How is gradient descent and model optimization used in linear regression?

Gradient descent is the primary algorithm used to train linear regression models. It works by iteratively adjusting the model's coefficients (weights) to minimize a cost function, typically mean squared error. This minimization is achieved by calculating the gradient (the direction of steepest ascent) of the cost function with respect to the coefficients and taking a step in the opposite direction. The size of this step is controlled by the learning rate. While basic gradient descent is effective, various optimized versions like Adam or RMSprop exist to improve convergence speed and stability. For specific scenarios, alternative optimization methods might be employed, especially for non-differentiable cost functions or when direct optimization of evaluation metrics is required.