Gradient descent - why the partial derivative?

Derivatives are an important tool in machine learning, and they are used in gradient descent algorithms to optimize the performance of a model. Gradient descent is an iterative optimization algorithm that is used to find the minimum of a given function. It works by taking small steps in the direction of the negative gradient of the function at each iteration. The size of these steps is determined by the derivative of the function at each point.

The derivative tells us how quickly a function is changing with respect to its input variables. This information can be used to determine which direction we should take our next step in order to minimize our cost function. By taking smaller steps in the direction of the negative gradient, we can ensure that we reach our minimum faster and more accurately than if we took larger steps.

What will happen when we take larger steps ?

When we take larger steps in Gradient Descent, it can cause the algorithm to overshoot the minimum point. This means that instead of converging to the minimum point, it will go past it and then oscillate around it. This can lead to slower convergence and longer training times.
In addition, taking larger steps can also lead to instability in the model. If the step size is too large, then the model may not converge at all or may diverge instead of converging. This can lead to inaccurate results or even complete failure of the model.

Finally, taking larger steps can also lead to local minima traps. If the step size is too large, then it may cause the algorithm to get stuck in a local minima instead of finding the global minima. This means that even though there may be a better solution available, the algorithm will not be able to find it due to getting stuck in a local minima trap.

So in conclusion , derivatives are an essential tool for optimizing models using gradient descent algorithms in machine learning. They provide us with valuable information about how quickly a function is changing with respect to its input variables, which allows us to take smaller steps towards our desired solution more accurately and efficiently than if we took larger steps without considering derivatives.