Stochastic Approximation Step

Problem

Take one stochastic approximation step with a decreasing gain.

Return x - (a / (k + b)) * grad, where k is the iteration index.

Hint

The gain a / (k + b) must shrink over iterations for convergence.

case 1

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

expected: 0

case 2

in: [1,2,0.5,1,4]

expected: 0.8

case 3

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

expected: 0.2

case 4

in: [2,0,0.1,1,9]

expected: 2

Starter codePython

def stochastic_approximation_step(x, grad, a, b, k):
    # Your code here
    pass

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