuna/samplers/_nsgaiii/_sampler.py

@@ -47,11 +47,11 @@ class NSGAIIISampler(BaseSampler):
 
     - `An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based
       Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints
-      <https://doi.org/10.1109/TEVC.2013.2281535>`_
+      <https://doi.org/10.1109/TEVC.2013.2281535>`__
     - `An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based
       Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive
       Approach
-      <https://doi.org/10.1109/TEVC.2013.2281534>`_
+      <https://doi.org/10.1109/TEVC.2013.2281534>`__
 
     Args:
         reference_points:

optuna/samplers/_qmc.py

@@ -42,11 +42,11 @@ class QMCSampler(BaseSampler):
 
     - `Bergstra, James, and Yoshua Bengio. Random search for hyper-parameter optimization.
       Journal of machine learning research 13.2, 2012.
-      <https://jmlr.org/papers/v13/bergstra12a.html>`_
+      <https://jmlr.org/papers/v13/bergstra12a.html>`__
 
     We use the QMC implementations in Scipy. For the details of the QMC algorithm,
     see the Scipy API references on `scipy.stats.qmc
-    <https://scipy.github.io/devdocs/reference/stats.qmc.html>`_.
+    <https://scipy.github.io/devdocs/reference/stats.qmc.html>`__.
 
     .. note:
         If your search space contains categorical parameters, it samples the categorical

optuna/samplers/_tpe/sampler.py

@@ -73,17 +73,17 @@ class TPESampler(BaseSampler):
     For further information about TPE algorithm, please refer to the following papers:
 
     - `Algorithms for Hyper-Parameter Optimization
-      <https://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf>`_
+      <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>`_
+      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>`_
+      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://doi.org/10.1145/3377930.3389817>`_
-    - `Multiobjective Tree-Structured Parzen Estimator <https://doi.org/10.1613/jair.1.13188>`_
+      Problems <https://doi.org/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:
@@ -154,23 +154,23 @@ def objective(trial):
         weights:
             A function that takes the number of finished trials and returns a weight for them.
             See `Making a Science of Model Search: Hyperparameter Optimization in Hundreds of
-            Dimensions for Vision Architectures <http://proceedings.mlr.press/v28/bergstra13.pdf>`_
-            for more details.
+            Dimensions for Vision Architectures
+            <http://proceedings.mlr.press/v28/bergstra13.pdf>`__ for more details.
 
             .. note::
                 In the multi-objective case, this argument is only used to compute the weights of
                 bad trials, i.e., trials to construct `g(x)` in the `paper
-                <https://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf>`_
+                <https://papers.nips.cc/paper/4443-algorithms-for-hyper-parameter-optimization.pdf>`__
                 ). The weights of good trials, i.e., trials to construct `l(x)`, are computed by a
                 rule based on the hypervolume contribution proposed in the `paper of MOTPE
-                <https://doi.org/10.1613/jair.1.13188>`_.
+                <https://doi.org/10.1613/jair.1.13188>`__.
         seed:
             Seed for random number generator.
         multivariate:
             If this is :obj:`True`, the multivariate TPE is used when suggesting parameters.
             The multivariate TPE is reported to outperform the independent TPE. See `BOHB: Robust
             and Efficient Hyperparameter Optimization at Scale
-            <http://proceedings.mlr.press/v80/falkner18a.html>`_ for more details.
+            <http://proceedings.mlr.press/v80/falkner18a.html>`__ for more details.
 
             .. note::
                 Added in v2.2.0 as an experimental feature. The interface may change in newer
@@ -547,7 +547,7 @@ def hyperopt_parameters() -> dict[str, Any]:
         Example:
 
             Create a :class:`~optuna.samplers.TPESampler` instance with the default
-            parameters of `hyperopt <https://github.com/hyperopt/hyperopt/tree/0.1.2>`_.
+            parameters of `hyperopt <https://github.com/hyperopt/hyperopt/tree/0.1.2>`__.
 
             .. testcode::
 

optuna/samplers/nsgaii/_crossovers/_blxalpha.py

@@ -22,7 +22,7 @@ class BLXAlphaCrossover(BaseCrossover):
 
     - `Eshelman, L. and J. D. Schaffer.
       Real-Coded Genetic Algorithms and Interval-Schemata. FOGA (1992).
-      <https://doi.org/10.1016/B978-0-08-094832-4.50018-0>`_
+      <https://doi.org/10.1016/B978-0-08-094832-4.50018-0>`__
 
     Args:
         alpha:

optuna/samplers/nsgaii/_crossovers/_sbx.py

@@ -23,7 +23,7 @@ class SBXCrossover(BaseCrossover):
     - `Deb, K. and R. Agrawal.
       “Simulated Binary Crossover for Continuous Search Space.”
       Complex Syst. 9 (1995): n. pag.
-      <https://www.complex-systems.com/abstracts/v09_i02_a02/>`_
+      <https://www.complex-systems.com/abstracts/v09_i02_a02/>`__
 
     Args:
         eta:

optuna/samplers/nsgaii/_crossovers/_spx.py

@@ -25,7 +25,7 @@ class SPXCrossover(BaseCrossover):
       David E. Goldberg and Kumara Sastry and Kumara Sastry
       Progress Toward Linkage Learning in Real-Coded GAs with Simplex Crossover.
       IlliGAL Report. 2000.
-      <https://www.researchgate.net/publication/2388486_Progress_Toward_Linkage_Learning_in_Real-Coded_GAs_with_Simplex_Crossover>`_
+      <https://www.researchgate.net/publication/2388486_Progress_Toward_Linkage_Learning_in_Real-Coded_GAs_with_Simplex_Crossover>`__
 
     Args:
         epsilon:

optuna/samplers/nsgaii/_crossovers/_undx.py

@@ -25,7 +25,7 @@ class UNDXCrossover(BaseCrossover):
       for real-coded genetic algorithms,
       Proceedings of the 1999 Congress on Evolutionary Computation-CEC99
       (Cat. No. 99TH8406), 1999, pp. 1581-1588 Vol. 2
-      <https://doi.org/10.1109/CEC.1999.782672>`_
+      <https://doi.org/10.1109/CEC.1999.782672>`__
 
     Args:
         sigma_xi:

optuna/samplers/nsgaii/_crossovers/_uniform.py

@@ -20,7 +20,7 @@ class UniformCrossover(BaseCrossover):
     - `Gilbert Syswerda. 1989. Uniform Crossover in Genetic Algorithms.
       In Proceedings of the 3rd International Conference on Genetic Algorithms.
       Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 2-9.
-      <https://www.researchgate.net/publication/201976488_Uniform_Crossover_in_Genetic_Algorithms>`_
+      <https://www.researchgate.net/publication/201976488_Uniform_Crossover_in_Genetic_Algorithms>`__
 
     Args:
         swapping_prob: