01_gradient_descent.ipynb

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  "metadata": {
    "anaconda-cloud": {},
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.3"
    },
    "colab": {
      "name": "01 gradient_descent (2).ipynb",
      "version": "0.3.2",
      "provenance": []
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "YLZL63HZgvgT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R-1wb9Rkgvgd",
        "colab_type": "text"
      },
      "source": [
        "## Методы оптимизации\n",
        "\n",
        "Как было показано на лекции, большинство методов машинного обучения сводятся к поиску параметров, которые минимизируют ошибку на тренировочной выборке:\n",
        "$$\n",
        "\\min_{w} L(f(x, w), y)\n",
        "$$\n",
        "Здесь:\n",
        "\n",
        "* $L$ — функция потерь\n",
        "* $w$ — настраиваемые веса алгоритма\n",
        "* $y$ — вектор ответов\n",
        "* $x$ — вектор значений\n",
        "* $f$ — функция, принимающая вектор в качестве аргумента и выдающая числовое значение.\n",
        "\n",
        "\n",
        "\n",
        "В более общем виде задачу можно записать так:\n",
        "$$\n",
        "\\min_{x} f(x)\n",
        "$$\n",
        "Здесь:\n",
        "* $x$ — вектор значений\n",
        "* $f$ — функция, принимающая вектор в качестве аргумента и выдающая числовое значение.\n",
        "\n",
        "На семинаре рассмотрим подробнее методы минимизации функции, которые рассматривались на лекции."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c--eC-W8gvgf",
        "colab_type": "text"
      },
      "source": [
        "## Градиентный спуск\n",
        "\n",
        "Для оптимизации возьмем простую функцию $f(x) = x^3 - 2x^2 + 2$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sHqY5bo2gvgg",
        "colab_type": "code",
        "outputId": "36801c1b-305f-43dc-fe59-81226466fa79",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "f = lambda x: x ** 3 - 2*x ** 2 + 2\n",
        "df = lambda x: 3 * x ** 2 - 4 * x # производная\n",
        "x = np.linspace(-1, 2.5, 1000)\n",
        "plt.plot(x, f(x))\n",
        "plt.xlim([-1, 2.5])\n",
        "plt.ylim([0, 3])\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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h5xeP0LJ3Q22e8UpEPgBmA1Eikgv8DggAMMYsAJYBlwIZQDVwd2eF7Qyf7czD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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5q1EPngEgvgs",
        "colab_type": "text"
      },
      "source": [
        "И определим функцию, которая будет оптимизировать функцию $f(x)$ градиентным спуском с заданным постоянным шагом (он же learning rate, темп обучения)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_tpj5sAVgvgt",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def optimize_and_plot_steps(learning_rate, x_new=2, compute_learning_rate=None):\n",
        "    x_old = 0\n",
        "    # x_new — точка старта\n",
        "    eps = 0.0001\n",
        "    x_list, y_list = [x_new], [f(x_new)] # инициализируем список координат и значений функций при итерации\n",
        "    \n",
        "    # спускаемся, пока разница между координатами не достигла требуемой точности\n",
        "    i = 0\n",
        "    while abs(x_new - x_old) > eps:\n",
        "        # обновляем значение темпа обучения, если нам задана функция для этого\n",
        "        if compute_learning_rate is not None:\n",
        "            learning_rate = compute_learning_rate(i, learning_rate)\n",
        "            \n",
        "        x_old = x_new\n",
        "        # считаем направление спуска\n",
        "        # делаем шаг\n",
        "        # Ваш код здесь!\n",
        "        x_new = x_old - learning_rate * df(x_old)\n",
        "        # запоминаем очередной шаг минимизации\n",
        "        x_list.append(x_new)\n",
        "        y_list.append(f(x_new))\n",
        "        i += 1\n",
        "        \n",
        "    print(\"Найденный локальный минимум:\", x_new)\n",
        "    print(\"Количество шагов:\", len(x_list))\n",
        "    \n",
        "    plt.figure(figsize=[10,3])\n",
        "    \n",
        "    plt.subplot(1,2,1)\n",
        "    plt.scatter(x_list, y_list, c=\"r\", edgecolors='k')\n",
        "    plt.plot(x_list, y_list, c=\"r\")\n",
        "    plt.plot(x, f(x), c=\"b\")\n",
        "    plt.xlim([-1,2.5])\n",
        "    plt.ylim([0,3])\n",
        "    plt.title(\"Descent trajectory\")\n",
