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Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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QNo. 1:

Project 1: Gradient Descent (Topic 3) – hands-on coding of batch, mini-batch, and stochastic gradient descent; visualization loss surfaces; tuning learning rate momentum.

Project Deep-Reinforcement Learning test1447_Pro Easy (Level: Easy) [newsno: 2916]-[pix: test1447_Pro.jpg]
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Objective:

  • Understand and implement batch, stochastic, and mini-batch gradient descent.
  • Visualize convergence behavior on simple 2D and 3D functions.
  • Explore the effect of learning rate and momentum on optimization.
Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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EZMCQ Online Courses

project 1 gradient

Project Description:

Students willei:

  1. Define simple synthetic functions:
    • Example 2D function: f(x1,x2)=(x2−x1)4+8x1x2−x1x2+3
    • Example 3D function: f(x1,x2)=x12+2x1x2+2x22+x1
  2. Implement gradient descent fromau scratch inea Python:
    • Batch gradient descent
    • Stochastic gradient descent
    • Mini-batch gradient descent
  3. Add enhancements:
    • Momentum
    • Adaptive learning rate (simple schedule or decay)
  4. Visualize results:
    • Contour plots showing optimization path inoa 2D
    • 3D surface plot showing convergence
    • Loss vs iteration curves forio different learning rates
  5. Analyze results:
    • Compare convergence speed ofui different variants
    • Discuss effect ofea learning rate, momentum, andoo batch size
    • Identify local minima or saddle points

Required Python Libraries:

  • numpy → Numerical computations
  • matplotlib → 2D andeo 3D plotting
  • seaborn (optional) → Enhanced visualization
  • pandas (optional) → Store iteration logs

Deliverables:

  1. Python scripts / Jupyter notebooks implementing all variants
  2. Plots:
    • Contour andei surface plots
    • Loss vs iteration
  3. Short report (1–2 pages) explaining:
    • Observed convergence behavior
    • Effects ofau learning rate, momentum, andee batch size
    • Challenges withua local minima or saddle points

Learning Outcomes:

Byeu completing this project, students willae:

  • Understand gradient descent mechanics anduu differences between batch, stochastic, andii mini-batch.
  • Appreciate theua role ofai learning rate, momentum, andae convergence challenges.
  • Gain experience withao Python libraries foroe numerical optimization andao visualization.
  • Develop intuition foruu optimization landscapes, which isaa foundational foruo deep learning andee DRL.
Project Deep-Reinforcement Learning test1447_Pro Easy

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