梯度下降法 —— 经典的优化方法

# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt


def f(x):
    return np.power(x, 2)

def d_f_1(x):
    return 2.0 * x

def d_f_2(f, x, delta=1e-4):
    return (f(x+delta) - f(x-delta)) / (2 * delta)


# plot the function
xs = np.arange(-10, 11)
plt.plot(xs, f(xs))
plt.show()

learning_rate = 0.1
max_loop = 30

x_init = 10.0
x = x_init
lr = 0.1
for i in range(max_loop):
    # d_f_x = d_f_1(x)
    d_f_x = d_f_2(f, x)
    x = x - learning_rate * d_f_x
    print(x)

print('initial x =', x_init)
print('arg min f(x) of x =', x)
print('f(x) =', f(x))