12权重衰退

import torch
from torch import nn
from d2l import torch as d2l

# 权重衰退是最广泛使用的正则化的技术之一
# 生成数据集
n_train, n_test, num_inputs, batch_size = 20, 100, 200, 5
# 训练数据较小，过拟合容易发生
true_w, true_b = torch.ones((num_inputs, 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_inputs, 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 train(lambd):
    w, b = init_params()
    net, loss = lambda X: d2l.linreg(X, w, b), d2l.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()
            d2l.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(d2l.evaluate_loss(net, train_iter, loss))
            print(d2l.evaluate_loss(net, test_iter, loss))
            print("------------------------------------")
    print('w的L2范数是：', torch.norm(w).item())

# # 忽略正则化直接训练
# train(lambd=0)
# # 使用权重衰减
# train(lambd=3)


# 简洁实现
def train_concise(wd):
    # net = nn.Sequential(nn.Linear(num_inputs, 1))
    # for param in net.parameters():
    #     param.data.normal_()
    # loss = nn.MSELoss(reduction='none')
    # num_epochs, lr = 100, 0.003

    net = nn.Sequential(nn.Linear(num_inputs, 1))
    for param in net.parameters():
        param.data.normal_()
    loss = nn.MSELoss(reduction='none')
    num_epochs, lr = 100, 0.003
    # 优化器
    trainer = torch.optim.SGD(
        [{
            "params": net[0].weight,
            "weight_decay":wd
        },
        {
            "params":net[0].bias
        }],lr=lr
    )
    # trainer = torch.optim.SGD([
    #     {"params": net[0].weight, 'weight_decay': wd},
    #     {"params": net[0].bias}], lr=lr)

    for epoch in range(num_epochs):
        for X, y in train_iter:
            trainer.zero_grad()
            l = loss(net(X), y)
            # 为什么要mean
            l.mean().backward()
            trainer.step()


    # for epoch in range(num_epochs):
    #     for X, y in train_iter:
    #         with torch.enable_grad():
    #             trainer.zero_grad()
    #             l = loss(net(X), y)
    #         l.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(d2l.evaluate_loss(net, train_iter, loss))
            print(d2l.evaluate_loss(net, test_iter, loss))
            print("------------------------------------")
    print('w的L2范数是：', net[0].weight.norm().item())

# 忽略正则化直接训练
train_concise(0)
# 使用权重衰减
train_concise(3)