        "\n",
        "    plt.subplot(1,2,2)\n",
        "    plt.scatter(x_list,y_list,c=\"r\", edgecolors='k')\n",
        "    plt.plot(x_list,y_list,c=\"r\")\n",
        "    plt.plot(x,f(x), c=\"b\")\n",
        "    plt.xlim([1.2,2.1])\n",
        "    plt.ylim([0,3])\n",
        "    plt.title(\"Descent trajectory (zoomed in)\")\n",
        "    plt.show()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8cP_sfedgvgz",
        "colab_type": "text"
      },
      "source": [
        "Попробуем оптимизацию с шагом 0.1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wJijQoW_gvg1",
        "colab_type": "code",
        "outputId": "44f70554-b590-47fe-a101-76994c1a217f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        }
      },
      "source": [
        "optimize_and_plot_steps(0.1)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Найденный локальный минимум: 1.3334253508453249\n",
            "Количество шагов: 17\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ZEkQuIq+SZjnMuT/l59tyIQcdBOecY5MyDhkCP/1kQ7/Lly/yYVu2WOrZZx+r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\noAiObAsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gGntDxulgvg7",
        "colab_type": "text"
      },
      "source": [
        "Возьмем шаг побольше."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VoQ0aOtUgvg8",
        "colab_type": "code",
        "outputId": "cffab7ef-ff9e-49f5-f0f8-7a842cb3b621",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        }
      },
      "source": [
        "optimize_and_plot_steps(0.4)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Найденный локальный минимум: 1.3333020223878838\n",
            "Количество шагов: 15\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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gu+3ijiZnPEWBlWEiNbVqFfzrX7Dzzj7q7+qrYfJkuOQSqF077uiyW7WJVQhh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\nTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MA-SwqSmgvhB",
        "colab_type": "text"
      },
      "source": [
        "Что, если взять 0.5?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y-p05gEggvhD",
        "colab_type": "code",
        "outputId": "118e5acb-17f8-4507-f678-f753a17cfe4c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        }
      },
      "source": [
        "optimize_and_plot_steps(0.5)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Найденный локальный минимум: 0.0\n",
            "Количество шагов: 3\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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POUwkGd9/77lk883hgQd8kNasWdC/v6ZwSYUaa1IzGwL0AFqb2RygP9AIIITw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\npMj/AwRTudZTrw/EAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VOukuNZFgvhJ",
        "colab_type": "text"
      },
      "source": [
        "Застопорились в нуле, т.к. нашли точный локальный максимум. В нем производная равна нулю и мы никуда не можем сдвинуться. А если взять 0.49?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qAk_yK67gvhK",
        "colab_type": "code",
        "outputId": "831a917e-2505-442f-830c-02044a26fed9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        }
      },
      "source": [
        "optimize_and_plot_steps(0.49)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Найденный локальный минимум: 1.3333812706364907\n",
            "Количество шагов: 188\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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spk71O6j4lpUFTz8Nbdu6pSJMSMVNDjOmpObPdwO1LrvMtUpNnAj/+59bi9QE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\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZT61lK5ggvhN",
        "colab_type": "text"
      },
      "source": [
        "Что, если взять 0.51?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "45oBmkhMgvhP",
        "colab_type": "code",
        "outputId": "9efe4eaa-0f15-4421-8aa3-965677570acd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 308
        }
      },
      "source": [
        "optimize_and_plot_steps(0.51)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "error",
