Relative Parameter Change

Problem

Measure the relative change between two parameter vectors.

Return ||new - old||_2 / (||old||_2 + eps), where both norms are Euclidean over the components in common. This is a scale-free progress measure often used in convergence checks.

Hint

eps guards against division by zero when old is the zero vector.

Test cases

case 1

in: [[1,2],[1.1,2.2],1e-8]

expected: 0.09999999955278649

case 2

in: [[0,0],[1,1],0.5]

expected: 2.8284271247461903

case 3

in: [[3,-4],[3,-4],1e-8]

expected: 0

case 4

in: [[0.5,0.5],[0,0],0.01]

expected: 0.9860550753913473

Starter codePython

def relative_param_change(old, new, eps):
    # Your code here
    pass

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