Gradient Descent

What is Gradient Descent?

Gradient Descent is an optimization algorithm used to minimize a loss function by iteratively adjusting the model's parameters. In the context of machine learning, the "loss function" quantifies how well the model performs its task. The goal of Gradient Descent is to find the set of model parameters that minimize this loss, thereby making the model as accurate as possible.

The term "gradient" refers to the derivative of the loss function with respect to the model parameters. The gradient provides information about the slope or steepness of the loss function at a particular point. Gradient Descent utilizes this gradient information to make incremental updates to the model parameters in the direction that reduces the loss.

How Does Gradient Descent Work?

1. Initialization: Gradient Descent starts by initializing the model parameters with some arbitrary values.
2. Calculate the Gradient: Next, it calculates the gradient of the loss function with respect to these initial parameters. This gradient points in the direction of the steepest increase in the loss.
3. Update Parameters: The model parameters are then updated by subtracting a fraction of the gradient from the current parameter values. This fraction is called the "learning rate." It determines how large or small each step should be.
4. Iterate: Steps 2 and 3 are repeated iteratively. The algorithm continues updating the parameters in the direction that reduces the loss until a stopping criterion is met, such as a predefined number of iterations or when the change in the loss becomes very small.

The learning rate (Incremental Step) is a crucial hyperparameter in Gradient Descent. A small learning rate may lead to slow convergence, while a large one may cause the algorithm to overshoot the optimal solution or even diverge. Choosing an appropriate learning rate is often a matter of trial and error.

Types of Gradient Descent

There are three types of gradient descent learning algorithms: batch gradient descent, stochastic gradient descent and mini-batch gradient descent.

1. Batch Gradient Descent: In this method, the entire training dataset is used to compute the gradient in each iteration. It's computationally expensive but guarantees convergence to a global minimum (if it exists).
2. Stochastic Gradient Descent (SGD): SGD randomly selects one data point from the training set in each iteration to calculate the gradient. It's faster but has more parameter updates with high variance.
3. Mini-batch Gradient Descent: A compromise between Batch and SGD, mini-batch Gradient Descent divides the training dataset into small batches. It combines the benefits of both approaches and is commonly used in practice.

Why Is Gradient Descent Important?

Gradient Descent is a fundamental optimization technique in machine learning for several reasons:

1. Versatility: It can be applied to a wide range of machine learning models and loss functions.
2. Scalability: Gradient Descent is efficient and can handle large datasets and high-dimensional parameter spaces.
3. Global Optimization: With proper settings, Gradient Descent can find optimal or near-optimal solutions.
4. Deep Learning: Gradient Descent is the backbone of training deep neural networks, powering breakthroughs in fields like computer vision, natural language processing, and reinforcement learning.