7.6. RMSProp算法.ipynb

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        "<a href=\"https://colab.research.google.com/github/chongzicbo/Dive-into-Deep-Learning-tf.keras/blob/master/7.6.%20RMSProp%E7%AE%97%E6%B3%95.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "##7.6. RMSProp算法\n",
        "我们在“AdaGrad算法”一节中提到，因为调整学习率时分母上的变量 $s_t$ 一直在累加按元素平方的小批量随机梯度，所以目标函数自变量每个元素的学习率在迭代过程中一直在降低（或不变）。因此，当学习率在迭代早期降得较快且当前解依然不佳时，AdaGrad算法在迭代后期由于学习率过小，可能较难找到一个有用的解。为了解决这一问题，RMSProp算法对AdaGrad算法做了一点小小的修改。该算法源自Coursera上的一门课程，即“机器学习的神经网络” [1]。\n",
        "\n",
        "###7.6.1. 算法\n",
        "我们在“动量法”一节里介绍过指数加权移动平均。不同于AdaGrad算法里状态变量 $s_t$ 是截至时间步 $t$ 所有小批量随机梯度 $g_t$ 按元素平方和，RMSProp算法将这些梯度按元素平方做指数加权移动平均。具体来说，给定超参数$0 \\leq \\gamma < 1$，RMSProp算法在时间步 $t>0$ 计算\n",
        "$$\n",
        "\\boldsymbol{s}_t \\leftarrow \\gamma \\boldsymbol{s}_{t-1} + (1 - \\gamma) \\boldsymbol{g}_t \\odot \\boldsymbol{g}_t.\n",
        "$$\n",
        "和AdaGrad算法一样，RMSProp算法将目标函数自变量中每个元素的学习率通过按元素运算重新调整，然后更新自变量\n",
        "$$\n",
        "\\boldsymbol{x}_t \\leftarrow \\boldsymbol{x}_{t-1} - \\frac{\\eta}{\\sqrt{\\boldsymbol{s}_t + \\epsilon}} \\odot \\boldsymbol{g}_t,\n",
        "$$\n",
        "其中 $\\eta$ 是学习率， $\\epsilon$是为了维持数值稳定性而添加的常数，如 $10^{-6}$ 。因为RMSProp算法的状态变量 $s_t$ 是对平方项$\\boldsymbol{g}_t \\odot \\boldsymbol{g}_t$的指数加权移动平均，所以可以看作是最近$1/(1-\\gamma)$个时间步的小批量随机梯度平方项的加权平均。如此一来，自变量每个元素的学习率在迭代过程中就不再一直降低（或不变）。\n",
        "\n",
        "照例，让我们先观察RMSProp算法对目标函数$f(\\boldsymbol{x})=0.1x_1^2+2x_2^2$中自变量的迭代轨迹。回忆在“AdaGrad算法”一节使用的学习率为0.4的AdaGrad算法，自变量在迭代后期的移动幅度较小。但在同样的学习率下，RMSProp算法可以更快逼近最优解。"
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          "base_uri": "https://localhost:8080/",
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        }
      },
      "source": [
        "%matplotlib inline\n",
        "import math\n",
        "import tensorflow as tf\n",
        "import numpy as np\n",
        "from IPython import display\n",
        "import matplotlib.pyplot as plt\n",
        "from tensorflow import keras\n",
        "from tensorflow.keras import losses\n",
        "from tensorflow.data import Dataset\n",
        "import time"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
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              "<p style=\"color: red;\">\n",
              "The default version of TensorFlow in Colab will soon switch to TensorFlow 2.x.<br>\n",
              "We recommend you <a href=\"https://www.tensorflow.org/guide/migrate\" target=\"_blank\">upgrade</a> now \n",
              "or ensure your notebook will continue to use TensorFlow 1.x via the <code>%tensorflow_version 1.x</code> magic:\n",
              "<a href=\"https://colab.research.google.com/notebooks/tensorflow_version.ipynb\" target=\"_blank\">more info</a>.</p>\n"
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        "colab_type": "code",
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      "source": [
        "tf.enable_eager_execution()"
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      "source": [
        "###7.6.2. 从零开始实现\n",
        "接下来按照RMSProp算法中的公式实现该算法。"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0gFuh-zcZRHg",
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      "source": [
        "def rmsprop_2d(x1,x2,s1,s2):\n",
        "  g1,g2,eps=0.2*x1,4*x2,1e-6\n",
        "  s1=gamma*s1+(1-gamma)*g1**2\n",
        "  s2=gamma*s2+(1-gamma)*g2**2\n",
        "  x1-=eta /math.sqrt(s1+eps)*g1\n",
        "  x2-=eta/math.sqrt(s2+eps)*g2\n",
        "  return x1,x2,s1,s2\n",
        "\n",
        "def f_2d(x1,x2):\n",
        "  return 0.1*x1**2+2*x2**2  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
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      "source": [
        "def show_trace_2d(f,results):\n",
        "  plt.plot(*zip(*results),'-o',color='#ff7f0e')\n",
        "  x1,x2=np.meshgrid(np.arange(-5.5,1.0,0.1),np.arange(-3.0,1.0,0.1))\n",
        "  plt.contour(x1,x2,f(x1,x2),colors='#1f77b4')\n",
        "  plt.xlabel('x1')\n",
        "  plt.ylabel('x2')\n",
        "\n",
        "def train_2d(trainer):\n",
        "  x1,x2,s1,s2=-5,-2,0,0\n",
        "  results=[(x1,x2)]\n",
        "  for i in range(20):\n",
        "    x1,x2,s1,s2=trainer(x1,x2,s1,s2)\n",
        "    results.append((x1,x2))\n",
        "  print('epoch %d,x1 %f,x2 %f'%(i+1,x1,x2))\n",
        "  return results  "
      ],
      "execution_count": 0,
      "outputs": []
