Elastic Net Proximal Step

Problem

Apply the proximal operator of the elastic net after a gradient step.

Compute z = (w - lr * grad) / (1 + lr * l2), then soft-threshold z at t = lr * l1. Return z - t when z > t, z + t when z < -t, and 0.0 otherwise.

Hint

The L2 part shrinks multiplicatively before the L1 soft threshold.

case 1

in: [1,0.5,0.1,0.1,0.2]

expected: 0.9213725490196077

case 2

in: [0.05,0,0.1,1,0]

expected: 0

case 3

in: [-2,-0.5,0.1,0.2,0.5]

expected: -1.837142857142857

case 4

in: [0,0,0.1,0.5,1]

expected: 0

Starter codePython

def elastic_net_prox(w, grad, lr, l1, l2):
    # Your code here
    pass

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