Gradient Descent in Mathematics is a powerful optimization algorithm used in machine learning and statistics. It helps find the minimum of a function by iteratively moving in the direction of the steepest descent. Here's a brief overview:

Key Concepts

  • Function: A function maps an input to an output.
  • Gradient: The gradient of a function at a point is a vector that points in the direction of the steepest increase.
  • Descent: Moving in the direction of the steepest decrease to find the minimum.

How it Works

  1. Start with an initial guess for the minimum.
  2. Calculate the gradient at the current point.
  3. Move in the direction of the negative gradient (opposite direction of the steepest increase).
  4. Repeat steps 2 and 3 until convergence.

Example

Consider the function $f(x) = x^2$. The gradient at any point $x$ is $f'(x) = 2x$. To find the minimum, we move in the direction of $-f'(x) = -2x$.

Gradient Descent Visualization

For more information on optimization algorithms, check out our Optimization Techniques.