Here’s a cleaned-up and structured version of your notes on Gradient Descent, with explanations and clear formatting for better understanding:

Gradient Descent Overview

Objective

Minimize a cost function (e.g., Mean Squared Error) by iteratively updating model parameters (m and c in linear regression) using the gradient (slope) of the cost function.

Basic Gradient Descent Steps

1. Initialize m and c randomly
2. Repeat for n iterations or until convergence:
   • Compute derivatives (gradients):
     • Slope_m = ∂Cost/∂m
     • Slope_c = ∂Cost/∂c
   • Update parameters:
     • m = m - α * Slope_m
     • c = c - α * Slope_c
   • (α = learning rate)

❗ The final m and c are approximations, not the exact global minimum—but the algorithm converges quickly to a useful solution.

Learning Rate (α)

• Controls the step size in parameter updates
• Too high → overshooting the minimum
• Too low → slow convergence
• Adaptive α:
  • Start with a high value and reduce gradually
  • Helps in faster convergence early on, and stability later

Types of Gradient Descent

1. Batch Gradient Descent

• Uses entire dataset to compute gradients