          "ename": "OverflowError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mOverflowError\u001b[0m                             Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-11-19173c019366>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0moptimize_and_plot_steps\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.51\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m<ipython-input-6-5cfac41cb71c>\u001b[0m in \u001b[0;36moptimize_and_plot_steps\u001b[0;34m(learning_rate, x_new, compute_learning_rate)\u001b[0m\n\u001b[1;32m     19\u001b[0m         \u001b[0;31m# запоминаем очередной шаг минимизации\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0mx_list\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_new\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 21\u001b[0;31m         \u001b[0my_list\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_new\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     22\u001b[0m         \u001b[0mi\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-5-f487f45784f1>\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(x)\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m3\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mdf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m3\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m4\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mx\u001b[0m \u001b[0;31m# производная\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2.5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mOverflowError\u001b[0m: (34, 'Numerical result out of range')"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y4gOKAKkgvhV",
        "colab_type": "text"
      },
      "source": [
        "Мы улетели далеко влево. Это можно понять, распечатав значения x_new."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1OTKjGW-gvhX",
        "colab_type": "text"
      },
      "source": [
        "Теперь возьмём маленький шаг. Например, 0.05."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "etEM5UvPgvhY",
        "colab_type": "code",
        "outputId": "2f6286bb-77d6-489f-f90b-d220ceabbfc1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        }
      },
      "source": [
        "optimize_and_plot_steps(0.05)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Найденный локальный минимум: 1.3337297312792562\n",
            "Количество шагов: 32\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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gVljFr5KKpqIFziQqaPuyGTrwvFf0ibM+0R6HT9H2lb/R+rJqnwKq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\n8v8duh2BAXg/CwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uJDbaa4xgvhb",
        "colab_type": "text"
      },
      "source": [
        "0.01?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f7pqVBMqgvhc",
        "colab_type": "code",
        "outputId": "6b1cca21-f662-4c57-fb38-7c2082976ef3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        }
      },
      "source": [
        "optimize_and_plot_steps(0.01)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Найденный локальный минимум: 1.3356881625009205\n",
            "Количество шагов: 129\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RzJwJBx0EZ5wBU6b4HVH8WrhkCceTzOPcQDs+4x98ZR3WQytucpgx++uL578j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\nlVREjSJNX+QEPZ2r9f8YoS3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hGnNcaaKtj1Uwl58IlQaqutK7/yfQoITlKolIjoh8ISKh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\nRK5CYII=\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ifS8GIsQgvhf",
        "colab_type": "text"
      },
      "source": [
        "Чем меньше шаг, тем медленнее мы идём к минимум (и можем вдобавок застрять по пути). Чем больше темп обучения, тем большие расстояния мы перепрыгиваем (и имеем гипотетическую возможность найти минимум получше). Хорошая стратегия — начинать с достаточно большого шага (чтобы хорошо попутешествовать по функции), а потом постепенно его уменьшать, чтобы стабилизировать процесс обучения в каком-то локальном минимуме."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZtBH2WF0gvhh",
        "colab_type": "text"
      },
      "source": [
        "Теперь будем изменять шаг динамически:\n",
        "$lr(i + 1) = lr(i) * 0.9$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e5Vruebcgvhj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def compute_learning_rate(i, prev_lr):\n",
        "    return prev_lr * 0.9"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2dQLCrtJgvhn",
        "colab_type": "code",
        "outputId": "7d7aaeb8-11e8-4bff-c169-3f63322826fc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        }
      },
      "source": [
