docs/tutorials/optimizers_conditionalgradient.ipynb

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    "colab": {
      "name": "optimizers_conditionalgradient.ipynb",
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "accelerator": "GPU"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pGUYKbJNWNgj",
        "colab_type": "text"
      },
      "source": [
        "##### Copyright 2019 The TensorFlow Authors."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1PzPJglSWgnW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#@title Licensed under the Apache License, Version 2.0\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b5P4BEg1XYd5",
        "colab_type": "text"
      },
      "source": [
        "# TensorFlow Addons Optimizers: ConditionalGradient\n",
        "\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://www.tensorflow.org/addons/tutorials/optimizers_conditionalgradient\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/addons/blob/master/docs/tutorials/optimizers_conditionalgradient.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/addons/blob/master/docs/tutorials/optimizers_conditionalgradient.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://storage.googleapis.com/tensorflow_docs/addons/docs/tutorials/optimizers_conditionalgradient.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Faj8luWnYNSG",
        "colab_type": "text"
      },
      "source": [
        "# Overview\n",
        "This notebook will demonstrate how to use the Conditional Graident Optimizer from the Addons package."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MrDjqjY6YRYM",
        "colab_type": "text"
      },
      "source": [
        "# ConditionalGradient\n",
        "\n",
        "\n",
        "> Constraining the parameters of a neural network has been shown to be beneficial in training because of the underlying regularization effects.  Often, parameters are constrained via a soft penalty (which never guarantees the constraint satisfaction) or via a projection operation (which is computationally expensive). Conditional gradient (CG) optimizer, on the other hand, enforces the constraints strictly without the need for an expensive projection step. It works by minimizing a linear approximation of the objective within the constraint set. In this notebook, we demonstrate the appliction of Frobenius norm constraint via the CG optimizer on the MNIST dataset. CG is now available as a tensorflow API. More details of the optimizer are available at https://arxiv.org/pdf/1803.06453.pdf\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dooBaYGLYYnn",
        "colab_type": "text"
      },
      "source": [
        "## Setup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qYo0FkL4O7io",
        "colab_type": "code",
        "outputId": "7c40f5df-075a-4d9f-910e-7dff84c46b1f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "try:\n",
        "  %tensorflow_version 2.x\n",
        "except:\n",
        "  pass\n",
        "\n",
        "import tensorflow as tf"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "TensorFlow 2.x selected.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oPbEvhbCih0t",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import tensorflow_addons as tfa\n",
        "from matplotlib import pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kR0PnjrIirpJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Hyperparameters\n",
        "batch_size=64\n",
        "epochs=10"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-x0WBp-IYz7x",
        "colab_type": "text"
      },
      "source": [
        "# Build the Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4KzMDUT0i1QE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "model_1 = tf.keras.Sequential([\n",
        "    tf.keras.layers.Dense(64, input_shape=(784,), activation='relu', name='dense_1'),\n",
        "    tf.keras.layers.Dense(64, activation='relu', name='dense_2'),\n",
        "    tf.keras.layers.Dense(10, activation='softmax', name='predictions'),\n",
        "])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XGADNG3-Y7aa",
        "colab_type": "text"
      },
      "source": [
        "# Prep the Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d6a-kbM_i1b2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "248bd642-2d06-4da5-acbe-b1bf59d335b0"
      },
      "source": [
        "# Load MNIST dataset as NumPy arrays\n",
        "dataset = {}\n",
        "num_validation = 10000\n",
        "(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()\n",
        "\n",
        "# Preprocess the data\n",
        "x_train = x_train.reshape(-1, 784).astype('float32') / 255\n",
        "x_test = x_test.reshape(-1, 784).astype('float32') / 255"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11493376/11490434 [==============================] - 0s 0us/step\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sOlB-WqjZp1Y",
        "colab_type": "text"
      },
      "source": [
        "# Define a Custom Callback Function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8LCmRXUgZqyV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def frobenius_norm(m):\n",
