参考

3.12 权重衰减

本节介绍应对过拟合的常用方法

3.12.1 方法

正则化通过为模型损失函数添加惩罚项使学出的模型参数更小,是应对过拟合的常用手段。

3.12.2 高维线性回归实验

import torch
import torch.nn as nn
import numpy as np
import sys
sys.path.append("..") 
import d2lzh_pytorch as d2ln_train, n_test, num_inputs = 20, 100, 200
true_w, true_b = torch.ones(num_inputs, 1) * 0.01, 0.05features = torch.randn((n_train + n_test, num_inputs))
labels = torch.matmul(features, true_w) + true_b
labels += torch.tensor(np.random.normal(0, 0.01, size=labels.size()), dtype=torch.float)
train_features, test_features = features[:n_train, :], features[n_train:, :]
train_labels, test_labels = labels[:n_train], labels[n_train:]

3.13.3 从零开始实现

3.12.3.1 初始化模型参数

def init_params():w = torch.randn((num_inputs, 1), requires_grad=True)b = torch.zeros(1, requires_grad=True)return [w, b]

3.12.3.2 定义L2范数惩罚项

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

3.12.3.3 定义训练和测试

batch_size, num_epochs, lr = 1, 100, 0.003
net, loss = d2l.linreg, d2l.squared_lossdataset = torch.utils.data.TensorDataset(train_features, train_labels)
train_iter = torch.utils.data.DataLoader(dataset, batch_size, shuffle=True)def fit_and_plot(lambd):w, b = init_params()train_ls, test_ls = [], []for _ in range(num_epochs):for X, y in train_iter:# 添加了L2范数惩罚项l = loss(net(X, w, b), y) + lambd * l2_penalty(w)l = l.sum()if w.grad is not None:w.grad.data.zero_()b.grad.data.zero_()l.backward()d2l.sgd([w, b], lr, batch_size)train_ls.append(loss(net(train_features, w, b), train_labels).mean().item())test_ls.append(loss(net(test_features, w, b), test_labels).mean().item())d2l.semilogy(range(1, num_epochs + 1), train_ls, 'epochs', 'loss',range(1, num_epochs + 1), test_ls, ['train', 'test'])print('L2 norm of w:', w.norm().item())

3.12.3.4 观察过拟合

fit_and_plot(lambd=0)

3.12.3.5 使用权重衰减

fit_and_plot(lambd=5)

3.12.4 简洁实现

def fit_and_plot_pytorch(wd):# 对权重参数衰减。权重名称一般以weight结尾net = nn.Linear(num_inputs, 1)nn.init.normal_(net.weight, mean=0, std=1)nn.init.normal_(net.bias, mean=0 , std=1)optimizer_w = torch.optim.SGD(params=[net.weight], lr= lr, weight_decay=wd)  # 对权重进行衰减optimizer_b = torch.optim.SGD(params=[net.bias], lr=lr)  # 对偏差不进行衰减train_ls, test_ls = [], []for _ in range(num_epochs):for X, y in train_iter:l = loss(net(X), y).mean()optimizer_w.zero_grad()optimizer_b.zero_grad()l.backward()# 对两个optimizer实例分别调用step函数,从而分别更新权重和偏差optimizer_w.step()optimizer_b.step()train_ls.append(loss(net(train_features), train_labels).mean().item())test_ls.append(loss(net(test_features), test_labels).mean().item())d2l.semilogy(range(1, num_epochs + 1), train_ls, 'epochs', 'loss',range(1, num_epochs + 1), test_ls, ['train', 'test'])print('L2 norm of w:', net.weight.data.norm().item())fit_and_plot_pytorch(0)fit_and_plot_pytorch(3)