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+# Proposal for Parameter Distribution
+
+<!-- toc -->
+- [Summary](#summary)
+- [Motivation](#motivation)
+- [Design Details](#design-details)
+  - [Experiment API changes](#experiment-api-changes)
+  - [Correspondence for Katib Distributions and Framework Distributions](#correspondence-for-katib-distributions-and-framework-distributions)
+    - [Chocolate](#chocolate)
+    - [Goptuna](#goptuna)
+    - [Hyperopt](#hyperopt)
+    - [Optuna](#optuna)
+    - [Scikit-Optimize](#scikit-optimize)
+<!-- /toc -->
+
+## Summary
+This enhancement introduces `Distribution` to tuning parameters and remove redundantly `ParameterType`. 
+
+API field in the Experiment spec determine parameter type with distribution.  
+
+## Motivation
+Currently, Katib does not support determining a distribution for search space that samplers pick up parameters by users.
+
+Katib should be able to determine it by users since
+almost hyperparameter tuning algorithms (framework) can determine it by users.
+
+## Proposal
+We introduce a mechanism to determine a distribution for search space by users.
+That also means we introduce a mechanism to propagate distributions to suggestion-services and
+set them samplers of each framework.     
+
+## Design Details
+The proposal consists of a new Experiment API field and
+correspondence between Katib Distributions and Framework Distributions.
+
+### Experiment API changes
+We extend the Experiment API to introduce the new fields `Distribution` to configure the distribution for search space and
+remove the redundant fields `ParameterType`.
+
+```diff
+type ParameterSpec struct {
+	Name          string        `json:"name,omitempty"`
+- 	ParameterType ParameterType `json:"parameterType,omitempty"`
++ 	Distribution  Distribution  `json:"distribution,omitempty"`
+	FeasibleSpace FeasibleSpace `json:"feasibleSpace,omitempty"`
+}
+
+- type ParameterType string
++ type Distribution string
+
+const (
+- 	ParameterTypeUnknown     ParameterType = "unknown"
+- 	ParameterTypeDouble      ParameterType = "double"
+- 	ParameterTypeInt         ParameterType = "int"
+- 	ParameterTypeDiscrete    ParameterType = "discrete"
+- 	ParameterTypeCategorical ParameterType = "categorical"
++ 	UnknownDistribution         Distribution = "unknown"
++ 	CategoricalDistribution     Distribution = "categorical"
++ 	IntUniformDistribution      Distribution = "intUniform"
++ 	IntLogUniformDistribution   Distribution = "intLogUniform"
++ 	FloatUniformDistribution    Distribution = "floatUniform"
++ 	FloatLogUniformDistribution Distribution = "floatLogUniform"
+)
+```
+
+### Correspondence between Katib Distributions and Framework Distributions
+We extend suggestion services to be able to configure distributions for
+search space using libraries provided in each framework.
+
+#### Chocolate
+TODO
+
+#### Goptuna
+We can extend Goptuna Suggestion Service using Goptuna libraries shown in the below correspondence table for
+Katib Distributions and Goptuna Distributions.
+
+ref: https://github.com/c-bata/goptuna/blob/2245ddd9e8d1edba750839893c8a618f852bc1cf/distribution.go
+
+| Katib Distribution          | Goptuna Distribution                                 |
+|-----------------------------|------------------------------------------------------|
+| CategoricalDistribution     | CategoricalDistribution                              |
+| IntUniformDistribution      | IntUniformDistribution or StepIntUniformDistribution |
+| IntLogUniformDistribution   | IntUniformDistribution or StepIntUniformDistribution |
+| FloatUniformDistribution    | UniformDistribution                                  |
+| FloatLogUniformDistribution | LogUniformDistribution                               |
+
+
+#### Hyperopt
+We can extend Hyperopt Suggestion Service using Hyperopt libraries shown in the below correspondence table for
+Katib Distributions and Hyperopt Distributions.
+
+ref: http://hyperopt.github.io/hyperopt/getting-started/search_spaces/#parameter-expressions
+
+| Katib Distribution          | Hyperopt Distribution |
+|-----------------------------|-----------------------|
+| CategoricalDistribution     | hp.choice             |
+| IntUniformDistribution      | hp.quniform           |
+| IntLogUniformDistribution   | hp.qloguniform        |
+| FloatUniformDistribution    | hp.quniform           |
+| FloatLogUniformDistribution | hp.qloguniform        |
+
+#### Optuna
+We can extend Optuna Suggestion Service using Optuna libraries shown in the below correspondence table for
+Katib Distributions and Optuna Distributions.
+
+ref: https://optuna.readthedocs.io/en/stable/reference/distributions.html
+
+| Katib Distribution          | Optuna Distribution                   |
+|-----------------------------|---------------------------------------|
+| CategoricalDistribution     | distributions.CategoricalDistribution |
+| IntUniformDistribution      | distributions.IntDistribution         |
+| IntLogUniformDistribution   | distributions.IntDistribution         |
+| FloatUniformDistribution    | distributions.FloatDistribution       |
+| FloatLogUniformDistribution | distributions.FloatDistribution       |
+
+#### Scikit Optimize
+We can extend Scikit-Optimize Suggestion Service using Scikit-Optimize libraries shown in the below correspondence table for
+Katib Distributions and Scikit-Optimize Distributions.
+
+ref: https://scikit-optimize.github.io/stable/modules/classes.html#module-skopt.space.space
+
+| Katib Distribution          | Scikit-Optimize Distribution |
+|-----------------------------|------------------------------|
+| CategoricalDistribution     | space.Categorical            |
+| IntUniformDistribution      | space.Integer                |
+| IntLogUniformDistribution   | space.Integer                |
+| FloatUniformDistribution    | space.Real                   |
+| FloatLogUniformDistribution | space.Real                   |