LearningRateScheduling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "13b6200e",
   "metadata": {},
   "source": [
    "python3  \n",
    "Create Date: 2023-04-05  \n",
    "Author: Scc_hy  \n",
    "Func: Learning Rate Scheduling  \n",
    "Reference: https://d2l.ai/chapter_optimization/lr-scheduler.html  \n",
    "===============================================================================\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e36cd835",
   "metadata": {},
   "source": [
    "# 加载包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8951339f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "from tqdm.auto import tqdm\n",
    "import torch\n",
    "from torch import nn\n",
    "from torch.optim import lr_scheduler\n",
    "from torchvision import transforms\n",
    "import torchvision\n",
    "from argparse import Namespace\n",
    "from IPython import display\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib_inline import backend_inline\n",
    "import wandb\n",
    "import os\n",
    "import numpy as np\n",
    "import random\n",
    "os.environ[\"KMP_DUPLICATE_LIB_OK\"]=\"TRUE\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed72ce1d",
   "metadata": {},
   "source": [
    "# 重要函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c475b19",
   "metadata": {},
   "source": [
    "## 记录训练log 及 随机种子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ec5863a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set env random_seed = 2023\n"
     ]
    }
   ],
   "source": [
    "class Accumulator:\n",
    "    \"\"\"For accumulating sums over `n` variables.\"\"\"\n",
    "    def __init__(self, n):\n",
    "        \"\"\"Defined in :numref:`sec_utils`\"\"\"\n",
    "        self.data = [0.0] * n\n",
    "\n",
    "    def add(self, *args):\n",
    "        self.data = [a + float(b) for a, b in zip(self.data, args)]\n",
    "\n",
    "    def reset(self):\n",
    "        self.data = [0.0] * len(self.data)\n",
    "\n",
    "    def __getitem__(self, idx):\n",
    "        return self.data[idx]\n",
    "\n",
    "\n",
    "# 设置全局的随机种子\n",
    "def all_seed(seed = 6666):\n",
    "    \"\"\"\n",
    "    设置随机种子\n",
    "    \"\"\"\n",
    "    np.random.seed(seed)\n",
    "    random.seed(seed)\n",
    "    # CPU\n",
    "    torch.manual_seed(seed) \n",
    "    # GPU\n",
    "    if torch.cuda.is_available():\n",
    "        torch.cuda.manual_seed_all(seed)\n",
    "        torch.cuda.manual_seed(seed) \n",
    "    # python 全局\n",
    "    os.environ['PYTHONHASHSEED'] = str(seed) \n",
    "    # cudnn\n",
    "    torch.backends.cudnn.deterministic = True\n",
    "    torch.backends.cudnn.benchmark = False\n",
    "    torch.backends.cudnn.enabled = False\n",
    "    print(f'Set env random_seed = {seed}')\n",
    "\n",
    "    \n",
    "all_seed(2023)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "163a3b8b",
   "metadata": {},
   "source": [
    "## 绘制损失图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3db21d61",
   "metadata": {},
   "outputs": [],
   "source": [
    "def use_svg_display():\n",
    "    \"\"\"Use the svg format to display a plot in Jupyter.\n",
    "    Defined in :numref:`sec_calculus`\"\"\"\n",
    "    backend_inline.set_matplotlib_formats('svg')\n",
    "\n",
    "\n",
    "def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):\n",
    "    \"\"\"Set the axes for matplotlib.\n",
    "    Defined in :numref:`sec_calculus`\"\"\"\n",
    "    axes.set_xlabel(xlabel), axes.set_ylabel(ylabel)\n",
    "    axes.set_xscale(xscale), axes.set_yscale(yscale)\n",
    "    axes.set_xlim(xlim),     axes.set_ylim(ylim)\n",
    "    if legend:\n",
    "        axes.legend(legend)\n",
    "    axes.grid()\n",
    "    \n",
    "\n",
    "class Animator:\n",
    "    \"\"\"For plotting data in animation.\"\"\"\n",
    "    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,\n",
    "                 ylim=None, xscale='linear', yscale='linear',\n",
