MediumCalculusca-041

Gradient Descent One Step

Problem

Take one gradient descent step on f(x, y) = a*x^2 + b*y^2 + c*x*y from the given point with learning rate lr.

The gradient is [2*a*x + c*y, 2*b*y + c*x]. Return the updated point [x - lr * gx, y - lr * gy].

Hint

Step against the gradient: new_point = point - lr * gradient.

case 1

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

expected: [0.8,0.8]

case 2

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

expected: [0.5,0]

case 3

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

expected: [3,-2]

case 4

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

expected: [0,0]

Starter codePython

def gradient_descent_step(point, lr, a, b, c):
    # Return the updated [x, y]
    # Your code here
    pass

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