{
"cells": [
{
"cell_type": "markdown",
"id": "21eb8780",
"metadata": {
"origin_pos": 0
},
"source": [
"# 学习率调度器\n",
":label:`sec_scheduler`\n",
"\n",
"到目前为止，我们主要关注如何更新权重向量的优化算法，而不是它们的更新速率。\n",
"然而，调整学习率通常与实际算法同样重要，有如下几方面需要考虑：\n",
"\n",
"* 首先，学习率的大小很重要。如果它太大，优化就会发散；如果它太小，训练就会需要过长时间，或者我们最终只能得到次优的结果。我们之前看到问题的条件数很重要（有关详细信息，请参见 :numref:`sec_momentum`）。直观地说，这是最不敏感与最敏感方向的变化量的比率。\n",
"* 其次，衰减速率同样很重要。如果学习率持续过高，我们可能最终会在最小值附近弹跳，从而无法达到最优解。 :numref:`sec_minibatch_sgd`比较详细地讨论了这一点，在 :numref:`sec_sgd`中我们则分析了性能保证。简而言之，我们希望速率衰减，但要比$\\mathcal{O}(t^{-\\frac{1}{2}})$慢，这样能成为解决凸问题的不错选择。\n",
"* 另一个同样重要的方面是初始化。这既涉及参数最初的设置方式（详情请参阅 :numref:`sec_numerical_stability`），又关系到它们最初的演变方式。这被戏称为*预热*（warmup），即我们最初开始向着解决方案迈进的速度有多快。一开始的大步可能没有好处，特别是因为最初的参数集是随机的。最初的更新方向可能也是毫无意义的。\n",
"* 最后，还有许多优化变体可以执行周期性学习率调整。这超出了本章的范围，我们建议读者阅读 :cite:`Izmailov.Podoprikhin.Garipov.ea.2018`来了解个中细节。例如，如何通过对整个路径参数求平均值来获得更好的解。\n",
"\n",
"鉴于管理学习率需要很多细节，因此大多数深度学习框架都有自动应对这个问题的工具。\n",
"在本章中，我们将梳理不同的调度策略对准确性的影响，并展示如何通过*学习率调度器*（learning rate scheduler）来有效管理。\n",
"\n",
"## 一个简单的问题\n",
"\n",
"我们从一个简单的问题开始，这个问题可以轻松计算，但足以说明要义。\n",
"为此，我们选择了一个稍微现代化的LeNet版本（激活函数使用`relu`而不是`sigmoid`，汇聚层使用最大汇聚层而不是平均汇聚层），并应用于Fashion-MNIST数据集。\n",
"此外，我们混合网络以提高性能。\n",
"由于大多数代码都是标准的，我们只介绍基础知识，而不做进一步的详细讨论。如果需要，请参阅 :numref:`chap_cnn`进行复习。\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "fa35f5a3",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:22:40.885445Z",
"iopub.status.busy": "2023-08-18T07:22:40.884804Z",
"iopub.status.idle": "2023-08-18T07:22:43.950999Z",
"shell.execute_reply": "2023-08-18T07:22:43.950124Z"
},
"origin_pos": 2,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import math\n",
"import torch\n",
"from torch import nn\n",
"from torch.optim import lr_scheduler\n",
"from d2l import torch as d2l\n",
"\n",
"\n",
"def net_fn():\n",
" model = nn.Sequential(\n",
" nn.Conv2d(1, 6, kernel_size=5, padding=2), nn.ReLU(),\n",
" nn.MaxPool2d(kernel_size=2, stride=2),\n",
" nn.Conv2d(6, 16, kernel_size=5), nn.ReLU(),\n",
" nn.MaxPool2d(kernel_size=2, stride=2),\n",
" nn.Flatten(),\n",
" nn.Linear(16 * 5 * 5, 120), nn.ReLU(),\n",
" nn.Linear(120, 84), nn.ReLU(),\n",
" nn.Linear(84, 10))\n",
"\n",
" return model\n",
"\n",
"loss = nn.CrossEntropyLoss()\n",
"device = d2l.try_gpu()\n",
"\n",
"batch_size = 256\n",
"train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size=batch_size)\n",
"\n",
"# 代码几乎与d2l.train_ch6定义在卷积神经网络一章LeNet一节中的相同\n",
"def train(net, train_iter, test_iter, num_epochs, loss, trainer, device,\n",
" scheduler=None):\n",
" net.to(device)\n",
" animator = d2l.Animator(xlabel='epoch', xlim=[0, num_epochs],\n",
" legend=['train loss', 'train acc', 'test acc'])\n",
"\n",
" for epoch in range(num_epochs):\n",
" metric = d2l.Accumulator(3) # train_loss,train_acc,num_examples\n",
" for i, (X, y) in enumerate(train_iter):\n",
