第3讲  梯度下降法 源代码

B站 刘二大人 ，传送门PyTorch 深度学习实践 梯度下降法

深度学习算法中，并没有过多的局部最优点。

import matplotlib.pyplot as plt

# prepare the training set
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

# initial guess of weight 
w = 1.0

# define the model linear model y = w*x
def forward(x):
    return x*w

#define the cost function MSE 
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)

# define the gradient function  gd
def gradient(xs,ys):
    grad = 0
    for x, y in zip(xs,ys):
        grad += 2*x*(x*w - y)
    return grad / len(xs)

epoch_list = []
cost_list = []
print('predict (before training)', 4, forward(4))
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 learning rate
    print('epoch:', epoch, 'w=', w, 'loss=', cost_val)
    epoch_list.append(epoch)
    cost_list.append(cost_val)

print('predict (after training)', 4, forward(4))
plt.plot(epoch_list,cost_list)
plt.ylabel('cost')
plt.xlabel('epoch')
plt.show() 

随机梯度下降法 源代码

随机梯度下降法在神经网络中被证明是有效的。效率较低(时间复杂度较高)，学习性能较好。

随机梯度下降法和梯度下降法的主要区别在于：

1、损失函数由cost()更改为loss()。cost是计算所有训练数据的损失，loss是计算一个训练数据的损失。对应于源代码则是少了两个for循环。

2、梯度函数gradient()由计算所有训练数据的梯度更改为计算一个训练数据的梯度。

3、本算法中的随机梯度主要是指，每次拿一个训练数据来训练，然后更新梯度参数。本算法中梯度总共更新100(epoch)x3 = 300次。梯度下降法中梯度总共更新100(epoch)次。

import matplotlib.pyplot as plt

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

w = 1.0

def forward(x):
    return x*w

# calculate loss function
def loss(x, y):
    y_pred = forward(x)
    return (y_pred - y)**2

# define the gradient function  sgd
def gradient(x, y):
    return 2*x*(x*w - y)

epoch_list = []
loss_list = []
print('predict (before training)', 4, forward(4))
for epoch in range(100):
    for x,y in zip(x_data, y_data):
        grad = gradient(x,y)
        w = w - 0.01*grad    # update weight by every grad of sample of training set
        print("\tgrad:", x, y,grad)
        l = loss(x,y)
    print("progress:",epoch,"w=",w,"loss=",l)
    epoch_list.append(epoch)
    loss_list.append(l)

print('predict (after training)', 4, forward(4))
plt.plot(epoch_list,loss_list)
plt.ylabel('loss')
plt.xlabel('epoch')
plt.show()