        "    \"\"\"This function is to calculate the frobenius norm of the matrix of all\n",
        "    layer's weight.\n",
        "  \n",
        "    Args:\n",
        "        m: is a list of weights param for each layers.\n",
        "    \"\"\"\n",
        "    total_reduce_sum = 0\n",
        "    for i in range(len(m)):\n",
        "        total_reduce_sum = total_reduce_sum + tf.math.reduce_sum(m[i]**2)\n",
        "    norm = total_reduce_sum**0.5\n",
        "    return norm"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "udSvzKm4Z5Zr",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "CG_frobenius_norm_of_weight = []\n",
        "CG_get_weight_norm = tf.keras.callbacks.LambdaCallback(\n",
        "    on_epoch_end=lambda batch, logs: CG_frobenius_norm_of_weight.append(\n",
        "        frobenius_norm(model_1.trainable_weights).numpy()))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qfhE1DfwZC1i",
        "colab_type": "text"
      },
      "source": [
        "# Train and Evaluate: Using CG as Optimizer\n",
        "\n",
        "Simply replace typical keras optimizers with the new tfa optimizer "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6-AMaOYEi1kK",
        "colab_type": "code",
        "outputId": "28534147-5ccd-48cf-f8b5-a6afdcf7612a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 382
        }
      },
      "source": [
        "# Compile the model\n",
        "model_1.compile(\n",
        "    optimizer=tfa.optimizers.ConditionalGradient(\n",
        "        learning_rate=0.99949, lambda_=203),  # Utilize TFA optimizer\n",
        "    loss=tf.keras.losses.SparseCategoricalCrossentropy(),\n",
        "    metrics=['accuracy'])\n",
        "\n",
        "history_cg = model_1.fit(\n",
        "    x_train,\n",
        "    y_train,\n",
        "    batch_size=batch_size,\n",
        "    validation_data=(x_test, y_test),\n",
        "    epochs=epochs,\n",
        "    callbacks=[CG_get_weight_norm])"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/10\n",
            "60000/60000 [==============================] - 5s 85us/sample - loss: 0.3745 - accuracy: 0.8894 - val_loss: 0.2323 - val_accuracy: 0.9275\n",
            "Epoch 2/10\n",
            "60000/60000 [==============================] - 3s 50us/sample - loss: 0.1908 - accuracy: 0.9430 - val_loss: 0.1538 - val_accuracy: 0.9547\n",
            "Epoch 3/10\n",
            "60000/60000 [==============================] - 3s 49us/sample - loss: 0.1497 - accuracy: 0.9548 - val_loss: 0.1473 - val_accuracy: 0.9560\n",
            "Epoch 4/10\n",
            "60000/60000 [==============================] - 3s 49us/sample - loss: 0.1306 - accuracy: 0.9612 - val_loss: 0.1215 - val_accuracy: 0.9609\n",
            "Epoch 5/10\n",
            "60000/60000 [==============================] - 3s 49us/sample - loss: 0.1211 - accuracy: 0.9636 - val_loss: 0.1114 - val_accuracy: 0.9660\n",
            "Epoch 6/10\n",
            "60000/60000 [==============================] - 3s 48us/sample - loss: 0.1125 - accuracy: 0.9663 - val_loss: 0.1260 - val_accuracy: 0.9640\n",
            "Epoch 7/10\n",
            "60000/60000 [==============================] - 3s 50us/sample - loss: 0.1108 - accuracy: 0.9665 - val_loss: 0.1009 - val_accuracy: 0.9697\n",
            "Epoch 8/10\n",
            "60000/60000 [==============================] - 3s 51us/sample - loss: 0.1081 - accuracy: 0.9676 - val_loss: 0.1129 - val_accuracy: 0.9647\n",
            "Epoch 9/10\n",
            "60000/60000 [==============================] - 3s 50us/sample - loss: 0.1065 - accuracy: 0.9675 - val_loss: 0.1058 - val_accuracy: 0.9683\n",
            "Epoch 10/10\n",
            "60000/60000 [==============================] - 3s 51us/sample - loss: 0.1039 - accuracy: 0.9683 - val_loss: 0.1126 - val_accuracy: 0.9646\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8OJp4So9bYYR",
        "colab_type": "text"
      },
      "source": [
        "# Train and Evaluate: Using SGD as Optimizer"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SuizUueqn449",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "model_2 = tf.keras.Sequential([\n",
        "    tf.keras.layers.Dense(64, input_shape=(784,), activation='relu', name='dense_1'),\n",
        "    tf.keras.layers.Dense(64, activation='relu', name='dense_2'),\n",
        "    tf.keras.layers.Dense(10, activation='softmax', name='predictions'),\n",
        "])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V8QC3xCwbfNl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "SGD_frobenius_norm_of_weight = []\n",
        "SGD_get_weight_norm = tf.keras.callbacks.LambdaCallback(\n",
        "    on_epoch_end=lambda batch, logs: SGD_frobenius_norm_of_weight.append(\n",
        "        frobenius_norm(model_2.trainable_weights).numpy()))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9BNi4yXGcDlg",
        "colab_type": "code",
        "outputId": "be21bdc7-c693-4663-fa5a-f036fc4b6140",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 382
