Add Question 189: Compute Direct Preference Optimization Loss

[zhenhuan-yang]

Summary

This PR adds a new medium-difficulty Deep Learning question on computing Direct Preference Optimization (DPO) loss for language model alignment.

Question Details

• ID: 189
• Title: Compute Direct Preference Optimization Loss
• Difficulty: Medium
• Category: Deep Learning

Implementation

• ✅ Complete solution with proper numerical stability using np.log1p
• ✅ Comprehensive educational content covering DPO theory and Bradley-Terry model
• ✅ Mathematical formulation with LaTeX
• ✅ 4 diverse test cases with varying parameters
• ✅ Example with detailed reasoning

Validation

• ✅ Build successful
• ✅ Schema validation passed
• ✅ All test cases pass

Educational Value

Covers an important modern technique for LLM alignment that's simpler and more stable than traditional RLHF, making it highly relevant for current ML practitioners.