gradient_descent.py

def fn(x):
    return x**2 + 0.2*(x-2)**5 + 2*x**3

# initialization
x = Variable(3.)
target = 42.
print('---- Initial Value ----')
print('fn(x): {}'.format(fn(x)))
print('Target: {}'.format(target))
print('intial guess for x: {}'.format(x))


for n in range(20):
    L = (fn(x) - target)**2
    L.backward()
    # gradient descent update
    x.value = x.value - 1e-4 * x.gradient
    # clear the gradients
    x.clear_gradient()

print('---- Converged Value ----')    
print('fn(x): {}'.format(fn(x)))
print('Target: {}'.format(target))
print('converged x: {}'.format(x))


'''
# Wolfram alpha minimum:
# min{(x^2 + 0.2 (x - 2)^5 + 2 x^3 - 42)^2} = 0 at x≈2.60158
# Output:
'''
---- Initial Value ----
fn(x): < Variable value: 63.2, gradient: 0.0 >
Target: 42.0
intial guess for x: < Variable value: 3.0, gradient: 0.0 >
---- Converged Value ----
fn(x): < Variable value: 42.00014691908245, gradient: 0.0 >
Target: 42.0
converged x: < Variable value: 2.601581019114941, gradient: 0.0 >
'''