Pathwise Derivative Estimate

Problem

The pathwise (reparameterization) estimator of the gradient of E[f(mu + sigma * eps)] with respect to mu is the sample average of f'(mu + sigma * eps_i).

For f(x) = sum(coeffs[i] * x^i) and a list of standard normal samples epsilons, return that average.

Hint

Unlike the score-function estimator, the pathwise estimator differentiates the sample directly.

Test cases

case 1

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

expected: 2

case 2

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

expected: 0

case 3

in: [[0,0,1],2,0,[5]]

expected: 4

case 4

in: [[0,1],0,3,[1,-1,2]]

expected: 1

Starter codePython

def pathwise_derivative(coeffs, mu, sigma, epsilons):
    # Your code here
    pass

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