    "                 fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,\n",
    "                 figsize=(3.5, 2.5)):\n",
    "        \"\"\"Defined in :numref:`sec_utils`\"\"\"\n",
    "        # Incrementally plot multiple lines\n",
    "        if legend is None:\n",
    "            legend = []\n",
    "        use_svg_display()\n",
    "        self.fig, self.axes = plt.subplots(nrows, ncols, figsize=figsize)\n",
    "        if nrows * ncols == 1:\n",
    "            self.axes = [self.axes, ]\n",
    "        # Use a lambda function to capture arguments\n",
    "        self.config_axes = lambda: set_axes(\n",
    "            self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)\n",
    "        self.X, self.Y, self.fmts = None, None, fmts\n",
    "\n",
    "    def add(self, x, y, clear_flag=True):\n",
    "        # Add multiple data points into the figure\n",
    "        if not hasattr(y, \"__len__\"):\n",
    "            y = [y]\n",
    "        n = len(y)\n",
    "        if not hasattr(x, \"__len__\"):\n",
    "            x = [x] * n\n",
    "        if not self.X:\n",
    "            self.X = [[] for _ in range(n)]\n",
    "        if not self.Y:\n",
    "            self.Y = [[] for _ in range(n)]\n",
    "        for i, (a, b) in enumerate(zip(x, y)):\n",
    "            if a is not None and b is not None:\n",
    "                self.X[i].append(a)\n",
    "                self.Y[i].append(b)\n",
    "        self.axes[0].cla()\n",
    "        for x, y, fmt in zip(self.X, self.Y, self.fmts):\n",
    "            self.axes[0].plot(x, y, fmt)\n",
    "        self.config_axes()\n",
    "        display.display(self.fig)\n",
    "        if clear_flag:\n",
    "            display.clear_output(wait=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67b00fbf",
   "metadata": {},
   "source": [
    "## 加载数据与网络"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4c48f3f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gpu(i=0):\n",
    "    \"\"\"获取GPU设备\"\"\"\n",
    "    return torch.device(f'cuda:{i}')\n",
    "\n",
    "\n",
    "def num_gpus():\n",
    "    \"\"\"获取GPU个数\"\"\"\n",
    "    return torch.cuda.device_count()\n",
    "\n",
    "\n",
    "def try_gpu(i=0):\n",
    "    \"\"\"\n",
    "    尝试并获取第i个GPU\n",
    "    \"\"\"\n",
    "    if num_gpus() >= i + 1:\n",
    "        return gpu(i)\n",
    "    return torch.device('cpu')\n",
    "\n",
    "\n",
    "def load_data_fashion_mnist(batch_size, resize=None):\n",
    "    \"\"\"Download the Fashion-MNIST dataset and then load it into memory.\n",
    "    Defined in :numref:`sec_utils`\"\"\"\n",
    "    trans = [transforms.ToTensor()]\n",
    "    if resize:\n",
    "        trans.insert(0, transforms.Resize(resize))\n",
    "    trans = transforms.Compose(trans)\n",
    "    mnist_train = torchvision.datasets.FashionMNIST(\n",
    "        root=\"./data\", train=True, transform=trans, download=True)\n",
    "    mnist_test = torchvision.datasets.FashionMNIST(\n",
    "        root=\"./data\", train=False, transform=trans, download=True)\n",
    "    return (torch.utils.data.DataLoader(mnist_train, batch_size, shuffle=True, num_workers=4),\n",
    "            torch.utils.data.DataLoader(mnist_test, batch_size, shuffle=False, num_workers=4))\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"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b9e2e06",
   "metadata": {},
   "source": [
    "##  训练测试评估"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d0f88e05",
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy(y_hat, y):\n",
    "    \"\"\"Compute the number of correct predictions.\n",
    "    Defined in :numref:`sec_utils`\"\"\"\n",
    "    argmax = lambda x, *args, **kwargs: x.argmax(*args, **kwargs)\n",
    "    astype = lambda x, *args, **kwargs: x.type(*args, **kwargs)\n",
    "    reduce_sum = lambda x, *args, **kwargs: x.sum(*args, **kwargs)\n",
    "    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:\n",