        "optimize_and_plot_steps(0.4, compute_learning_rate=compute_learning_rate)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Найденный локальный минимум: 1.3333376009455882\n",
            "Количество шагов: 7\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5tWdP9g0YQJmdO3XB7Pqofv2gfXsdP8rqo0Jm1So9U/OOO+Jrfi1jTPT64QcY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\n09/IUngSGwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K8ZFArn8gvhs",
        "colab_type": "text"
      },
      "source": [
        "Если сравнивать с постоянным темпом обучения, то мы нашли минимум в 2 раза быстрее."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UGdu2F12gvht",
        "colab_type": "code",
        "outputId": "f02fb6c7-2619-4b7a-96cf-612d956a3c83",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 261
        }
      },
      "source": [
        "optimize_and_plot_steps(0.4)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Найденный локальный минимум: 1.3333020223878838\n",
            "Количество шагов: 15\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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gu+3ijiZnPEWBlWEiNbVqFfzrX7Dzzj7q7+qrYfJkuOQSqF077uiyW7WJVQhh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\nTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gvTCqqe5gvhx",
        "colab_type": "text"
      },
      "source": [
        "Это, конечно, искуственный пример, но такая же идея используются для обучения алгоритмов машинного обучения с миллионами параметров, функции потерь которых имеют очень сложную структуру и не поддаются визуализации."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yX8qvF4jgvhy",
        "colab_type": "text"
      },
      "source": [
        "## Настройка линейной регрессии с помощью градиентного спуска\n",
        "\n",
        "Рассмотрим теперь реальные данные и попробуем использовать градиентный спуск для решения задачи линейной регрессии."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R5iqlO0ogvh0",
        "colab_type": "text"
      },
      "source": [
        "Загрузите файл food_trucks.txt. В нём два столбца значений — количество жителей в городе и доход грузовика с уличной едой в этом городе."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rvYa7KlKgvh2",
        "colab_type": "code",
        "outputId": "c0b7eb14-ca92-4350-a433-d18a7e3f39ba",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        }
      },
      "source": [
        "import pandas as pd\n",
        "\n",
        "df = pd.read_csv(\"./food_trucks.txt\", header=None)\n",
        "df.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>6.1101</td>\n",
              "      <td>17.5920</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>5.5277</td>\n",
              "      <td>9.1302</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>8.5186</td>\n",
              "      <td>13.6620</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>7.0032</td>\n",
              "      <td>11.8540</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.8598</td>\n",
              "      <td>6.8233</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        0        1\n",
              "0  6.1101  17.5920\n",
              "1  5.5277   9.1302\n",
              "2  8.5186  13.6620\n",
              "3  7.0032  11.8540\n",
              "4  5.8598   6.8233"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mexr9fQAgvh5",
        "colab_type": "text"
      },
      "source": [
        "Визуализируйте данные. По оси X — население города, по оси Y — доход грузовика."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PR9Ruhwsgvh6",
        "colab_type": "code",
        "outputId": "93412bee-045a-4185-8f7d-33c24e6e8de7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 486
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.figure(figsize=(10, 8))\n",
        "plt.scatter(df[0], df[1])\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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/BgBYOKeW+Wqtbxvw1I+MuS0AAHPH2XwAAA0IUwAADQhTAAANCFMAAA2cdZ+pTtnc6uXq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\nMAUA0IAwBQDQgDAFANCAMAUA0MD/D0jJ5fCQ/9cmAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RB10_jkigvh_",
        "colab_type": "text"
      },
      "source": [
        "Вспомним функцию потерь линейной регрессии:\n",
        "$$\n",
        "L(w) = \\frac{1}{2m} \\sum_{i=1}^m (h(x^i, w) - y^i)^2\n",
        "$$\n",
