问题描述：求解y1 = xx -2 x +3 + 0.01*(-1到1的随机值) 与 y2 = 0 的最小距离点（x,y）

给定x范围（0，3）

不使用学习框架，手动编写梯度下降公式求解，提示：x = x - alp*(y1-y2)导数（alp为学习率）

函数图像为：

代码内容：

import numpy as np 
import matplotlib.pyplot as plt


def get_loss(x):
    c,r = x.shape
    loss = (x**2 - 2*x + 3) + (0.01*(2*np.random.rand(c,r)-1))
    return(loss)

x = np.arange(0,3,0.01).reshape(-1,1)


"""plt.title("loss")
plt.plot(get_loss(np.array(x)))
plt.show()"""


def get_grad(x):
    grad = 2 * x -2
    return(grad)

np.random.seed(31415)
x_ = np.random.rand(1)*3
x_s = []
alp = 0.001
print("X0",x_)
for e in range(2000):

    x_ = x_ - alp*(get_grad(x_))
    x_s.append(x_)
    if(e%100 == 0):
        print(e,"steps,x_ = ",x_)

plt.title("loss")
plt.plot(get_loss(np.array(x_s)))
plt.show()

运行结果：

X0 [1.93745582]
0 steps,x_ =  [1.93558091]
100 steps,x_ =  [1.76583547]
200 steps,x_ =  [1.6268875]
300 steps,x_ =  [1.51314929]
400 steps,x_ =  [1.42004698]
500 steps,x_ =  [1.34383651]
600 steps,x_ =  [1.28145316]
700 steps,x_ =  [1.23038821]
800 steps,x_ =  [1.18858814]
900 steps,x_ =  [1.15437199]
1000 steps,x_ =  [1.12636379]
1100 steps,x_ =  [1.1034372]
1200 steps,x_ =  [1.08467026]
1300 steps,x_ =  [1.06930826]
1400 steps,x_ =  [1.05673344]
1500 steps,x_ =  [1.04644011]
1600 steps,x_ =  [1.03801434]
1700 steps,x_ =  [1.03111727]
1800 steps,x_ =  [1.02547157]
1900 steps,x_ =  [1.02085018]

图片