Descent Lemma Bound

Problem

Evaluate the descent lemma upper bound for a scalar step.

Return f_x + grad * delta + 0.5 * L * delta ** 2, where L is the gradient Lipschitz constant. This bounds f at the new point along the gradient direction.

Hint

The quadratic penalty 0.5 * L * delta ** 2 upper-bounds the curvature term.

Test cases

case 1

in: [1,2,0.1,4]

expected: 1.22

case 2

in: [0,-1,0.5,2]

expected: -0.25

case 3

in: [3,0,1,10]

expected: 8

case 4

in: [2,1,-0.5,4]

expected: 2

Starter codePython

def descent_lemma_bound(f_x, grad, delta, L):
    # Your code here
    pass

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