Add hierarchical search space documentation

[Copilot]

Documentation Update: Add Hierarchical Search Space

This PR adds comprehensive documentation for hierarchical (conditional) search spaces to the Tune User Defined Function page, addressing the request in the issue.

Completed Tasks

• Explore the repository to understand hierarchical search space implementation
• Review existing documentation structure
• Review test cases and examples for hierarchical search space usage
• Add hierarchical search space section to documentation with:
  • Explanation of what hierarchical search spaces are
  • Syntax and usage examples using tune.choice() with nested dictionaries
  • Example showing conditional hyperparameter dependencies
  • Code example demonstrating practical usage
• Review and validate documentation changes
  • Added clarifying comments to example placeholder functions
  • Validated all examples syntactically
  • Tested examples work with FLAML API
• Run pre-commit to fix formatting issues

Summary

The documentation now includes a new "Hierarchical search space" section in the Search space subsection. It provides:

1. Clear explanation: Describes what hierarchical search spaces are and when they're useful
2. Syntax guidance: Explains how to use tune.choice() with nested dictionaries
3. Three comprehensive examples:
   • Model selection with model-specific hyperparameters
   • Mixed choices with constants and nested spaces
   • Nested hierarchical spaces for organizing related hyperparameters
4. Important usage notes: Compatibility with search algorithms and usage tips

All examples have been validated and formatting has been fixed with pre-commit.

Original prompt

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This section details on the original issue you should resolve

<issue_title>Add hierarchical search space to the documentation</issue_title>
<issue_description>https://microsoft.github.io/FLAML/docs/Use-Cases/Tune-User-Defined-Function#search-space</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes Add hierarchical search space to the documentation #873

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[thinkall]

@copilot, run "pre-commit run --all-files" to fix formatting issues.

[Copilot]

@copilot, run "pre-commit run --all-files" to fix formatting issues.

Done! Pre-commit has been run and formatting issues have been fixed in commit 554aea5.