" net.train()\n",
" trainer.zero_grad()\n",
" X, y = X.to(device), y.to(device)\n",
" y_hat = net(X)\n",
" l = loss(y_hat, y)\n",
" l.backward()\n",
" trainer.step()\n",
" with torch.no_grad():\n",
" metric.add(l * X.shape[0], d2l.accuracy(y_hat, y), X.shape[0])\n",
" train_loss = metric[0] / metric[2]\n",
" train_acc = metric[1] / metric[2]\n",
" if (i + 1) % 50 == 0:\n",
" animator.add(epoch + i / len(train_iter),\n",
" (train_loss, train_acc, None))\n",
"\n",
" test_acc = d2l.evaluate_accuracy_gpu(net, test_iter)\n",
" animator.add(epoch+1, (None, None, test_acc))\n",
"\n",
" if scheduler:\n",
" if scheduler.__module__ == lr_scheduler.__name__:\n",
" # UsingPyTorchIn-Builtscheduler\n",
" scheduler.step()\n",
" else:\n",
" # Usingcustomdefinedscheduler\n",
" for param_group in trainer.param_groups:\n",
" param_group['lr'] = scheduler(epoch)\n",
"\n",
" print(f'train loss {train_loss:.3f}, train acc {train_acc:.3f}, '\n",
" f'test acc {test_acc:.3f}')"
]
},
{
"cell_type": "markdown",
"id": "32c9a5d9",
"metadata": {
"origin_pos": 5
},
"source": [
"让我们来看看如果使用默认设置，调用此算法会发生什么。\n",
"例如设学习率为$0.3$并训练$30$次迭代。\n",
"留意在超过了某点、测试准确度方面的进展停滞时，训练准确度将如何继续提高。\n",
"两条曲线之间的间隙表示过拟合。\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "c830419f",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:22:43.955399Z",
"iopub.status.busy": "2023-08-18T07:22:43.954810Z",
"iopub.status.idle": "2023-08-18T07:24:50.626624Z",
"shell.execute_reply": "2023-08-18T07:24:50.625712Z"
},
"origin_pos": 7,
"tab": [
"pytorch"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"train loss 0.128, train acc 0.951, test acc 0.885\n"
]
},
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"lr, num_epochs = 0.3, 30\n",
"net = net_fn()\n",
"trainer = torch.optim.SGD(net.parameters(), lr=lr)\n",
"train(net, train_iter, test_iter, num_epochs, loss, trainer, device)"
]
},
{
"cell_type": "markdown",
"id": "52310b75",
"metadata": {
"origin_pos": 10
},
"source": [
"## 学习率调度器\n",
"\n",
"我们可以在每个迭代轮数（甚至在每个小批量）之后向下调整学习率。\n",
"例如，以动态的方式来响应优化的进展情况。\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "f849cce9",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:24:50.630736Z",
"iopub.status.busy": "2023-08-18T07:24:50.630110Z",
"iopub.status.idle": "2023-08-18T07:24:50.636043Z",
"shell.execute_reply": "2023-08-18T07:24:50.635027Z"
},
"origin_pos": 12,
"tab": [
"pytorch"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"learning rate is now 0.10\n"
]
}
],
"source": [
"lr = 0.1\n",
"trainer.param_groups[0][\"lr\"] = lr\n",
"print(f'learning rate is now {trainer.param_groups[0][\"lr\"]:.2f}')"
]
},
{
"cell_type": "markdown",
"id": "4f8fbbe5",
"metadata": {
"origin_pos": 15
},
"source": [
"更通常而言，我们应该定义一个调度器。\n",
"当调用更新次数时，它将返回学习率的适当值。\n",
