作用：最小化一个损失函数

  1. import numpy as np
  2. import matplotlib.pyplot as plt
  3. plot_x = np.linspace(-1, 6, 141)
  4. plot_y = (plot_x - 2.5) ** 2 -1
  5. plt.plot(plot_x, plot_y)

image.png

  1. def Dj(theta):
  2.     return 2 * (theta - 2.5)
  4. def J(theta):
  5.     return (theta - 2.5) ** 2 - 1
  6. theta = 0.0
  7. eta = 0.1
  8. theta_history = []
  9. while True:
  10.     gradient = Dj(theta)
  11.     last_theat = theta
  12.     theta = theta - eta * gradient
  13.     theta_history.append(theta)
  14.     if abs(J(theta) - J(last_theat)) < 1e-8:
  15.         break
  16. print(theta)
  17. print(J(theta))
  18. plt.plot(plot_x, J(plot_x))
  19. plt.scatter(np.array(theta_history), J(np.array(theta_history)), color='r')

image.png