Proximal Gradient L1 Step

Problem

One proximal gradient step for an L1-penalized objective evaluates z = w - lr * grad, then applies the soft threshold with parameter lr * lambda.

Given w, grad, lr, and lambda, return the updated vector.

Hint

Soft threshold each coordinate after the gradient step.

case 1

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

expected: [0.8999999999999999,1.9999999999999998]

case 2

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

expected: [-0.5,-0.5]

case 3

in: [[3,-3],[0,0],0.1,0.5]

expected: [2.95,-2.95]

Starter codePython

def proximal_gradient_l1_step(w, grad, lr, lam):
    # Your code here
    pass

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