"让我们定义一个简单的方法，将学习率设置为$\\eta = \\eta_0 (t + 1)^{-\\frac{1}{2}}$。\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "082e8fdc",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:24:50.640033Z",
"iopub.status.busy": "2023-08-18T07:24:50.639295Z",
"iopub.status.idle": "2023-08-18T07:24:50.644640Z",
"shell.execute_reply": "2023-08-18T07:24:50.643726Z"
},
"origin_pos": 16,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"class SquareRootScheduler:\n",
" def __init__(self, lr=0.1):\n",
" self.lr = lr\n",
"\n",
" def __call__(self, num_update):\n",
" return self.lr * pow(num_update + 1.0, -0.5)"
]
},
{
"cell_type": "markdown",
"id": "555add43",
"metadata": {
"origin_pos": 17
},
"source": [
"让我们在一系列值上绘制它的行为。\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "80c65d0e",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:24:50.648321Z",
"iopub.status.busy": "2023-08-18T07:24:50.647670Z",
"iopub.status.idle": "2023-08-18T07:24:50.813569Z",
"shell.execute_reply": "2023-08-18T07:24:50.812039Z"
},
"origin_pos": 18,
"tab": [
"pytorch"
]
},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"scheduler = SquareRootScheduler(lr=0.1)\n",
"d2l.plot(torch.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])"
]
},
{
"cell_type": "markdown",
"id": "8f51d518",
"metadata": {
"origin_pos": 19
},
"source": [
"现在让我们来看看这对在Fashion-MNIST数据集上的训练有何影响。\n",
"我们只是提供调度器作为训练算法的额外参数。\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "97efd99f",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:24:50.818216Z",
"iopub.status.busy": "2023-08-18T07:24:50.817433Z",
"iopub.status.idle": "2023-08-18T07:26:48.861761Z",
"shell.execute_reply": "2023-08-18T07:26:48.860789Z"
},
"origin_pos": 21,
"tab": [
"pytorch"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"train loss 0.270, train acc 0.901, test acc 0.876\n"
]
},
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"net = net_fn()\n",
"trainer = torch.optim.SGD(net.parameters(), lr)\n",
"train(net, train_iter, test_iter, num_epochs, loss, trainer, device,\n",
" scheduler)"
]
},
{
"cell_type": "markdown",
"id": "cf2f8f37",
"metadata": {
"origin_pos": 24
},
"source": [
"这比以前好一些：曲线比以前更加平滑，并且过拟合更小了。\n",
"遗憾的是，关于为什么在理论上某些策略会导致较轻的过拟合，有一些观点认为，较小的步长将导致参数更接近零，因此更简单。\n",
"但是，这并不能完全解释这种现象，因为我们并没有真正地提前停止，而只是轻柔地降低了学习率。\n",
"\n",
"## 策略\n",
"\n",
"虽然我们不可能涵盖所有类型的学习率调度器，但我们会尝试在下面简要概述常用的策略：多项式衰减和分段常数表。\n",
"此外，余弦学习率调度在实践中的一些问题上运行效果很好。\n",
"在某些问题上，最好在使用较高的学习率之前预热优化器。\n",
"\n",
"### 单因子调度器\n",
"\n",
"多项式衰减的一种替代方案是乘法衰减，即$\\eta_{t+1} \\leftarrow \\eta_t \\cdot \\alpha$其中$\\alpha \\in (0, 1)$。\n",
"为了防止学习率衰减到一个合理的下界之下，\n",
"更新方程经常修改为$\\eta_{t+1} \\leftarrow \\mathop{\\mathrm{max}}(\\eta_{\\mathrm{min}}, \\eta_t \\cdot \\alpha)$。\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "1cb0ffae",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:26:48.867074Z",
"iopub.status.busy": "2023-08-18T07:26:48.866476Z",
"iopub.status.idle": "2023-08-18T07:26:49.021313Z",
