PyTorch深度学习——梯度下降算法、随机梯度下降算法及实例
根据化简之后的公式，就可以编写代码，对 https://latex.csdn.net/eq?w 进行训练，具体代码如下：import numpy as np
import matplotlib.pyplot as plt
x_data =
y_data =
w = 1.0
def forward(x):
return x * w
def cost(xs, ys):
cost = 0
for x, y in zip(xs, ys):
y_pred = forward(x)
cost += (y_pred - y) ** 2
return cost / len(xs)
def gradient(xs, ys):
grad = 0
for x, y in zip(xs, ys):
grad += 2 * x * (x * w - y)
return grad / len(xs)
print('训练前的预测', 4, forward(4))
cost_list = []
epoch_list = []
# 开始训练(100次训练)
for epoch in range(150):
epoch_list.append(epoch)
cost_val = cost(x_data, y_data)
cost_list.append(cost_val)
grad_val = gradient(x_data, y_data)
w -= 0.1 * grad_val
print('Epoch:', epoch, 'w=', w, 'loss=', cost_val)
print('训练之后的预测', 4, forward(4))
# 画图
plt.plot(epoch_list, cost_list)
plt.ylabel('Cost')
plt.xlabel('Epoch')
plt.show() 运行截图如图所示：
Epoch是训练次数，Cost是误差，可以看到随着训练次数的增加，误差越来越小，趋近于0.
随机梯度下降算法 随机梯度下降算法与梯度下降算法的不同之处在于，随机梯度下降算法不再计算损失函数之和的导数，而是随机选取任一随机函数计算导数，随机的决定 https://latex.csdn.net/eq?w 下次的变化趋势，具体公式变化如图：
具体代码如下：import numpy as np
import matplotlib.pyplot as plt
x_data =
y_data =
w = 1.0
def forward(x):
return x * w
def loss(x, y):
y_pred = forward(x)
return (y_pred - y) ** 2
def gradient(x, y):
return 2 * x * (x * w - y)
print('训练前的预测', 4, forward(4))
epoch_list = []
loss_list = []
# 开始训练(100次训练)
for epoch in range(100):
for x, y in zip(x_data, y_data):
grad = gradient(x, y)
w -= 0.01 * grad
l = loss(x, y)
loss_list.append(l)
epoch_list.append(epoch)
print('Epoch:', epoch, 'w=', w, 'loss=', l)
print('训练之后的预测', 4, forward(4))
# 画图
plt.plot(epoch_list, loss_list)
plt.ylabel('Loss')
plt.xlabel('Epoch')
plt.grid(1)
plt.show()运行截图如图所示
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