# What is Stochastic gradient descent

##### Stochastic Gradient Descent: An Overview

Stochastic gradient descent (SGD) is a widely used optimization algorithm in machine learning, especially in deep learning. It is an extension of gradient descent that is used to minimize the cost function of a learning algorithm.

SGD is an iterative algorithm that updates the model’s parameters based on the error gradient at each step. The gradient is calculated using a small subset (batch) of the training data, rather than the entire dataset. This makes SGD particularly suitable for large datasets because it is computationally efficient and can update the model in real-time.

##### Why Use Stochastic Gradient Descent?

SGD is one of the most popular optimization algorithms used in deep learning because it has several advantages over traditional optimization techniques:

• Efficiency: SGD is computationally efficient because it uses a small batch of training data to update the model weights. This means that it can train larger datasets in a shorter amount of time compared to more traditional methods.
• Real-time updates: SGD updates the model weights in real-time, which means that it can adjust the model weights as new data becomes available. This is particularly useful in applications where the data is constantly changing, such as in financial forecasting or online advertising.
• Reduced Overfitting: During training, models can become overfit to the training data. SGD, by only using a small subset of the data, helps avoid overfitting by introducing noise into the optimization process. This prevents the model from focusing too much on any particular data point.
##### How Does Stochastic Gradient Descent Work?

The basic idea behind stochastic gradient descent is that in each iteration, a small batch of training data is randomly selected from the whole training set. Then, the gradient of the cost function is calculated with respect to the subset of the data, and the model weights are updated based on that gradient. This process is repeated until the cost function converges.

The formula for updating the weights of the model using SGD is:

w(t+1) = w(t) - α∇f(w(t); x(i); y(i))

Where:

• w: The weights of the model
• t: The current iteration number
• α: The learning rate
• ∇f(w(t); x(i); y(i)): The gradient of the cost function with respect to the weights

At each iteration, a new random batch of data is used to calculate the gradient and update the weights:

Δw(t) = - α(1/m)Σ(i=1:m)∇f(w(t);x(i);y(i))

Where:

• Δw(t): The change in the weights at iteration t
• m: The number of examples in the batch of data
• Σ(i=1:m)∇f(w(t);x(i);y(i)): The sum of the gradients of the cost function with respect to the weights for each example in the batch

The learning rate, α, is a hyperparameter that controls the step size taken by the algorithm in the direction of the gradient. If the learning rate is too high, the algorithm may overshoot the minimum and diverge. If the learning rate is too low, the algorithm may converge very slowly or get stuck in a local minimum.

##### SGD Variants

There are several variants of stochastic gradient descent, each with its strengths and weaknesses:

Batch gradient descent is the simplest variant of SGD. It uses the entire training set at each iteration to update the model weights. Batch gradient descent can be computationally expensive for large datasets because it requires the entire dataset to fit into memory.

Mini-batch gradient descent is a compromise between batch gradient descent and stochastic gradient descent. It uses a small batch of data at each iteration to update the model weights. Mini-batch gradient descent is computationally efficient, and it also introduces noise into the optimization process, which helps avoid overfitting.

###### Online Learning:

Online learning is similar to stochastic gradient descent. The difference is that online learning updates the model weights one example at a time rather than in batches. Online learning can be useful when working with streaming data that is constantly changing.