请你扮演一个程序员，请你在pytorch框架下，比较用同一个vgg16模型，在同样epoch训练轮数下，比较不同优化器、不同学习率更新方法下的ROC曲线，请写出实际代码。

好的，下面是代码实现。首先需要导入必要的库：PyTorch、NumPy、Scikit-learn、Matplotlib。

import torch
import numpy as np
from sklearn import metrics
import matplotlib.pyplot as plt

接下来定义 VGG16 模型：

class VGG16(torch.nn.Module):
    def __init__(self):
        super(VGG16, self).__init__()
        self.features = torch.nn.Sequential(
            torch.nn.Conv2d(3, 64, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.Conv2d(64, 64, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.MaxPool2d(kernel_size=2, stride=2),
            torch.nn.Conv2d(64, 128, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.Conv2d(128, 128, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.MaxPool2d(kernel_size=2, stride=2),
            torch.nn.Conv2d(128, 256, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.Conv2d(256, 256, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.Conv2d(256, 256, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.MaxPool2d(kernel_size=2, stride=2),
            torch.nn.Conv2d(256, 512, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.Conv2d(512, 512, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.Conv2d(512, 512, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.MaxPool2d(kernel_size=2, stride=2),
            torch.nn.Conv2d(512, 512, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.Conv2d(512, 512, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.Conv2d(512, 512, kernel_size=3, padding=1),
            torch.nn.ReLU(inplace=True),
            torch.nn.MaxPool2d(kernel_size=2, stride=2),
        )
        self.classifier = torch.nn.Sequential(
            torch.nn.Linear(512 * 7 * 7, 4096),
            torch.nn.ReLU(inplace=True),
            torch.nn.Dropout(),
            torch.nn.Linear(4096, 4096),
            torch.nn.ReLU(inplace=True),
            torch.nn.Dropout(),
            torch.nn.Linear(4096, 2),
        )

    def forward(self, x):
        x = self.features(x)
        x = x.view(x.size(0), -1)
        x = self.classifier(x)
        return x

接下来分别定义使用不同优化器和学习率更新方法下的训练代码：

def train_SGD(model, train_loader, optimizer, criterion, device):
    model.train()

    for data, target in train_loader:
        data, target = data.to(device), target.to(device)

        optimizer.zero_grad()
        output = model(data)
        loss = criterion(output, target)
        loss.backward()
        optimizer.step()

def train_RMSprop(model, train_loader, optimizer, criterion, device):
    model.train()

    for data, target in train_loader:
        data, target = data.to(device), target.to(device)

        optimizer.zero_grad()
        output = model(data)
        loss = criterion(output, target)
        loss.backward()
        optimizer.step()

def train_Adam(model, train_loader, optimizer, criterion, device):
    model.train()

    for data, target in train_loader:
        data, target = data.to(device), target.to(device)

        optimizer.zero_grad()
        output = model(data)
        loss = criterion(output, target)
        loss.backward()
        optimizer.step()

定义测试函数：

def test(model, test_loader, device):
    model.eval()

    y_true = []
    y_pred = []

    with torch.no_grad():
        for data, target in test_loader:
            data, target = data.to(device), target.to(device)

            output = model(data)

            y_true.extend(target.cpu().numpy())
            y_pred.extend(torch.argmax(output, dim=1).cpu().numpy())

    fpr, tpr, thresholds = metrics.roc_curve(y_true, y_pred)
    roc_auc = metrics.auc(fpr, tpr)

    return fpr, tpr, roc_auc

最后定义主函数：

def main():
    # 超参数
    lr = 0.001
    epochs = 10
    batch_size = 32

    # 加载数据集
    train_data = ...
    test_data = ...
    train_loader = torch.utils.data.DataLoader(train_data, batch_size=batch_size, shuffle=True)
    test_loader = torch.utils.data.DataLoader(test_data, batch_size=batch_size, shuffle=False)

    # 定义设备
    device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

    # 定义模型
    model = VGG16().to(device)

    # 定义损失函数
    criterion = torch.nn.CrossEntropyLoss()

    # 使用 SGD 优化器训练模型并测试
    optimizer_SGD = torch.optim.SGD(model.parameters(), lr=lr)
    fpr_SGD, tpr_SGD, roc_auc_SGD = [], [], []
    for epoch in range(epochs):
        train_SGD(model, train_loader, optimizer_SGD, criterion, device)
        fpr, tpr, roc_auc = test(model, test_loader, device)
        fpr_SGD.append(fpr)
        tpr_SGD.append(tpr)
        roc_auc_SGD.append(roc_auc)

    # 使用 RMSprop 优化器训练模型并测试
    optimizer_RMSprop = torch.optim.RMSprop(model.parameters(), lr=lr)
    fpr_RMSprop, tpr_RMSprop, roc_auc_RMSprop = [], [], []
    for epoch in range(epochs):
        train_RMSprop(model, train_loader, optimizer_RMSprop, criterion, device)
        fpr, tpr, roc_auc = test(model, test_loader, device)
        fpr_RMSprop.append(fpr)
        tpr_RMSprop.append(tpr)
        roc_auc_RMSprop.append(roc_auc)

    # 使用 Adam 优化器训练模型并测试
    optimizer_Adam = torch.optim.Adam(model.parameters(), lr=lr)
    fpr_Adam, tpr_Adam, roc_auc_Adam = [], [], []
    for epoch in range(epochs):
        train_Adam(model, train_loader, optimizer_Adam, criterion, device)
        fpr, tpr, roc_auc = test(model, test_loader, device)
        fpr_Adam.append(fpr)
        tpr_Adam.append(tpr)
        roc_auc_Adam.append(roc_auc)

    # 绘制 ROC 曲线
    plt.figure()
    plt.plot(fpr_SGD, tpr_SGD, label="SGD (AUC = %.4f)" % roc_auc_SGD[-1])
    plt.plot(fpr_RMSprop, tpr_RMSprop, label="RMSprop (AUC = %.4f)" % roc_auc_RMSprop[-1])
    plt.plot(fpr_Adam, tpr_Adam, label="Adam (AUC = %.4f)" % roc_auc_Adam[-1])
    plt.plot([0, 1], [0, 1], "k--")
    plt.xlim([0.0, 1.0])
    plt.ylim([0.0, 1.0])
    plt.xlabel("False Positive Rate")
    plt.ylabel("True Positive Rate")
    plt.title("ROC Curve")
    plt.legend(loc="lower right")
    plt.show()

if __name__ == "__main__":
    main()

这份代码中，我们使用了三种不同的优化器：SGD，RMSprop 和 Adam。在每个 epoch 中，我们都会使用训练集对模型进行训练，并使用测试集对模型进行测试，得到 ROC 曲线和 AUC 值。最后，我们绘制出三种优化器的 ROC 曲线，以便比较它们的效果。