梯度下降的实现

import numpy as np
import matplotlib.pyplot as plt
from scipy.misc import derivative

def f(x):
    return x**3 + x**2

d = derivative(f, 1.0, dx=1e-6)
print(d)

def lossFunction(x):
    return (x-2.5)**2-1

# 在-1到6的范围内构建140个点
plot_x = np.linspace(-1,6,141)
# plot_y 是对应的损失函数值
plot_y = lossFunction(plot_x)

plt.plot(plot_x,plot_y)
#plt.show()

"""
算法：计算损失函数J在当前点的对应导数
输入：当前数据点theta
输出：点在损失函数上的导数
"""
def dLF(theta):
    return derivative(lossFunction, theta, dx=1e-6)

theta = 0.0
eta = 0.1
epsilon = 1e-6
while True:
    # 每一轮循环后，要求当前这个点的梯度是多少
    gradient = dLF(theta)
    last_theta = theta
    # 移动点，沿梯度的反方向移动步长eta
    theta = theta - eta * gradient
    # 判断theta是否达到最小值
    # 因为梯度在不断下降，因此新theta的损失函数在不断减小
    # 看差值是否达到了要求
    if(abs(lossFunction(theta) - lossFunction(last_theta)) < epsilon):
        break

print(theta)
print(lossFunction(theta))

theta_history = []
def gradient_descent(initial_theta, eta, epsilon=1e-6):
    theta = initial_theta
    theta_history.append(theta)
    while True:
        # 每一轮循环后，要求当前这个点的梯度是多少
        gradient = dLF(theta)
        last_theta = theta
        # 移动点，沿梯度的反方向移动步长eta
        theta = theta - eta * gradient
        theta_history.append(theta)
        # 判断theta是否达到损失函数最小值的位置
        if(abs(lossFunction(theta) - lossFunction(last_theta)) < epsilon):
            break

def plot_theta_history():
    plt.plot(plot_x,plot_y)
    plt.plot(np.array(theta_history), lossFunction(np.array(theta_history)), color='red', marker='o')
    plt.show()

eta=0.1
theta_history = []
gradient_descent(0., eta)
plot_theta_history()
print("梯度下降查找次数：",len(theta_history))