Control Variate Step

Problem

Take one gradient step with a control variate.

Form the unbiased estimate est = grad_sample - grad_control + grad_control_mean, then return [w - lr * est, est]. The control variate reduces variance when grad_control tracks grad_sample.

Hint

The control variate is mean-zero, so the estimator stays unbiased.

Test cases

case 1

in: [[1,2],[0.5,0.5],[0.4,0.6],[0.45,0.55],0.1]

expected: [[0.945,1.955],[0.55,0.45000000000000007]]

case 2

in: [[0,0],[1,-1],[0.5,-0.5],[0.25,-0.25],0.5]

expected: [[-0.375,0.375],[0.75,-0.75]]

case 3

in: [[2,-1],[1,0.5],[0.5,1],[0.25,0.5],0.2]

expected: [[1.85,-1],[0.75,0]]

Starter codePython

def control_variate_step(w, grad_sample, grad_control, grad_control_mean, lr):
    # Returns [w_new, est]
    # Your code here
    pass

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