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      },
      "source": [
        "eta,gamma=0.4,0.9\n",
        "show_trace_2d(f_2d,train_2d(rmsprop_2d))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch 20,x1 -0.010599,x2 0.000000\n"
          ],
          "name": "stdout"
        },
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GElne/dUnGExm+dmH3sD65nCVeifMGeNFWVUWuLxQSNni8A4zrbT+EhEHYUkz2RrForRC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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4YybqCEAiTwQ",
        "colab_type": "code",
        "outputId": "0d29678b-00cf-441b-ae01-c180af380d4c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 127
        }
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')\n",
        "\n",
        "def get_data_ch7():\n",
        "  data=np.genfromtxt('/content/drive/My Drive/data/d2l-zh-tensoflow/airfoil_self_noise.dat',delimiter='\\t')\n",
        "  data=(data-data.mean(axis=0))/data.std(axis=0)\n",
        "  return tf.constant(data[:1500,:-1]),tf.constant(data[:1500,-1])\n",
        "\n",
        "features,labels=get_data_ch7()  "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Go to this URL in a browser: https://accounts.google.com/o/oauth2/auth?client_id=947318989803-6bn6qk8qdgf4n4g3pfee6491hc0brc4i.apps.googleusercontent.com&redirect_uri=urn%3aietf%3awg%3aoauth%3a2.0%3aoob&response_type=code&scope=email%20https%3a%2f%2fwww.googleapis.com%2fauth%2fdocs.test%20https%3a%2f%2fwww.googleapis.com%2fauth%2fdrive%20https%3a%2f%2fwww.googleapis.com%2fauth%2fdrive.photos.readonly%20https%3a%2f%2fwww.googleapis.com%2fauth%2fpeopleapi.readonly\n",
            "\n",
            "Enter your authorization code:\n",
            "··········\n",
            "Mounted at /content/drive\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tuo4vuE3ie04",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def init_rmsprop_states():\n",
        "  s_w=tf.Variable(tf.zeros(shape=(features.shape[1],1),dtype=tf.double))\n",
        "  s_b=tf.Variable(tf.zeros(1,dtype=tf.double))\n",
        "  return (s_w,s_b)\n",
        "\n",
        "def rmsprop(params,states,hyperparams,loss,t):\n",
        "  gamma,eps=hyperparams['gamma'],1e-6\n",
        "  for p,s in zip(params,states):\n",
        "    dl_dp=t.gradient(loss,p)\n",
        "    s.assign(gamma*s+(1-gamma)*tf.square(dl_dp))\n",
        "    p.assign_sub(hyperparams['lr']*dl_dp/tf.sqrt(s+eps))  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3YfyVXkRjwzo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def train_ch7(trainer_fn,states,hyperparams,features,labels,batch_size=10,num_epochs=2):\n",
        "  net,loss=linreg,squared_loss\n",
        "  w=tf.Variable(tf.random.normal(stddev=0.01,shape=(features.shape[1],1),dtype=tf.double))\n",
        "  b=tf.Variable(tf.zeros(1,dtype=tf.double))\n",
        "\n",
        "  def eval_loss():\n",
        "    return tf.reduce_mean(loss(net(features,w,b),labels)).numpy()\n",
        "\n",
        "  ls=[eval_loss()]\n",
        "\n",
        "  data_iter=Dataset.from_tensor_slices((features,labels)).shuffle(buffer_size=1000).batch(batch_size)\n",
        "\n",
        "  for _ in range(num_epochs):\n",
        "    start=time.time()\n",
        "    for batch_i,(X,y) in enumerate(data_iter):\n",
        "      with tf.GradientTape(persistent=True) as t:\n",
        "        t.watch([w,b])\n",
        "        l=tf.reduce_mean(loss(net(X,w,b),y)) #使用平均损失\n",
        "\n",
        "      trainer_fn([w,b],states,hyperparams,l,t) #迭代模型参数\n",
        "\n",
        "      if(batch_i+1)*batch_size %100==0:\n",
        "        ls.append(eval_loss()) #每100个样本记录下当前训练误差\n",
        "  # 打印结果和作图\n",
        "  print('loss: %f, %f sec per epoch' % (ls[-1], time.time() - start))\n",
        "  set_figsize()\n",
        "  plt.plot(np.linspace(0, num_epochs, len(ls)), ls)\n",
        "  plt.xlabel('epoch')\n",
        "  plt.ylabel('loss')  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yJeuwEUlkJ_9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "\n",
        "def use_svg_display():\n",
        "  #用矢量图显示\n",
        "  display.set_matplotlib_formats('svg')\n",
        "def set_figsize(figsize=(3.5,2.5)):\n",
        "  use_svg_display()\n",
        "  #设置图的尺寸\n",
        "  plt.rcParams['figure.figsize']=figsize\n",
        "  \n",
        "  \n",
        "def linreg(X,w,b):\n",
        "  return tf.matmul(X,w)+b \n",