        "Здесь $h(x, w) = w^Tx = w_0 + w_1 x_1$ (предполагается, что $x_0=1$ — дополнительный признак для удобства).\n",
        "$(x^i, y^i)$ — i-ый объект выборки.\n",
        "Тогда правило обновления весов будет выглядеть следующим образом:\n",
        "$$\n",
        "w_j = w_j - \\eta \\cdot \\frac{1}{m}\\sum_{i=1}^m(h(x^i, w) - y^i) x^i_j.\n",
        "$$\n",
        "Здесь $x^i_j$ — j-ая компонента i-ого объекта."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "djLDBgyagviB",
        "colab_type": "text"
      },
      "source": [
        "Определите функцию потерь и её производную. Эти функции имеют один аргумент — вектор весов $w$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "un1xvTf9gviB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "L = lambda w: np.mean((X @ w - y)**2) / 2.\n",
        "dL = lambda w: np.mean((X @ w - y)[..., None] * X, axis=0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kqyNQvQwgviE",
        "colab_type": "code",
        "outputId": "2406343f-7883-43bc-94fb-453c0a6db5f7",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "X = np.stack((np.ones(len(df)), df[0]), axis=1)\n",
        "y = df[1].values\n",
        "w = np.ones(2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 3.32066495, 24.23489308])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zchuisiIgviJ",
        "colab_type": "text"
      },
      "source": [
        "Напишите функцию минимизации $L(w)$ с помощью градиентного спуска, аналогичную optimize_and_plot_steps. На вход она принимает параметры обучения (темп обучения и начальное значение весов), оптимизирует итеративно функцию потерь, печатает итерации и визуализирует уменьшение функции потерь и найденное решение. Запустите функцию с постоянным темпом обучения и прокомментируйте результаты."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JkZ9maEPgviL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def optimize_and_plot_steps(learning_rate, x_new=np.ones(2), compute_learning_rate=None):\n",
        "    x_old = np.zeros(2)\n",
        "    # x_new — точка старта\n",
        "    eps = 0.0001\n",
        "    x_list, y_list = [x_new], [L(x_new)] # инициализируем список координат и значений функций при итерации\n",
        "    \n",
        "    # спускаемся, пока разница между координатами не достигла требуемой точности\n",
        "    i = 0\n",
        "    while np.mean(abs(x_new - x_old)) > eps:\n",
        "        # обновляем значение темпа обучения, если нам задана функция для этого\n",
        "        if compute_learning_rate is not None:\n",
        "            learning_rate = compute_learning_rate(i, learning_rate)\n",
        "            \n",
        "        x_old = x_new\n",
        "        # считаем направление спуска\n",
        "        # делаем шаг\n",
        "        x_new = x_old - learning_rate * dL(x_old)# Ваш код здесь!\n",
        "        \n",
        "        # запоминаем очередной шаг минимизации\n",
        "        x_list.append(x_new)\n",
        "        y_list.append(L(x_new))\n",
        "        i += 1\n",
        "    return x_new"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gMsP-SrVgviN",
        "colab_type": "code",
        "outputId": "960edb9e-0dcc-4b22-9f23-047ebf87c113",
        "colab": {}
      },
      "source": [
        "optimize_and_plot_steps(0.01, compute_learning_rate=None)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-3.7952   ,  1.1829292])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EZOBk7mGgviP",
        "colab_type": "text"
      },
      "source": [
        "Измените функцию минимизации так, чтобы темп обучения мог меняться динамически, аналогично примеру выше. Запустите функцию и прокомментируйте результаты."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "RVrMPCt-gviR",
        "colab_type": "text"
      },
      "source": [
        "## Стохастический градиентный спуск (SGD)\n",
        "\n",
        "При стандартном («batch») градиентном спуске для корректировки параметров модели используется градиент. Градиент обычно считается как сумма градиентов, вызванных каждым элементом обучения. Вектор параметров изменяется в направлении антиградиента с заданным шагом. Поэтому стандартному градиентному спуску требуется один проход по обучающим данным до того, как он сможет менять параметры.\n",
        "\n",
