Optimization on Learning Journal

Gradient Descent: From Intuition to Implementation

Tue, 19 May 2026 00:00:00 +0000

What is Gradient Descent?

Gradient descent minimizes a function by iteratively stepping in the direction of steepest descent.

The Intuition

Imagine standing blindfolded on a hilly landscape. You want the lowest point. Strategy: feel the slope, step downhill, repeat.

The Math

Given a loss function $L(\theta)$, update parameters as:

$$\theta = \theta - \alpha \nabla L(\theta)$$

where $\alpha$ is the learning rate.

A Simple Implementation

def gradient_descent(grad_fn, theta, lr=0.01, steps=100):
 for _ in range(steps):
 theta -= lr * grad_fn(theta)
 return theta

Key Takeaways

Learning rate too large: diverges. Too small: slow.
Vanilla GD uses the full dataset per step.
Mini-batch GD is the practical default in deep learning.