Introduction

In the realm of machine learning and optimization, gradient descent is a fundamental algorithm that lies at the heart of many models and techniques. It is a powerful optimization algorithm used to minimize the error or cost function of a model by iteratively updating its parameters based on the gradient of the cost function. In this blog post, we will explore the inner workings of gradient descent, its variants, and its significance in training machine learning models.

What is Gradient Descent?

Gradient descent is an iterative optimization algorithm used to find the minimum of a differentiable function, typically the cost function in machine learning models. The core idea behind gradient descent is to take steps proportional to the negative gradient of the function at the current point, thereby moving towards the minimum.

How Gradient Descent Works

The algorithm starts with an initial set of parameters and iteratively adjusts them to minimize the cost function. The key idea behind gradient descent is to move in the direction of steepest decrease in the cost function. This direction is determined by the negative gradient of the cost function with respect to the parameters.

Iterative Optimization

At each iteration, the parameters are updated based on the gradient and a learning rate. The learning rate controls the size of the steps taken during optimization. A too small learning rate may lead to slow convergence, while a too large learning rate may cause overshooting.

Types of Gradient Descent

There are different variants of gradient descent, each with its own characteristics:

1. Batch Gradient Descent

• Batch gradient descent, also known as vanilla gradient descent, involves computing the gradient of the cost function with respect to the parameters over the entire training dataset.
• It provides accurate gradient estimates but can be computationally expensive, especially with large datasets.
• Batch gradient descent updates the parameters once per epoch, where an epoch is a complete pass through the entire training dataset.

2. Stochastic Gradient Descent (SGD):

• In stochastic gradient descent, the gradient is computed using only a single training example at a time.
• It updates the parameters after processing each training example, making it computationally efficient, especially for large datasets.
• SGD has more noise in the gradient estimate due to the high variance introduced by using individual examples, which can make convergence more erratic.
• Despite the noise, SGD can converge faster due to frequent updates.

3. Mini-Batch Gradient Descent:

• Mini-batch gradient descent strikes a balance between batch gradient descent and SGD.
• It computes the gradient by randomly selecting a small subset or mini-batch of training examples.
• Mini-batch gradient descent combines the advantages of both batch gradient descent (accurate gradient estimation) and SGD (computational efficiency).
• It is commonly used in practice and is suitable for most scenarios.

Figure 1. Types of gradient descent