        "При стохастическом градиентном спуске значение градиента аппроксимируются градиентом функции стоимости, вычисленном только на одном элементе обучения. Затем параметры изменяются пропорционально приближенному градиенту. Таким образом параметры модели изменяются после каждого объекта обучения. Для больших массивов данных стохастический градиентный спуск может дать значительное преимущество в скорости по сравнению со стандартным градиентным спуском.\n",
        "\n",
        "Между этими двумя видами градиентного спуска существует компромисс, называемый иногда «mini-batch». В этом случае градиент аппроксимируется суммой для небольшого количества обучающих образцов."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IajYlAergviR",
        "colab_type": "text"
      },
      "source": [
        "\\begin{eqnarray}\n",
        "g &=& \\frac{1}{m}\\nabla_w \\sum_i L(f(x^{(i)};w), y^{(i)}) \\\\\n",
        "w &=& w - \\eta \\times g\n",
        "\\end{eqnarray}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E8933ElDgvij",
        "colab_type": "text"
      },
      "source": [
        " "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6gcCk9gzgvil",
        "colab_type": "text"
      },
      "source": [
        "**Метод накопления импульса (Momentum)** \n",
        "\n",
        "Использует экспоненциальное скользящее среднее чтобы накапливать градиент целевой функции. Чем ближе $\\alpha$ к единице, тем больше окно накопления и сильнее сглаживание — накопленные градиенты начинают влиять сильнее, чем каждый очередной градиент."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZfmkLp01gvil",
        "colab_type": "text"
      },
      "source": [
        "\\begin{eqnarray}\n",
        "v &=& \\alpha v - (1 - \\alpha) \\nabla_w \\big(\\frac{1}{m}\\sum_i \n",
        "L(f(x^{(i)};w), y^{(i)}) \\big) \\\\\n",
        "w &=& w + v\n",
        "\\end{eqnarray}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u149f9g3gvin",
        "colab_type": "text"
      },
      "source": [
        "**AdaGrad**  \n",
        "\n",
        "Эффективно перемасштабирует шаг обучения\n",
        "для каждого параметра в отдельности, учитывая историю всех прошлых градиентов для\n",
        "этого параметра. Это делается путем деления каждого элемента в\n",
        "градиенте $g$ на квадратный корень суммы квадратов прошлых соответствующих элементов\n",
        "градиента. Перемасштабирование таким способом эффективно уменьшает шаг обучения для\n",
        "параметров, которые имеют большую величину градиента. Также метод уменьшает сам шаг\n",
        "обучения со временем, так как сумма квадратов увеличивается с каждой итерацией. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F2xJ9Y1Ggvin",
        "colab_type": "text"
      },
      "source": [
        "\\begin{eqnarray}\n",
        "g &=& \\frac{1}{m}\\nabla_w \\sum_i L(f(x^{(i)};w), y^{(i)}) \\\\\n",
        "s &=& s + g^{T}g \\\\\n",
        "w &=& w - \\eta \\times \\frac{g} {\\sqrt{s+eps}}\n",
        "\\end{eqnarray}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K3iRJoWygvio",
        "colab_type": "text"
      },
      "source": [
        "**RMSProp**\n",
        "\n",
        "Очень похож по принципу работы на метод Adagrad. Единственное его отличие в том, что шкалирующий член\n",
        "$s$ вычисляется, как экспоненциальное скользящее среднее вместо кумулятивной суммы, это позволяет сгладить выбросы."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0nIWOZVUgvio",
        "colab_type": "text"
      },
      "source": [
        "\\begin{eqnarray}\n",
        "g &=& \\frac{1}{m}\\nabla_w \\sum_i L(f(x^{(i)};w), y^{(i)}) \\\\\n",
        "s &=& \\mathrm{decay\\_rate}\\times s + (1-\\mathrm{decay\\_rate}) g^{T}g \\\\\n",
        "w &=& w - \\eta \\times \\frac{g}{\\sqrt{s+eps}}\n",
        "\\end{eqnarray}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n7YgRAWhgvir",
        "colab_type": "text"
      },
      "source": [
        "**Adam**\n",
        "\n",
        "Можно рассматривать как комбинацию RMSProp и Метода накопления импульса. Обновление весов выглядит как в RMSProp за исключением того что вместо обычного градиента используется градиент сглаженный экспоненциальным скользящим средним и убывающего шага.\n",
        "\n",
        "Рекомендованные значения $\\epsilon = 1e-8$, $\\beta_1 = 0.9$, $\\beta_2 = 0.999$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4M11Mrmdgvis",
        "colab_type": "text"
      },
      "source": [
        "\\begin{eqnarray}\n",
        "g &=& \\frac{1}{m}\\nabla_w \\sum_i L(f(x^{(i)};w), y^{(i)}) \\\\\n",
