Introduction
Gradient descent is one of the most popular and widely used optimization algorithms in machine learning. It's the engine that powers many models, from simple linear regression to complex neural networks. But what exactly is it, and how does it work? This post will provide a gentle introduction to the core concepts of gradient descent.
The Intuition: Walking Down a Mountain
Imagine you're on a foggy mountain and your goal is to reach the lowest point, the valley. Because of the fog, you can't see the entire landscape. To find your way down, you'd likely look at the ground beneath your feet and take a step in the direction where the slope is steepest downwards. You would repeat this process, taking step after step, until you can no longer go any further down.
This is exactly the intuition behind gradient descent. The "mountain" is our cost function, which we want to minimize. The "steps" we take are the updates to our model's parameters.
How It Works
In more technical terms, gradient descent is an iterative optimization algorithm for finding the local minimum of a differentiable function. Here's a breakdown of the process:
- Start with an initial guess: The algorithm begins with an initial set of values for the model's parameters (e.g., weights and biases).
- Calculate the gradient: The gradient is a vector that points in the direction of the steepest ascent of the cost function. To move towards the minimum, we need to go in the opposite direction of the gradient.
- Update the parameters: We update the parameters by taking a small step in the direction of the negative gradient. The size of this step is controlled by a parameter called the learning rate.
- Repeat: We repeat steps 2 and 3 until the algorithm converges, meaning the cost function is at a minimum and further updates to the parameters don't significantly decrease the cost.
The Learning Rate
The learning rate is a crucial hyperparameter. It determines how big of a step we take in each iteration.
- A small learning rate will lead to slow convergence, as we are taking very small steps.
- A large learning rate can cause the algorithm to overshoot the minimum and fail to converge. It might even diverge, with the cost increasing with each iteration.
Finding a good learning rate is often a process of trial and error.
Types of Gradient Descent
There are three main variations of gradient descent:
- Batch Gradient Descent: The gradient is calculated using the entire training dataset for each update. This is computationally expensive for large datasets but provides a stable path to the minimum.
- Stochastic Gradient Descent (SGD): The parameters are updated using only a single training example at each step. This is much faster, but the path to the minimum can be noisy and erratic.
- Mini-batch Gradient Descent: This is a compromise between the two. It updates the parameters using a small batch of training examples. This balances the stability of batch gradient descent with the speed of SGD and is the most common implementation.
Conclusion
Gradient descent is a fundamental algorithm in the machine learning toolkit. By iteratively moving in the direction of the negative gradient, it allows us to minimize a cost function and train our models. Understanding how it works is a stepping stone to understanding more complex machine learning concepts.