Gradient Descent

July 2, 2025in Data, Google

Gradient descent is a powerful optimization algorithm used in machine learning to minimize a function, often a cost function, by iteratively adjusting parameters. It works by taking steps in the direction of the negative gradient, which is the direction of steepest decrease of the function. This process continues until the algorithm converges to a minimum point.

1. The Goal: In machine learning, the goal is often to find the best set of parameters (weights and biases) for a model that minimizes the error or cost when predicting outputs from inputs. Gradient descent is a method to achieve this.

2. The Cost Function: A cost function (also called a loss function) quantifies the error of the model’s predictions. The goal of gradient descent is to find the parameters that minimize this cost function.

3. The Gradient: The gradient of a function at a given point represents the direction of the steepest ascent. In other words, it indicates the direction in which the function’s value increases the most.

4. The Iterative Process:

Initialization: The algorithm starts with an initial guess for the model’s parameters.
Gradient Calculation: At each iteration, the gradient of the cost function is calculated with respect to the current parameters.
Parameter Update: The parameters are updated by moving a small step in the opposite direction of the gradient. This is done by subtracting a fraction (determined by the learning rate) of the gradient from the current parameter values.
Iteration: This process of calculating the gradient and updating the parameters is repeated until the algorithm converges to a minimum or a certain number of iterations is reached.

5. Different Variants:

Batch Gradient Descent: Uses the entire training dataset to compute the gradient at each iteration. This is computationally expensive for large datasets.
Stochastic Gradient Descent (SGD): Uses a single training example to compute the gradient at each iteration. This is faster than batch gradient descent but can be noisy.
Mini-batch Gradient Descent: Uses a small subset of the training data (a mini-batch) to compute the gradient. This offers a good balance between speed and stability.
Other variants: Algorithms like Adam, RMSprop, and Momentum are also used, which incorporate momentum and adaptive learning rates to improve convergence.

6. Importance of Learning Rate: The learning rate (also known as step size) is a crucial hyperparameter. It determines the size of the steps taken during parameter updates. If the learning rate is too large, the algorithm may overshoot the minimum and fail to converge. If it’s too small, convergence may be slow.