        "m &=& \\beta_1 m + (1-\\beta_1) g\\\\\n",
        "s &=& \\beta_2 v + (1-\\beta_2) g^{T}g \\\\\n",
        "w &=& w - \\eta \\times \\frac{\\sqrt{1 -  \\beta_2^t}}{ 1 - \\beta_1^t} \\times \\frac{ m }{ \\sqrt{s+eps}}\n",
        "\\end{eqnarray}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "44U1Wb4ygvit",
        "colab_type": "text"
      },
      "source": [
        "Рассмотрим популярные методы оптимизации, используемые для обучения нейронных сетей, на примере сверточной нейронной сети, обученной на датасете MNIST, с помощью Tensorflow.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bJRg1O9Pgvit",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "%matplotlib inline\n",
        "\n",
        "import numpy as np\n",
        "import tensorflow as tf\n",
        "from tensorflow.examples.tutorials.mnist import input_data\n",
        "from tensorflow.contrib.layers import variance_scaling_initializer\n",
        "\n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.datasets import load_boston"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1lUoJRVZgviv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def weight_variable(name, shape):\n",
        "    he_normal = variance_scaling_initializer(factor=2.0, mode='FAN_IN', uniform=False,\n",
        "                                             seed=None, dtype=tf.float32) \n",
        "    return tf.get_variable(name, shape=shape, initializer=he_normal)\n",
        "\n",
        "def bias_variable(shape):\n",
        "    initial = tf.constant(0.1, shape=shape)\n",
        "    return tf.Variable(initial)\n",
        "\n",
        "def conv2d(x, W):\n",
        "    return tf.nn.conv2d(x, W, strides=[1,1,1,1], padding='SAME')\n",
        "\n",
        "def max_pool_2x2(x):\n",
        "    return tf.nn.max_pool(x, ksize=[1,2,2,1], strides=[1,2,2,1], padding='SAME')\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s-7cCQZzgvix",
        "colab_type": "code",
        "outputId": "925ad39b-a2dc-4323-b84d-a07cab255840",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 534
        }
      },
      "source": [
        "#dataset\n",
        "mnist = input_data.read_data_sets(\"./MNIST_data/\", one_hot=True)\n",
        "\n",
        "#parameters\n",
        "learning_rate = 0.001\n",
        "training_epochs = 500\n",
        "batch_size = 50\n",
        "display_step = 100"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:From <ipython-input-3-daa1ec3d51be>:1: read_data_sets (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Please use alternatives such as official/mnist/dataset.py from tensorflow/models.\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:260: maybe_download (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Please write your own downloading logic.\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/contrib/learn/python/learn/datasets/base.py:252: _internal_retry.<locals>.wrap.<locals>.wrapped_fn (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Please use urllib or similar directly.\n",
            "Successfully downloaded train-images-idx3-ubyte.gz 9912422 bytes.\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:262: extract_images (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Please use tf.data to implement this functionality.\n",
            "Extracting ./MNIST_data/train-images-idx3-ubyte.gz\n",
            "Successfully downloaded train-labels-idx1-ubyte.gz 28881 bytes.\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:267: extract_labels (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Please use tf.data to implement this functionality.\n",
            "Extracting ./MNIST_data/train-labels-idx1-ubyte.gz\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:110: dense_to_one_hot (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Please use tf.one_hot on tensors.\n",
            "Successfully downloaded t10k-images-idx3-ubyte.gz 1648877 bytes.\n",
            "Extracting ./MNIST_data/t10k-images-idx3-ubyte.gz\n",
            "Successfully downloaded t10k-labels-idx1-ubyte.gz 4542 bytes.\n",
            "Extracting ./MNIST_data/t10k-labels-idx1-ubyte.gz\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:290: DataSet.__init__ (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Please use alternatives such as official/mnist/dataset.py from tensorflow/models.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0CCHVXo9gviz",
        "colab_type": "code",