    "        y_hat = argmax(y_hat, axis=1)\n",
    "    cmp = astype(y_hat, y.dtype) == y\n",
    "    return float(reduce_sum(astype(cmp, y.dtype)))\n",
    "\n",
    "\n",
    "def evaluate_accuracy_gpu(net, data_iter, device=None):\n",
    "    \"\"\"Compute the accuracy for a model on a dataset using a GPU.\n",
    "    Defined in :numref:`sec_utils`\"\"\"\n",
    "    size = lambda x, *args, **kwargs: x.numel(*args, **kwargs)\n",
    "    if isinstance(net, nn.Module):\n",
    "        net.eval()  # Set the model to evaluation mode\n",
    "        if not device:\n",
    "            device = next(iter(net.parameters())).device\n",
    "    # No. of correct predictions, no. of predictions\n",
    "    metric = Accumulator(2)\n",
    "    with torch.no_grad():\n",
    "        for X, y in data_iter:\n",
    "            if isinstance(X, list):\n",
    "                X = [x.to(device) for x in X]\n",
    "            else:\n",
    "                X = X.to(device)\n",
    "            y = y.to(device)\n",
    "            metric.add(accuracy(net(X), y), size(y))\n",
    "    return metric[0] / metric[1]\n",
    "\n",
    "\n",
    "def train(model, train_iter, test_iter, config, scheduler=None):\n",
    "    device = config.device\n",
    "    loss = config.loss\n",
    "    opt = config.opt\n",
    "    num_epochs = config.num_epochs\n",
    "    model.to(device)\n",
    "    animator = Animator(xlabel='epoch', xlim=[0, num_epochs],\n",
    "                            legend=['train loss', 'train acc', 'test acc'])\n",
    "    \n",
    "    ep_total_steps = len(train_iter)\n",
    "    for ep in range(num_epochs):\n",
    "        tq_bar = tqdm(enumerate(train_iter))\n",
    "        tq_bar.set_description(f'[ Epoch {ep+1}/{num_epochs} ]')\n",
    "        # train_loss, train_acc, num_examples\n",
    "        metric = Accumulator(3)\n",
    "        for idx, (X, y) in tq_bar:\n",
    "            final_flag = (ep_total_steps == idx + 1) & (num_epochs == ep + 1)\n",
    "            model.train()\n",
    "            opt.zero_grad()\n",
    "            X, y = X.to(device), y.to(device)\n",
    "            y_hat = model(X)\n",
    "            l = loss(y_hat, y)\n",
    "            l.backward()\n",
    "            opt.step()\n",
    "            with torch.no_grad():\n",
    "                metric.add(l * X.shape[0], accuracy(y_hat, y), X.shape[0])\n",
    "            train_loss = metric[0] / metric[2]\n",
    "            train_acc = metric[1] / metric[2]\n",
    "            tq_bar.set_postfix({\n",
    "                \"loss\" : f\"{train_loss:.3f}\",\n",
    "                \"acc\" : f\"{train_acc:.3f}\",\n",
    "            })\n",
    "            if (idx + 1) % 50 == 0:\n",
    "                animator.add(ep + idx / len(train_iter), (train_loss, train_acc, None), clear_flag=not final_flag)\n",
    "\n",
    "        test_acc = evaluate_accuracy_gpu(model, test_iter)\n",
    "        animator.add(ep+1, (None, None, test_acc), clear_flag=not final_flag)\n",
    "        if scheduler:\n",
    "            if scheduler.__module__ == lr_scheduler.__name__:\n",
    "                # 使用 PyTorch In-Built scheduler\n",
    "                scheduler.step()\n",
    "            else:\n",
    "                # 使用自定义 scheduler\n",
    "                for param_group in opt.param_groups:\n",
    "                    param_group['lr'] = scheduler(ep) \n",
    "\n",
    "    print(f'train loss {train_loss:.3f}, train acc {train_acc:.3f}, '\n",
    "          f'test acc {test_acc:.3f}')\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "def test(train_iter, test_iter, scheduler=None):\n",
    "    net = net_fn()\n",
    "    cfg = Namespace(\n",
    "        device=try_gpu(),\n",
    "        loss=nn.CrossEntropyLoss(),\n",
    "        lr=0.3, \n",
    "        num_epochs=10,\n",
    "        opt=torch.optim.SGD(net.parameters(), lr=0.3)\n",
    "    )\n",
    "    train(net, train_iter, test_iter, cfg, scheduler)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16eb3d3c",
