Quadratic Stability Upper Step

Problem

Gradient descent on f(x) = 0.5 * a * x^2 oscillates unless the learning rate satisfies 0 < lr < 2 / a.

Given the curvature a > 0, return the upper stability bound 2 / a.

Hint

The iterate multiplier is 1 - lr * a; keep its magnitude below one.

case 1

in: [1]

expected: 2

case 2

in: [4]

expected: 0.5

case 3

in: [0.5]

expected: 4

Starter codePython

def quadratic_stability_upper_step(a):
    # Your code here
    pass

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