Quadratic Closed Form Iterate

Problem

For f(x) = 0.5 * a * x^2, gradient descent with step lr produces x_k = x0 * (1 - lr * a)^k.

Given x0, lr, a, and the number of steps k, return x_k.

Hint

The iterate is geometric in the factor (1 - lr * a).

case 1

in: [1,0.1,2,5]

expected: 0.3276800000000001

case 2

in: [2,0.5,1,3]

expected: 0.25

case 3

in: [1,1,2,4]

expected: 1

Starter codePython

def quadratic_closed_form_iterate(x0, lr, a, steps):
    # Your code here
    pass

3 test cases · run your code against them in the editor