Quantile Gradient Step

Problem

Take one gradient step for the pinball (quantile) loss with target quantile q.

Let residual = w * x - y; the subgradient factor is q - 1 when residual < 0 and q otherwise. Return w - lr * factor * x.

Hint

The pinball subgradient is q - 1 below the target and q above it.

case 1

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

expected: 0.9

case 2

in: [0,1,2,0.5,0.1]

expected: 0.05

case 3

in: [1,1,1,0.9,0.2]

expected: 0.82

case 4

in: [-1,2,-3,0.1,0.1]

expected: -1.02

Starter codePython

def quantile_gradient_step(w, x, y, q, lr):
    # Your code here
    pass

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