Exercise: Using Gradient Descent to Minimize a Cost Function

Approach to minimize the cost function

In this exercise, our task is to find the best set of parameters in order to minimize the following hypothetical cost function: $y = f(x) = x^2 – 2x$. To do this, we will employ gradient descent, which was described in the preceding lesson. Perform the following steps to complete the exercise:

1. Create a function that returns the value of the cost function and look at the value of the cost function over a range of parameters. You can use the following code to do this:

   X_poly = np.linspace(-3,5,81)
   print(X_poly[:5], '...', X_poly[-5:]) 
   def cost_function(X): 
       return X * (X-2) 
   y_poly = cost_function(X_poly) 
   plt.plot(X_poly, y_poly) 
   plt.xlabel('Parameter value') 
   plt.ylabel('Cost function') 
   plt.title('Error surface')
   

   You will obtain the following plot of the cost function: