Gradient descent is arguably the most well-recognized optimization strategy utilized in deep learning and machine learning. Data scientists often use it when there is a chance of combining each algorithm with training models. Understanding the gradient descent algorithm is relatively straightforward, and implementing it is even simpler. Let us discuss the inner workings of gradient descent, its different types, and its advantages. 

What is Gradient Descent?

Programmers utilize gradient descent as an optimization algorithm when training machine learning models. Based on convex functions,  the gradient descent iteratively tweaks some of its parameters to minimize a particular function to its minimum.

Data scientists use gradient descent to find a function’s parameter values that reduce cost functions as much as possible. They start by establishing the beginning parameter’s values. The gradient descent utilizes calculus for iteratively adjusting values to minimize a specific cost function. You must know what gradients are to comprehend gradient descent fully.

Understanding Gradient

A gradient’s primary function is to measure changes in every weight in respect of change in errors. Think of gradients as a function’s slope. The slop will be steeper based on the gradient’s height – it is a favorable condition for models as they can learn quickly. However, the model will discontinue learning if the slope becomes zero. Mathematically speaking, a gradient could be best described as a limited derivative in regards to its inputs. 

Think of a blindfolded person wanting to climb a hill’s top with minimal effort. He will most likely take long steps towards the steepest possible direction. However, this person’s steps will become smaller to prevent overshooting. You can use the gradient to describe this process mathematically.

Gradients beginning from X0 and ending at X1 are significantly longer than those starting from X3 and concluding at X4. Why? Because the hill’s slope/steepness determines the length of the vector. It provides an ideal representation of the hill analogy discussed earlier as it becomes less steep as the person climbs higher. 

How Does Gradient Descent Work?

Rather than climbing a hill, imagine gradient descent as going down to a valley’s bottom. Understanding this analogy is simpler, as it is an algorithm for minimization that lessens a specific function. Let us understand gradient descent with the help of an equation:

b represents the climber’s next position

a signifies his present position

minus refers to the gradient descent’s minimization part

The gamma located in the center represents a waiting factor

(Δf (a) ) signifies the steepest descent’s direction

You might be confused by this formula initially, but it is more straightforward than you think. It informs us about the next position we must go: the direction of descent.

Why is Learning Rate so important?

It is essential to set learning rates to their appropriate values to help gradient descent reach local minimums. So, it would be best not to set them excessively high or low. It is critical because reaching the minimum could become complicated with overly long steps. Therefore, if we set learning rates to smaller values, the gradient descent could eventually arrive at its local minimums. However, it may take some time. 

How to ensure it Functions Optimally

An excellent way to ensure gradient descent functions optimally is by organizing cost function while the optimization is running. Enter the amount repetitions on the X-axis, and cost function’s value will enter the y-axis. It will help you see cost function’s value after each gradient descent’s iteration while also letting you spot the learning rate’s accuracy. You can also try various values and plot them together. 

The cost function will reduce after each iteration if the gradient descent is functioning optimally. The gradient descent converges when it is unable to reduce the cost-function and stays on the same level.The amount of iterations gradient descent requires for convergence varies drastically. Sometimes it takes fifty iterations, and other times it could go as high as two or three million. It causes difficulty when estimating the iterations ahead of time. 

Some algorithms can automatically inform you if there has been a convergence in gradient descent. However, it would be best to establish a convergence threshold in advance, which is also quite tough to estimate. It is a significant reason why simple plots are best for convergence testing. 

Different Gradient Descent Types

You will find three well-recognized gradient descent types. Let us take a close look at them:

Batch Gradient Descent

Also known as vanilla gradient descent, the batch gradient descent calculates errors for every example in the training dataset. However, it does so only after each training example goes through rigorous evaluation. It is fair to compare this process to a cycle. Some individuals also refer to is as a training epoch.

Batch gradient descent has several advantages. Its computational efficiency, in particular, is extremely handy as it develops stable convergence and stable error gradient. That said, batch gradient descent has some disadvantages too. Sometimes, its stable error gradient can result in an unfavorable state of convergence. Furthermore, it also needs the training dataset’s presence in its algorithm and memory. 

Stochastic Gradient Descent

SGD provides updates for individual parameters for every training example. It helps provide attention to each example, ensuring that the process is error-free. Depending on the issue, this can help SGD become faster compared to batch gradient descent. Its regular updates provide us detailed improvement rates. 

That said, these updates are computationally expensive, especially when comparing them to the approach used by batch gradient descent. Furthermore, the update’s frequency can cause noisy gradients and could prevent the error rate from decreasing. Instead, the error rate jumps around and becomes problematic in the long run. 

Mini-Batch Gradient Descent

Data scientists use mini-batch gradient descent as a go-to method. Why? Because it is a perfect blend of stochastic gradient descent and batch gradient descent’s concepts. It splits the datasets (training) into batches and runs an update for every batch, creating a balance between the BGD’s efficiency and SCD’s robustness. 

Popular mini-batches range between fifty and two hundred and fifty-six, but like several other machine learning methods, there are no clear rules as it varies from one application to the other. People use it as a go-to option for training neural networks. It is also a popular gradient descent type within the deep learning landscape.