"shell.execute_reply": "2023-08-18T07:26:49.020038Z"
},
"origin_pos": 25,
"tab": [
"pytorch"
]
},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"class FactorScheduler:\n",
" def __init__(self, factor=1, stop_factor_lr=1e-7, base_lr=0.1):\n",
" self.factor = factor\n",
" self.stop_factor_lr = stop_factor_lr\n",
" self.base_lr = base_lr\n",
"\n",
" def __call__(self, num_update):\n",
" self.base_lr = max(self.stop_factor_lr, self.base_lr * self.factor)\n",
" return self.base_lr\n",
"\n",
"scheduler = FactorScheduler(factor=0.9, stop_factor_lr=1e-2, base_lr=2.0)\n",
"d2l.plot(torch.arange(50), [scheduler(t) for t in range(50)])"
]
},
{
"cell_type": "markdown",
"id": "191f4c5d",
"metadata": {
"origin_pos": 26
},
"source": [
"接下来，我们将使用内置的调度器，但在这里仅解释它们的功能。\n",
"\n",
"### 多因子调度器\n",
"\n",
"训练深度网络的常见策略之一是保持学习率为一组分段的常量，并且不时地按给定的参数对学习率做乘法衰减。\n",
"具体地说，给定一组降低学习率的时间点，例如$s = \\{5, 10, 20\\}$，\n",
"每当$t \\in s$时，降低$\\eta_{t+1} \\leftarrow \\eta_t \\cdot \\alpha$。\n",
"假设每步中的值减半，我们可以按如下方式实现这一点。\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "5c235d55",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:26:49.025730Z",
"iopub.status.busy": "2023-08-18T07:26:49.024933Z",
"iopub.status.idle": "2023-08-18T07:26:49.204184Z",
"shell.execute_reply": "2023-08-18T07:26:49.203112Z"
},
"origin_pos": 28,
"tab": [
"pytorch"
]
},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"net = net_fn()\n",
"trainer = torch.optim.SGD(net.parameters(), lr=0.5)\n",
"scheduler = lr_scheduler.MultiStepLR(trainer, milestones=[15, 30], gamma=0.5)\n",
"\n",
"def get_lr(trainer, scheduler):\n",
" lr = scheduler.get_last_lr()[0]\n",
" trainer.step()\n",
" scheduler.step()\n",
" return lr\n",
"\n",
"d2l.plot(torch.arange(num_epochs), [get_lr(trainer, scheduler)\n",
" for t in range(num_epochs)])"
]
},
{
"cell_type": "markdown",
"id": "e80a8605",
"metadata": {
"origin_pos": 31
},
"source": [
"这种分段恒定学习率调度背后的直觉是，让优化持续进行，直到权重向量的分布达到一个驻点。\n",
"此时，我们才将学习率降低，以获得更高质量的代理来达到一个良好的局部最小值。\n",
"下面的例子展示了如何使用这种方法产生更好的解决方案。\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "f999a96a",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:26:49.208130Z",
"iopub.status.busy": "2023-08-18T07:26:49.207506Z",
"iopub.status.idle": "2023-08-18T07:28:47.899463Z",
"shell.execute_reply": "2023-08-18T07:28:47.898543Z"
},
"origin_pos": 33,
"tab": [
"pytorch"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"train loss 0.191, train acc 0.928, test acc 0.889\n"
]
},
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"train(net, train_iter, test_iter, num_epochs, loss, trainer, device,\n",
" scheduler)"
]
},
{
"cell_type": "markdown",
"id": "655df579",
"metadata": {
"origin_pos": 36
},
"source": [
"### 余弦调度器\n",
"\n",
"余弦调度器是 :cite:`Loshchilov.Hutter.2016`提出的一种启发式算法。\n",