   "metadata": {},
   "source": [
    "# 可视化网络"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "96df0fec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 0.0144, -0.0174,  0.0073,  0.0854,  0.0385,  0.0430, -0.0826, -0.1383,\n",
      "         -0.1272,  0.1016]], grad_fn=<AddmmBackward0>)\n",
      "============== Diagnostic Run torch.onnx.export version 2.0.0+cpu ==============\n",
      "verbose: False, log level: Level.ERROR\n",
      "======================= 0 NONE 0 NOTE 0 WARNING 0 ERROR ========================\n",
      "\n",
      "Serving 'tmp.onnx' at http://localhost:8080\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "('localhost', 8080)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 可视化网络\n",
    "from torch import onnx\n",
    "import netron\n",
    "\n",
    "d = torch.rand(1, 1, 28, 28)\n",
    "m = net_fn()\n",
    "o = m(d)\n",
    "print(o)\n",
    "onnx_path = \"tmp.onnx\"\n",
    "onnx.export(m, d, onnx_path)\n",
    "netron.start(onnx_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "13324829",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stopping http://localhost:8080\n"
     ]
    }
   ],
   "source": [
    "netron.stop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6c68f48b",
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from torchviz import make_dot\n",
    "g = make_dot(o)\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47220df4",
   "metadata": {},
   "source": [
    "# 数据加载"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e6f99fb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 256\n",
    "train_iter, test_iter = load_data_fashion_mnist(batch_size=batch_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7315ffa9",
   "metadata": {},
   "source": [
    "# 学习率时间表试验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "61629530",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_lr(scheduler):\n",
    "    lr = scheduler.get_last_lr()[0]\n",
    "    scheduler.optimizer.step()\n",
    "    scheduler.step()\n",
    "    return lr\n",
    "\n",
    "def plot_scheduler(scheduler, num_epochs=10):\n",
    "    s = scheduler.__class__.__name__\n",
    "    if scheduler.__module__ == lr_scheduler.__name__:\n",
    "        print('pytorch build lr_scheduler')\n",
    "        plot_y = [get_lr(scheduler) for _ in range(num_epochs)]\n",
    "    else:\n",
    "        plot_y = [scheduler(t) for t in range(num_epochs)]\n",
    "\n",
    "    plt.title(f'train with learning rate scheduler: {s}')\n",
    "    plt.plot(torch.arange(num_epochs), plot_y)\n",
    "    plt.xlabel('num_epochs')\n",
    "    plt.ylabel('learning_rate')\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6715889e",
   "metadata": {},
   "source": [
    "## 1- 无时间表试验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "aa81d108",
   "metadata": {},
   "outputs": [
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   "source": [
    "## 2- SquareRootScheduler\n",
    "\n",
    "更新公式：\n",
    "$$\\alpha =\\alpha*\\sqrt{num\\_update + 1}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "76da00db",
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   "source": [
    "class SquareRootScheduler:\n",
    "    \"\"\"\n",
    "    使用均方根scheduler\n",
    "    每一个epoch更新一次\n",
    "    \"\"\"\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)\n",
    "\n",
    "scheduler = SquareRootScheduler(lr=0.1)\n",
    "plot_scheduler(scheduler)"
   ]
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   "id": "b5e7e7ef",
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    "test(train_iter, test_iter, scheduler)"
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  {
   "cell_type": "markdown",
   "id": "65155bd4",
   "metadata": {},
   "source": [
    "## 3- FactorScheduler\n",
    "\n",
    "$\\eta_{t+1} \\leftarrow \\mathop{\\mathrm{max}}(\\eta_{\\mathrm{min}}, \\eta_t \\cdot \\alpha)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fa62f89e",
