Add self improving prompts notebook

[MohitRajCode]

This PR adds a new example notebook demonstrating a simple
self-improving prompt loop using Gemini models.

The notebook shows how a prompt can be iteratively refined
using model-generated critique to improve response quality.

Closes #1113

[review-notebook-app]

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[gemini-code-assist]

Summary of Changes

Hello @mohithacker01, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request introduces a new example notebook that showcases a self-improving prompt mechanism with Gemini models. The core concept demonstrated is the iterative refinement of model outputs, where the model itself generates critiques to enhance the quality of its responses. This approach aims to improve AI-generated content without requiring constant manual prompt adjustments, providing a valuable pattern for applications like customer support bots and automated content refinement.

Highlights

• New Example Notebook: A new Jupyter notebook, self_improving_prompts.ipynb, has been added to the examples directory.
• Self-Improving Prompts: The notebook demonstrates a self-improving prompt loop using Gemini models, where the model iteratively refines its own responses.
• Model-Generated Critique: It showcases how model-generated critique can be used to enhance the quality of responses without manual prompt tuning.

Changelog

• examples/prompting/self_improving_prompts.ipynb
  • This new Jupyter notebook has been added to illustrate the self-improving prompt pattern.
  • It contains Python code that utilizes the google.genai library to interact with Gemini models.
  • The notebook defines functions for generating an initial response, critiquing it, and then improving it based on the critique.
  • An example scenario for refining a customer service response is provided.
  • Users are required to set a GEMINI_API_KEY environment variable to run the notebook.

Activity

• No human activity (comments, reviews) has been recorded on this pull request yet.

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[gemini-code-assist]

Code Review

This pull request adds a new notebook demonstrating a self-improving prompt loop, which is a valuable example. However, the notebook needs several updates to align with the repository's style guide before it can be merged. The main issues include missing setup elements like the pip installation and Colab badge, the use of hardcoded values instead of interactive forms, and structural improvements for better readability. Additionally, the new notebook should be referenced in the README.md files in the examples/ and examples/prompting/ directories as per the style guide.