"它所依据的观点是：我们可能不想在一开始就太大地降低学习率，而且可能希望最终能用非常小的学习率来“改进”解决方案。\n",
"这产生了一个类似于余弦的调度，函数形式如下所示，学习率的值在$t \\in [0, T]$之间。\n",
"\n",
"$$\\eta_t = \\eta_T + \\frac{\\eta_0 - \\eta_T}{2} \\left(1 + \\cos(\\pi t/T)\\right)$$\n",
"\n",
"这里$\\eta_0$是初始学习率，$\\eta_T$是当$T$时的目标学习率。\n",
"此外，对于$t > T$，我们只需将值固定到$\\eta_T$而不再增加它。\n",
"在下面的示例中，我们设置了最大更新步数$T = 20$。\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "ccd9120f",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:28:47.903646Z",
"iopub.status.busy": "2023-08-18T07:28:47.903033Z",
"iopub.status.idle": "2023-08-18T07:28:48.107251Z",
"shell.execute_reply": "2023-08-18T07:28:48.106198Z"
},
"origin_pos": 38,
"tab": [
"pytorch"
]
},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
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"needs_background": "light"
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"output_type": "display_data"
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"source": [
"class CosineScheduler:\n",
" def __init__(self, max_update, base_lr=0.01, final_lr=0,\n",
" warmup_steps=0, warmup_begin_lr=0):\n",
" self.base_lr_orig = base_lr\n",
" self.max_update = max_update\n",
" self.final_lr = final_lr\n",
" self.warmup_steps = warmup_steps\n",
" self.warmup_begin_lr = warmup_begin_lr\n",
" self.max_steps = self.max_update - self.warmup_steps\n",
"\n",
" def get_warmup_lr(self, epoch):\n",
" increase = (self.base_lr_orig - self.warmup_begin_lr) \\\n",
" * float(epoch) / float(self.warmup_steps)\n",
" return self.warmup_begin_lr + increase\n",
"\n",
" def __call__(self, epoch):\n",
" if epoch < self.warmup_steps:\n",
" return self.get_warmup_lr(epoch)\n",
" if epoch <= self.max_update:\n",
" self.base_lr = self.final_lr + (\n",
" self.base_lr_orig - self.final_lr) * (1 + math.cos(\n",
" math.pi * (epoch - self.warmup_steps) / self.max_steps)) / 2\n",
" return self.base_lr\n",
"\n",
"scheduler = CosineScheduler(max_update=20, base_lr=0.3, final_lr=0.01)\n",
"d2l.plot(torch.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])"
]
},
{
"cell_type": "markdown",
"id": "e732fa0f",
"metadata": {
"origin_pos": 39
},
"source": [
"在计算机视觉的背景下，这个调度方式可能产生改进的结果。\n",
"但请注意，如下所示，这种改进并不一定成立。\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "6f53d237",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:28:48.113142Z",
"iopub.status.busy": "2023-08-18T07:28:48.112226Z",
"iopub.status.idle": "2023-08-18T07:30:43.364866Z",
"shell.execute_reply": "2023-08-18T07:30:43.363967Z"
},
"origin_pos": 41,
"tab": [
"pytorch"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"train loss 0.207, train acc 0.923, test acc 0.892\n"
]
},
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"net = net_fn()\n",
"trainer = torch.optim.SGD(net.parameters(), lr=0.3)\n",
"train(net, train_iter, test_iter, num_epochs, loss, trainer, device,\n",
" scheduler)"
]
},
