实现： # -*- coding: UTF-8 -*- """     练习使用随机梯度下降算法 """ import numpy as np import math __author__ = 'zhen' # 生成测试数据 x = 2 * np.random.rand(100, 1)  # 随机生成100*1的二维数组，值分别在0~2之间 y = 4 + 3 * x + np.random.randn(100, 1)  # 随机生成100*1的二维数组，值分别在4~11之间 x_b = np.c_[np.ones((100, 1)), x] print("x矩阵内容如下：\n{}".format(x_b[0:3])) n_epochs = 100 t0, t1 = 1, 10 m = n_epochs def learning_schedule(t):  # 模拟实现动态修改步长     return t0 / (t + t1) theta = np.random.randn(2, 1) for epoch in range(n_epochs):     for i in range(m):         random_index = np.random.randint(m)         x_i = x_b[random_index:random_index+1]         y_i = y[random_index:random_index+1] gradients = 2 * x_i.T.dot(x_i.dot(theta)-y_i)  # 调用公式         learning_rate = learning_schedule(epoch * m + i)         theta = theta - learning_rate * gradients     if epoch % 30 == 0:         print("抽样查看：\n{}".format(theta)) print("最终结果：\n{}".format(theta)) # 计算误差 error = math.sqrt(math.pow((theta[0][0] - 4), 2) + math.pow((theta[1][0] - 3), 2)) print("误差：\n{}".format(error)) 结果：