Pytorch深度学习实践|第3讲|梯度下降

目前跟着b站“刘二大人”学习pytorch实践课程

网址：https://www.bilibili.com/video/BV1Y7411d7Ys?p=3&vd_source=32b3ab6f83a7264145dc021d4ff722f6

 1. 梯度下降Gradient Descent

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 说明：

1. GD(梯度下降）算法是朝着梯度的反方向迭代

2. 可能最后结果是局部最优（如图所示）

# 梯度下降【Gradient Descent】
import matplotlib.pyplot as plt

# 准备数据
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

# 初始猜测的权值
w = 1.0

# 预测函数
def forward(x):
    return x * w


# 损失函数(所有训练数据损失求平均）
def cost(xs, ys):
    cost = 0.0
    for x, y in zip(xs, ys):
        y_pred = forward(x)  # 预测
        cost += (y_pred - y) ** 2
    return cost / len(xs)


# 求梯度函数
def gradient(xs, ys):
    grad = 0.0
    for x, y in zip(xs, ys):
        grad += 2 * x * (x * w - y)
    return grad / len(xs)

print("Predict (before training)", 4, forward(4))
epoch_list = []
cost_list = []

# 梯度下降开始迭代
for epoch in range(100):
    cost_val = cost(x_data, y_data)
    grad_val = gradient(x_data, y_data)
    w -= 0.01 * grad_val  # 0.01为自己设定的学习率
    print('Epoch=', epoch, 'w=', w, 'loss=', cost_val)
    epoch_list.append(epoch)
    cost_list.append(cost_val)

print('Predict(after training)', 4, forward(4))

#作图
plt.plot(epoch_list, cost_list)
plt.xlabel('epoch')
plt.ylabel('cost')
plt.show()

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2. 随机梯度下降（Stochastic Gradient Descent） 

两者区别：

1. GD是对所有训练数据计算梯度，然后求其均值；梯度之间没有关联

2. SGD是对每一个训练数据计算梯度，前后梯度之间有关联 

# 随机梯度下降【Stochastic Gradient Descent】
import matplotlib.pyplot as plt

# 准备数据
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

# 初始猜测的权值
w = 1.0

# 预测函数
def forward(x):
    return x * w

# 损失函数(每一个训练数据求损失）
def loss(x, y):
    y_pred = forward(x)
    return (y_pred - y) ** 2

# 求梯度函数(每一个训练数据都要算一个损失)
def gradient(x, y):
    grad = 2 * x * (x * w - y)
    return grad

print("Predict (before training)", 4, forward(4))
epoch_list = []
loss_list = []

# 梯度下降开始迭代
for epoch in range(100):
    for x, y in zip(x_data, y_data):
        grad_val = gradient(x, y)
        w -= 0.01 * grad_val  # 0.01为自己设定的学习率
        print("\tgrad:", x, y, grad_val)
        l = loss(x, y)

        epoch_list.append(epoch)
        loss_list.append(l)
    print("progress:", epoch, 'w=', w, "loss=", l)

print('Predict(after training)', 4, forward(4))

#作图
plt.plot(epoch_list, loss_list)
plt.xlabel('epoch')
plt.ylabel('loss')
plt.show()