Importance Sampling Variance

Problem

Estimate the variance of the importance-sampling return estimator from samples of weight times return: Var = E[(wG)^2] - E[wG]^2. An empty batch returns 0.0.

Hint

Large importance weights inflate estimator variance quickly.

Test cases

case 1

in: [[1,1],[1,3]]

expected: 1

case 2

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

expected: 0.25

case 3

in: [[1],[5]]

expected: 0

case 4

in: [[],[]]

expected: 0

Starter codePython

def importance_sampling_variance(weights, returns):
    # Your code here
    pass

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