10权重衰减

"""
正则化是处理过拟合的常用方法：在训练集的损失函数中加入惩罚项，以降低学习到的模型的复杂度。
保持模型简单的一个特别的选择是使用L2惩罚的权重衰减。这会导致学习算法更新步骤中的权重衰减。
"""

import torch
from torch import nn
from d2l import torch as d2l
import liliPytorch as lp

n_train, n_test, num_input, batch_size = 20, 100, 200, 5
true_w, true_b = torch.ones((num_input,1)) * 0.01, 0.05

train_data = d2l.synthetic_data(true_w, true_b, n_train)
train_iter = d2l.load_array(train_data, batch_size)

test_data = d2l.synthetic_data(true_w, true_b, n_test)
test_iter = d2l.load_array(test_data, batch_size, is_train=False)


#初始化模型参数
def init_params():
    w = torch.normal(0,1,size=(num_input,1), requires_grad=True)
    b = torch.zeros(1,requires_grad=True)
    return [w,b]

#定义L2范数惩罚
def l2_penalty(w):
    return torch.sum(w.pow(2)) / 2

def l1_penalty(w):
    return torch.sum(torch.abs(w))

# 定义模型
def linreg(X, w, b):
    """线性回归模型"""
    return torch.matmul(X, w) + b

# 定义损失函数
def squared_loss(y_hat, y):
    """均方损失函数"""
    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2

# 定义优化函数
def sgd(params, lr, batch_size):
    """小批量随机梯度下降"""
    # 更新参数时不需要计算梯度
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad / batch_size  # 参数更新
            param.grad.zero_()  # 梯度清零

#定义训练代码实现
def train(lambd):
    w, b = init_params()
    net, loss = lambda X: linreg(X, w, b), squared_loss
    num_epochs, lr = 100, 0.003
    animator = d2l.Animator(xlabel='epochs', ylabel='loss', yscale='log',
                            xlim=[5, num_epochs], legend=['train', 'test'])
    for epoch in range(num_epochs):
        for X, y in train_iter:
            # 增加了L2范数惩罚项，
            # 广播机制使l2_penalty(w)成为一个长度为batch_size的向量
            l = loss(net(X), y) + lambd * l2_penalty(w)
            l.sum().backward()
            sgd([w, b], lr, batch_size)
        if (epoch + 1) % 5 == 0:
            animator.add(epoch + 1, (d2l.evaluate_loss(net, train_iter, loss),
                                     d2l.evaluate_loss(net, test_iter, loss)))
    print('w的L2范数是：', torch.norm(w).item())


#忽略正则化直接训练¶
# train(lambd=0)
#w的L2范数是： 14.630496978759766

# 使用权重衰减
# train(lambd=3)
# d2l.plt.show() 


#权重衰减-简洁实现
def train_concise(wd):
    net = nn.Sequential(nn.Linear(num_input, 1))
    for param in net.parameters():
        param.data.normal_()
    loss = nn.MSELoss(reduction='none')
    num_epochs, lr = 100, 0.003
    # 偏置参数没有衰减
    trainer = torch.optim.SGD([
        {"params":net[0].weight,'weight_decay': wd},
        {"params":net[0].bias}], lr=lr)
    animator = lp.Animator(xlabel='epochs', ylabel='loss', yscale='log',
                            xlim=[5, num_epochs], legend=['train', 'test'])
    for epoch in range(num_epochs):
        for X, y in train_iter:
            trainer.zero_grad()
            l = loss(net(X), y)
            l.mean().backward()
            trainer.step()
        if (epoch + 1) % 5 == 0:
            animator.add(epoch + 1,
                         (d2l.evaluate_loss(net, train_iter, loss),
                          d2l.evaluate_loss(net, test_iter, loss)))
    print('w的L2范数：', net[0].weight.norm().item())

train_concise(0)
d2l.plt.show() 
# w的L2范数是： 0.33992505073547363

运行结果：