title: "Gradient Descent & Numerical Optimization" description: "The soul of ML training! From Gradient Descent to Adam Optimizer, implement various optimizers with Vibe Coding." duration: "120 minutes" difficulty: "Advanced"
Gradient Descent & Numerical Optimization
Machine learning is fundamentally an optimization problem: find parameters that minimize the loss function.
This course starts from basic gradient descent, progressively implementing Momentum, RMSProp, Adam and other modern optimizers.
Course Outline
- Gradient Descent Fundamentals - intuitive calculus, basic GD algorithm
- Momentum & Adam - adding momentum and adaptive learning rates
- SGD & Mini-Batch - stochastic optimization for large-scale data
- Automatic Differentiation - building an autograd engine from scratch
- Hands-On: Linear Regression - integrate all optimizers
Key Takeaways
- Gradient descent is the core optimization algorithm in machine learning
- Gradient direction = fastest increase direction
- Learning rate determines step size
- SGD approximates gradients with random samples
- Momentum accelerates convergence
- Adam combines Momentum + RMSProp
- Understanding optimizer variants is crucial for deep learning training