This app implements the gradient descent optimisation algorithm to minimise a function
This AI web app implements the gradient descent optimization algorithm to minimize the function f(x)=x2+3x+2. Below is a detailed explanation of each step and the concepts used:
The learning rate is a crucial parameter in the gradient descent algorithm, determining the size of the steps taken towards the minimum.
The function optimizeFunction()
initializes several variables:
learningRate
: Retrieved from user input, this parameter controls the step size during the gradient descent update.tolerance
: A small threshold value to determine when the algorithm should stop iterating. It checks if the change in xx between iterations is small enough to assume convergence.x
and prevX
: These variables represent the current and previous values of xx during the iterations. x
is initialized at 0 as a starting point for the optimization.The core of the algorithm is a loop that repeatedly updates x to move towards the minimum of the function. Key components include:
gradient
: This is the derivative of the function f(x)=x2+3x+2, evaluated as 2x+3. The gradient tells us the slope of the function at any point x, and thus the direction to move to decrease f(x).deltaX
: This is the change to apply to xx, computed as the negative of the product of the learning rate and the gradient. The negative sign indicates that we are moving opposite to the gradient to seek a minimum (since gradient points towards the steepest increase).After each update, the algorithm checks whether the absolute difference between the current and previous x values is less than the tolerance. This condition checks for convergence, i.e., whether further iterations are unlikely to produce significant changes, indicating that the minimum (or a local minimum) is reached.
Once the loop exits, the final values of x and f(x) are displayed. This gives the optimal x that minimizes the function along with the corresponding function value.
The calculateFunctionValue(x)
function is a helper that computes f(x) for any x. It's used to show the optimized function value at the end of the process.
AI Terminology:
Function f(x)=x2+3x+2