{
"cell_type": "markdown",
"id": "bc2e52ff",
"metadata": {
"origin_pos": 44
},
"source": [
"### 预热\n",
"\n",
"在某些情况下，初始化参数不足以得到良好的解。\n",
"这对某些高级网络设计来说尤其棘手，可能导致不稳定的优化结果。\n",
"对此，一方面，我们可以选择一个足够小的学习率，\n",
"从而防止一开始发散，然而这样进展太缓慢。\n",
"另一方面，较高的学习率最初就会导致发散。\n",
"\n",
"解决这种困境的一个相当简单的解决方法是使用预热期，在此期间学习率将增加至初始最大值，然后冷却直到优化过程结束。\n",
"为了简单起见，通常使用线性递增。\n",
"这引出了如下表所示的时间表。\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "89ebf1cb",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:30:43.368785Z",
"iopub.status.busy": "2023-08-18T07:30:43.368179Z",
"iopub.status.idle": "2023-08-18T07:30:43.508443Z",
"shell.execute_reply": "2023-08-18T07:30:43.507219Z"
},
"origin_pos": 46,
"tab": [
"pytorch"
]
},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"scheduler = CosineScheduler(20, warmup_steps=5, base_lr=0.3, final_lr=0.01)\n",
"d2l.plot(torch.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])"
]
},
{
"cell_type": "markdown",
"id": "b104d0e4",
"metadata": {
"origin_pos": 47
},
"source": [
"注意，观察前5个迭代轮数的性能，网络最初收敛得更好。\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "f9da4ce3",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:30:43.513191Z",
"iopub.status.busy": "2023-08-18T07:30:43.512099Z",
"iopub.status.idle": "2023-08-18T07:32:34.996401Z",
"shell.execute_reply": "2023-08-18T07:32:34.995507Z"
},
"origin_pos": 49,
"tab": [
"pytorch"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"train loss 0.261, train acc 0.904, test acc 0.878\n"
]
},
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"net = net_fn()\n",
"trainer = torch.optim.SGD(net.parameters(), lr=0.3)\n",
"train(net, train_iter, test_iter, num_epochs, loss, trainer, device,\n",
" scheduler)"
]
},
{
"cell_type": "markdown",
"id": "dcf78d30",
"metadata": {
"origin_pos": 52
},
"source": [
"预热可以应用于任何调度器，而不仅仅是余弦。\n",
"有关学习率调度的更多实验和更详细讨论，请参阅 :cite:`Gotmare.Keskar.Xiong.ea.2018`。\n",
"其中，这篇论文的点睛之笔的发现：预热阶段限制了非常深的网络中参数的发散程度 。\n",
"这在直觉上是有道理的：在网络中那些一开始花费最多时间取得进展的部分，随机初始化会产生巨大的发散。\n",
"\n",
"## 小结\n",
"\n",
"* 在训练期间逐步降低学习率可以提高准确性，并且减少模型的过拟合。\n",
"* 在实验中，每当进展趋于稳定时就降低学习率，这是很有效的。从本质上说，这可以确保我们有效地收敛到一个适当的解，也只有这样才能通过降低学习率来减小参数的固有方差。\n",
"* 余弦调度器在某些计算机视觉问题中很受欢迎。\n",
"* 优化之前的预热期可以防止发散。\n",
"* 优化在深度学习中有多种用途。对于同样的训练误差而言，选择不同的优化算法和学习率调度，除了最大限度地减少训练时间，可以导致测试集上不同的泛化和过拟合量。\n",
"\n",
"## 练习\n",
"\n",
"1. 试验给定固定学习率的优化行为。这种情况下可以获得的最佳模型是什么？\n",
"1. 如果改变学习率下降的指数，收敛性会如何改变？在实验中方便起见，使用`PolyScheduler`。\n",
"1. 将余弦调度器应用于大型计算机视觉问题，例如训练ImageNet数据集。与其他调度器相比，它如何影响性能？\n",
"1. 预热应该持续多长时间？\n",
"1. 可以试着把优化和采样联系起来吗？首先，在随机梯度朗之万动力学上使用 :cite:`Welling.Teh.2011`的结果。\n"
]
},
{
"cell_type": "markdown",
"id": "d09d87dd",
"metadata": {
"origin_pos": 54,
"tab": [
"pytorch"
]
},
"source": [
"[Discussions](https://discuss.d2l.ai/t/4334)\n"
]
}
],
"metadata": {
"language_info": {
"name": "python"
},
"required_libs": []
},
"nbformat": 4,
"nbformat_minor": 5
}