Gradient Descent Examples

Optimization · Axiom Academy

EXAMPLE Gradient Descent Optimization Master gradient descent through three progressively challenging examples Excellent work! You've mastered gradient descent through three different examples. Here's what we learned: Gradient Direction: The gradient always points in the direction of steepest ascent, so we move in the negative gradient direction to minimize the function. Learning Rate Impact: The learning rate controls step size. Too large causes oscillation or divergence; too small leads to slow convergence. Convergence Behavior: Simple quadratics converge quickly and smoothly, while complex functions like Rosenbrock require careful tuning and more iterations. Multidimensional Extension: Gradient descent naturally extends to multiple dimensions by computing partial derivatives with respect to each variable. Iterative Refinement: Each iteration brings us closer to the minimum by following the local gradient information. These examples demonstrate gradient descent's power and versatility across different problem types. Practice with different learning rates and starting points to build intuition!

This is the written version of the interactive lesson above. See the full Optimization course.