        }
      },
      "source": [
        "# Compile the model\n",
        "model_2.compile(\n",
        "    optimizer=tf.keras.optimizers.SGD(0.01),  # Utilize SGD optimizer\n",
        "    loss=tf.keras.losses.SparseCategoricalCrossentropy(),\n",
        "    metrics=['accuracy'])\n",
        "\n",
        "history_sgd = model_2.fit(\n",
        "    x_train,\n",
        "    y_train,\n",
        "    batch_size=batch_size,\n",
        "    validation_data=(x_test, y_test),\n",
        "    epochs=epochs,\n",
        "    callbacks=[SGD_get_weight_norm])"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/10\n",
            "60000/60000 [==============================] - 3s 46us/sample - loss: 0.9498 - accuracy: 0.7523 - val_loss: 0.4306 - val_accuracy: 0.8844\n",
            "Epoch 2/10\n",
            "60000/60000 [==============================] - 2s 41us/sample - loss: 0.3851 - accuracy: 0.8916 - val_loss: 0.3298 - val_accuracy: 0.9068\n",
            "Epoch 3/10\n",
            "60000/60000 [==============================] - 3s 42us/sample - loss: 0.3230 - accuracy: 0.9064 - val_loss: 0.2917 - val_accuracy: 0.9150\n",
            "Epoch 4/10\n",
            "60000/60000 [==============================] - 2s 41us/sample - loss: 0.2897 - accuracy: 0.9169 - val_loss: 0.2676 - val_accuracy: 0.9241\n",
            "Epoch 5/10\n",
            "60000/60000 [==============================] - 3s 43us/sample - loss: 0.2658 - accuracy: 0.9237 - val_loss: 0.2485 - val_accuracy: 0.9288\n",
            "Epoch 6/10\n",
            "60000/60000 [==============================] - 2s 41us/sample - loss: 0.2467 - accuracy: 0.9301 - val_loss: 0.2374 - val_accuracy: 0.9285\n",
            "Epoch 7/10\n",
            "60000/60000 [==============================] - 3s 42us/sample - loss: 0.2308 - accuracy: 0.9343 - val_loss: 0.2201 - val_accuracy: 0.9358\n",
            "Epoch 8/10\n",
            "60000/60000 [==============================] - 2s 41us/sample - loss: 0.2169 - accuracy: 0.9388 - val_loss: 0.2096 - val_accuracy: 0.9388\n",
            "Epoch 9/10\n",
            "60000/60000 [==============================] - 2s 42us/sample - loss: 0.2046 - accuracy: 0.9421 - val_loss: 0.2009 - val_accuracy: 0.9404\n",
            "Epoch 10/10\n",
            "60000/60000 [==============================] - 2s 41us/sample - loss: 0.1939 - accuracy: 0.9448 - val_loss: 0.1900 - val_accuracy: 0.9442\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1Myw0FVcd_Z9",
        "colab_type": "text"
      },
      "source": [
        "# Frobenius Norm of Weights: CG vs SGD"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0tJYQBRt-ZUl",
        "colab_type": "text"
      },
      "source": [
        "The current implementation of CG optimizer is based on Frobenius Norm, with considering Frobenius Norm as regularizer in the target function. Therefore, we compare CG’s regularized effect with SGD optimizer, which has not imposed Frobenius Norm regularizer."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ewf17MW1cJVI",
        "colab_type": "code",
        "outputId": "481d5d00-5642-458d-aa86-225d7faf07ff",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        }
      },
      "source": [
        "plt.plot(\n",
        "    CG_frobenius_norm_of_weight,\n",
        "    color='r',\n",
        "    label='CG_frobenius_norm_of_weights')\n",
        "plt.plot(\n",
        "    SGD_frobenius_norm_of_weight,\n",
        "    color='b',\n",
        "    label='SGD_frobenius_norm_of_weights')\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Frobenius norm of weights')\n",
        "plt.legend(loc=1)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f2cd4f5f6d8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ILMrri0MP1CqllOVJr551QKSIhDruH3d7+MP8Xici84B4oLaI7AUeB+JFJAZb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\n/wcesGWfCRN8HZXytsOHc9b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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JGtutiXuoZyx",
        "colab_type": "text"
      },
      "source": [
        "# Train and Validation Accuracy: CG vs SGD\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s-SNIr10o2va",
        "colab_type": "code",
        "outputId": "1226fcbd-b71a-442b-811c-7155edbe623d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        }
      },
      "source": [
        "plt.plot(history_cg.history['accuracy'], color='r', label='CG_train')\n",
        "plt.plot(history_cg.history['val_accuracy'], color='g', label='CG_test')\n",
        "plt.plot(history_sgd.history['accuracy'], color='pink', label='SGD_train')\n",
        "plt.plot(history_sgd.history['val_accuracy'], color='b', label='SGD_test')\n",
        "plt.xlabel('Epoch')\n",
        "plt.ylabel('Accuracy')\n",
        "plt.legend(loc=4)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f2cd4a3f668>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FnhSRsMskIpeJSImIlFRXV0etkD3Uu2zuJU3vrZQa5qIZIHYAE4Me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\nBgillFIhaYBQSikV0v8HucVv/ez1EcAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}