MediumCalculusca-270

Descent Lemma Smoothness Bound

Problem

The descent lemma for an L-smooth function states f(y) <= f(x) + grad f(x) dot (y - x) + (L/2) * ||y - x||^2.

Given f_x = f(x), the gradient vector g at x, the points x and y, and the smoothness constant L, return the bound value.

Hint

The quadratic term rewards smaller steps; the linear term uses the local gradient.

case 1

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

expected: 3

case 2

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

expected: 3.5

case 3

in: [0,[1,-1],[1,1],[1,1],4]

expected: 0

case 4

in: [3,[0,0],[2,2],[2,2],5]

expected: 3

Starter codePython

def descent_lemma_bound(f_x, g, x, y, L):
    # Your code here
    pass

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