MediumCalculusca-068

Gradient Descent Two Steps

Problem

Run two gradient descent steps on f(x, y) = a*x^2 + b*y^2 + c*x*y starting from point, with learning rate lr.

The gradient is [2*a*x + c*y, 2*b*y + c*x]. At each step move the point against the gradient computed at the current location, and return the final point as [x, y].

Hint

Recompute the gradient at the new point before taking the second step.

Test cases

case 1

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

expected: [0.64,0.64]

case 2

in: [[2,0],0.25,1,1,0]

expected: [0.5,0]

case 3

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

expected: [0,0]

case 4

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

expected: [1,2]

case 5

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

expected: [0.25,0.25]

Starter codePython

def gradient_descent_two(point, lr, a, b, c):
    # Return the point after two steps
    # Your code here
    pass

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