在多分类任务实验中手动实现 使用 𝑳𝟐 正则化

1 导入所需要的包

import torch  
import numpy as np  
import random  
from IPython import display  
from matplotlib import pyplot as plt  
import torchvision  
import torchvision.transforms as transforms   

2 下载MNIST数据集

mnist_train = torchvision.datasets.MNIST(root='../Datasets/MNIST', train=True, download=True, transform=transforms.ToTensor())  
mnist_test = torchvision.datasets.MNIST(root='../Datasets/MNIST', train=False,download=True, transform=transforms.ToTensor())  

3 读取数据

batch_size = 256 
train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True,num_workers=0)  
test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False,num_workers=0)  

4 初始化参数+定义隐藏层的激活函数

num_inputs,num_hiddens,num_outputs =784, 256,10
def init_param():
    W1 = torch.tensor(np.random.normal(0, 0.01, (num_hiddens,num_inputs)), dtype=torch.float32)  
    b1 = torch.zeros(1, dtype=torch.float32)  
    W2 = torch.tensor(np.random.normal(0, 0.01, (num_outputs,num_hiddens)), dtype=torch.float32)  
    b2 = torch.zeros(1, dtype=torch.float32)  
    params =[W1,b1,W2,b2]
    for param in params:  
        param.requires_grad_(requires_grad=True)  
    return W1,b1,W2,b2
def relu(x):  
    x = torch.max(input=x,other=torch.tensor(0.0))  
    return x  

5 定义模型

def net(X):  
    X = X.view((-1,num_inputs))  
    H = relu(torch.matmul(X,W1.t())+b1)  
    return torch.matmul(H,W2.t())+b2  

6 定义交叉熵损失函数和优化器

loss = torch.nn.CrossEntropyLoss()  
def SGD(paras,lr):  
    for param in params:  
        param.data -= lr * param.grad  

7 定义L2范数

def l2_penalty(w):
    return (w**2).sum()/2

8 定义训练函数

def train(net,train_iter,test_iter,loss,num_epochs,batch_size,lr=None,optimizer=None,mylambda=0):  
    train_ls, test_ls = [], []
    for epoch in range(num_epochs):
        ls, count = 0, 0
        for X,y in train_iter :
            X = X.reshape(-1,num_inputs)
            l=loss(net(X),y)+ mylambda*l2_penalty(W1) + mylambda*l2_penalty(W2)
            optimizer.zero_grad()
            l.backward()
            optimizer.step()
            ls += l.item()
            count += y.shape[0]
        train_ls.append(ls)
        ls, count = 0, 0
        for X,y in test_iter:
            X = X.reshape(-1,num_inputs)
            l=loss(net(X),y) + mylambda*l2_penalty(W1) + mylambda*l2_penalty(W2)
            ls += l.item()
            count += y.shape[0]
        test_ls.append(ls)
        if(epoch+1)%5==0:
            print('epoch: %d, train loss: %f, test loss: %f'%(epoch+1,train_ls[-1],test_ls[-1]))
    return train_ls,test_ls

9 开始训练模型

lr = 0.01  
num_epochs = 20 

Lamda = [0,0.1,0.2,0.3,0.4,0.5]
Train_ls, Test_ls = [], []
for lamda in Lamda:
    print("current lambda is %f"%lamda)
    W1,b1,W2,b2 = init_param()
    loss = torch.nn.CrossEntropyLoss()
    optimizer = torch.optim.SGD([W1,b1,W2,b2],lr = 0.001)
    train_ls, test_ls = train(net,train_iter,test_iter,loss,num_epochs,batch_size,lr,optimizer,lamda)   
    Train_ls.append(train_ls)
    Test_ls.append(test_ls)

10 绘制训练集和测试集的loss曲线

x = np.linspace(0,len(Train_ls[1]),len(Train_ls[1]))
plt.figure(figsize=(10,8))
for i in range(0,len(Lamda)):
    plt.plot(x,Train_ls[i],label= f'L2_Regularization:{Lamda [i]}',linewidth=1.5)
    plt.xlabel('different epoch')
    plt.ylabel('loss')
plt.legend(loc=2, bbox_to_anchor=(1.1,1.0),borderaxespad = 0.)
plt.title('train loss with L2_penalty')
plt.show()