Proximal Gradient Step 1D

Problem

Perform one proximal gradient step with a squared L2 regularizer.

Compute z = w - lr * grad, then apply the proximal operator of (lam / 2) * ||w||^2, which is z / (1 + 2 * lr * lam). Return the new value.

Hint

The squared L2 prox divides by 1 + 2 * lr * lam.

case 1

in: [1,0.5,0.1,0.2]

expected: 0.9134615384615384

case 2

in: [2,-1,0.5,0.1]

expected: 2.2727272727272725

case 3

in: [0,0,0.3,1]

expected: 0

case 4

in: [-1,2,0.2,0]

expected: -1.4

Starter codePython

def proximal_gradient_step(w, grad, lr, lam):
    # Your code here
    pass

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