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    "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=0.8, stop_factor_lr=1e-2, base_lr=0.6)\n",
    "plot_scheduler(scheduler)"
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    "## 4- Multi Factor Scheduler\n",
    "\n",
    "保持学习率分段恒定，并每隔一段时间将其降低一个给定的量。也就是说，给定一组何时降低速率的时间比如$ (s = \\{3, 8\\} )$  \n",
    "$decrease (\\eta_{t+1} \\leftarrow \\eta_t \\cdot \\alpha) \\ \\   t \\in s$  "
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   "id": "4e5cbf69",
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     "text": [
      "pytorch build lr_scheduler\n"
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   "source": [
    "net = net_fn()\n",
    "trainer = torch.optim.SGD(net.parameters(), lr=0.5)\n",
    "scheduler = lr_scheduler.MultiStepLR(trainer, milestones=[3, 8], gamma=0.5)\n",
    "\n",
    "plot_scheduler(scheduler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "17ffdf6f",
   "metadata": {},
   "outputs": [
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       "<Figure size 252x180 with 1 Axes>"
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   "source": [
    "test(train_iter, test_iter, scheduler)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "## 5- CosineScheduler\n",
    "\n",
    "Loshchilov和Hutter提出了一个相当令人困惑的启发式方法。它依赖于这样一种观察，即我们可能<font color=darkred>不想在一开始就大幅降低学习率</font>，此外，我们<font color=darkred>可能希望在最后使用非常小的学习率</font>来“完善”解决方案。这导致了一个类似余弦的时间表，具有以下函数形式，用于范围内的学习率$t \\in [0, T]$\n",
    "\n",
    "$$\\eta_t = \\eta_T + \\frac{\\eta_0 - \\eta_T}{2} \\left(1 + \\cos(\\frac{\\pi t}{T})\\right)$$\n",
    "\n",
    "注：\n",
    "- $\\eta_T$: 为最终的学习率\n",
    "- $\\eta_0$: 为最开始的学习率"
   ]
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  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "43c9ecc9",
   "metadata": {},
   "outputs": [],
   "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, step):\n",
    "        increase = (self.base_lr_orig - self.warmup_begin_lr) \\\n",
    "                       * float(step) / float(self.warmup_steps)\n",
    "        return self.warmup_begin_lr + increase\n",
    "\n",
    "    def __call__(self, step):\n",
    "        if step < self.warmup_steps:\n",
    "            return self.get_warmup_lr(step)\n",
    "        if step <= self.max_update:\n",
    "            self.base_lr = self.final_lr + (\n",
    "                self.base_lr_orig - self.final_lr) * (1 + math.cos(\n",
    "                math.pi * (step - self.warmup_steps) / self.max_steps)) / 2\n",
    "        return self.base_lr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c6c3c7bc",
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   "outputs": [
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     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "scheduler = CosineScheduler(max_update=10, base_lr=0.2, final_lr=0.02)\n",
    "plot_scheduler(scheduler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f40453a3",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
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     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test(train_iter, test_iter, scheduler)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24b93241",
   "metadata": {},
   "source": [
    "## 6- Warmup\n",
    "\n",
    "在某些情况下，初始化参数不足以保证良好的解决方案。对于一些先进的网络设计来说，这尤其是一个问题（`Transformer的训练常用该方法`），可能会导致不稳定的优化问题。\n",
    "我们可以通过选择一个足够小的学习率来解决这个问题，以防止一开始就出现分歧。不幸的是，这意味着进展缓慢。相反，学习率高最初会导致差异。\n",
    "\n",
    "对于这种困境，一个相当简单的解决方案是使用一个预热期，在此期间学习速率增加到其初始最大值，并冷却速率直到优化过程结束。为了简单起见，通常使用线性增加来实现这一目的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cd8cf8f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scheduler = CosineScheduler(max_update=10, warmup_steps=3, base_lr=0.2, final_lr=0.02)\n",
    "plot_scheduler(scheduler, 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "60fd0051",
   "metadata": {},
   "outputs": [
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