        "  \n",
        "def squared_loss(y_hat,y):\n",
        "  return (y_hat-tf.reshape(y,shape=y_hat.shape))**2/2  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VEUsB4dRj8Mp",
        "colab_type": "code",
        "outputId": "857e9ca6-c35f-4341-f619-ac8cbb11b30f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "train_ch7(rmsprop,init_rmsprop_states(),{'lr':0.01,'gamma':0.9},features,labels)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "loss: 0.242277, 0.678375 sec per epoch\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 252x180 with 1 Axes>"
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          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IQ-xTPm-oGU-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class LossHistory(keras.callbacks.Callback): \n",
        "  def on_train_begin(self, logs={}): \n",
        "    self.losses = [] \n",
        "    # self.val_losses = [] \n",
        "\n",
        "\n",
        "  def on_batch_end(self, batch, logs={}): \n",
        "    self.losses.append(logs.get('loss')) \n",
        "    # self.val_losses.append(logs.get('val_loss')) "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fgNwSLCinRif",
        "colab_type": "text"
      },
      "source": [
        "###7.6.3. 简洁实现\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5MSfr1MAkFbc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def train_keras_ch7(trainer_name,features,labels,batch_size=10,num_epochs=2):\n",
        "  net=keras.Sequential(keras.layers.Dense(1))\n",
        "  loss=losses.MeanSquaredError()\n",
        "  data_iter=Dataset.from_tensor_slices((features,labels)).shuffle(buffer_size=1000).batch(batch_size)\n",
        "  net.compile(optimizer=trainer_name,loss=loss,metrics=['mse'])\n",
        "  history=net.fit_generator(data_iter,epochs=num_epochs,callbacks=[LossHistory()])\n",
        "  loss_ls=history.history['loss']\n",
        "  set_figsize()\n",
        "  plt.plot(np.linspace(0,num_epochs,len(loss_ls)),loss_ls)\n",
        "  plt.xlabel('epoch')\n",
        "  plt.ylabel('loss')\n",
        "  plt.show()\n",
        "  return history"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FgGhkz7ElPkJ",
        "colab_type": "code",
        "outputId": "761dde1a-8ff2-4fca-bd01-eb204b980f28",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 639
        }
      },
      "source": [
        "train_keras_ch7(keras.optimizers.RMSprop(learning_rate=0.01,rho=0.8),features,labels,batch_size=50,num_epochs=10)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1/10\n",
            "30/30 [==============================] - 0s 13ms/step - loss: 2.0990 - mean_squared_error: 2.3427\n",
            "Epoch 2/10\n",
            "30/30 [==============================] - 0s 10ms/step - loss: 1.1065 - mean_squared_error: 1.2288\n",
            "Epoch 3/10\n",
            "30/30 [==============================] - 0s 11ms/step - loss: 0.6419 - mean_squared_error: 0.7091\n",
            "Epoch 4/10\n",
            "30/30 [==============================] - 0s 11ms/step - loss: 0.5009 - mean_squared_error: 0.5236\n",
            "Epoch 5/10\n",
            "30/30 [==============================] - 0s 11ms/step - loss: 0.4883 - mean_squared_error: 0.5054\n",
            "Epoch 6/10\n",
            "30/30 [==============================] - 0s 10ms/step - loss: 0.4882 - mean_squared_error: 0.5059\n",
            "Epoch 7/10\n",
            "30/30 [==============================] - 0s 11ms/step - loss: 0.4883 - mean_squared_error: 0.5062\n",
            "Epoch 8/10\n",
            "30/30 [==============================] - 0s 10ms/step - loss: 0.4884 - mean_squared_error: 0.5063\n",
            "Epoch 9/10\n",
            "30/30 [==============================] - 0s 11ms/step - loss: 0.4884 - mean_squared_error: 0.5064\n",
            "Epoch 10/10\n",
            "30/30 [==============================] - 0s 10ms/step - loss: 0.4884 - mean_squared_error: 0.5065\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
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          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tensorflow.python.keras.callbacks.History at 0x7fa8039b31d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lk9QF_j3lrLy",
        "colab_type": "text"
      },
      "source": [
        "###7.6.4. 小结\n",
        "* RMSProp算法和AdaGrad算法的不同在于，RMSProp算法使用了小批量随机梯度按元素平方的指数加权移动平均来调整学习率。"
      ]
    }
  ]
}