        "outputId": "ce87ae36-2b98-4afe-e3a5-7b7dfe46eb2f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 226
        }
      },
      "source": [
        "x = tf.placeholder(tf.float32, [None, 784])\n",
        "y_= tf.placeholder(tf.float32, [None, 10])\n",
        "x_image = tf.reshape(x, [-1,28,28,1])\n",
        "\n",
        "#layer 1\n",
        "W_conv1 = weight_variable(\"W1\", [5,5,1,32])\n",
        "b_conv1 = bias_variable([32])\n",
        "h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1) + b_conv1)\n",
        "h_pool1 = max_pool_2x2(h_conv1)\n",
        "\n",
        "#layer 2\n",
        "W_conv2 = weight_variable(\"W2\", [5,5,32,64])\n",
        "b_conv2 = bias_variable([64])\n",
        "h_conv2 = tf.nn.relu(conv2d(h_pool1, W_conv2) + b_conv2)\n",
        "h_pool2 = max_pool_2x2(h_conv2)\n",
        "\n",
        "#layer 3\n",
        "W_fc1 = weight_variable(\"W3\", [7*7*64, 1024])\n",
        "b_fc1 = bias_variable([1024])\n",
        "h_pool2_flat = tf.reshape(h_pool2, [-1,7*7*64])\n",
        "h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)\n",
        "\n",
        "#dropout\n",
        "keep_prob = tf.placeholder(tf.float32)\n",
        "h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)\n",
        "\n",
        "#layer 5\n",
        "W_fc2 = weight_variable(\"W5\", [1024, 10])\n",
        "b_fc2 = bias_variable([10])\n",
        "y_conv = tf.matmul(h_fc1_drop, W_fc2) + b_fc2\n",
        "\n",
        "cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=y_, logits=y_conv))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:From <ipython-input-4-e1ccbaa8b4c6>:25: calling dropout (from tensorflow.python.ops.nn_ops) with keep_prob is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Please use `rate` instead of `keep_prob`. Rate should be set to `rate = 1 - keep_prob`.\n",
            "WARNING:tensorflow:From <ipython-input-4-e1ccbaa8b4c6>:32: softmax_cross_entropy_with_logits (from tensorflow.python.ops.nn_ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "\n",
            "Future major versions of TensorFlow will allow gradients to flow\n",
            "into the labels input on backprop by default.\n",
            "\n",
            "See `tf.nn.softmax_cross_entropy_with_logits_v2`.\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wnGUdSnBgvi1",
        "colab_type": "text"
      },
      "source": [
        "сравним некоторые из описанных выше методы"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kbqgGxvDgvi_",
        "colab_type": "code",
        "outputId": "32d6cfb4-31dc-419a-98d7-b73ebdd35906",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        }
      },
      "source": [
        "#optimizers\n",
        "train_step1 = tf.train.GradientDescentOptimizer(learning_rate).minimize(cross_entropy)\n",
        "train_step2 = tf.train.MomentumOptimizer(learning_rate, momentum=0.9, use_nesterov=True).minimize(cross_entropy)\n",
        "train_step3 = tf.train.RMSPropOptimizer(learning_rate).minimize(cross_entropy)\n",
        "train_step4 = tf.train.AdamOptimizer(learning_rate).minimize(cross_entropy)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/training/rmsprop.py:119: calling Ones.__init__ (from tensorflow.python.ops.init_ops) with dtype is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Call initializer instance with the dtype argument instead of passing it to the constructor\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BEBag71dgvjD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "correct_prediction = tf.equal(tf.argmax(y_conv,1), tf.argmax(y_,1))\n",
        "accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))\n",
        "\n",
        "init = tf.global_variables_initializer()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8Oh6odCUgvjE",
        "colab_type": "code",
        "outputId": "2b420131-ee7f-4e5d-f795-b144afcddee3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 137
        }
      },
      "source": [
        "with tf.Session() as sess1:\n",
        "    sess1.run(init)\n",
        "\n",
        "    print(\"training with SGD optimizer...\")\n",
        "    avg_loss_sgd = np.zeros(training_epochs)\n",
        "    for epoch in range(training_epochs):\n",
        "        batch_xs, batch_ys = mnist.train.next_batch(batch_size)\n",
        "\n",
        "        _, loss = sess1.run([train_step1, cross_entropy], \n",
        "                            feed_dict={x: batch_xs, y_: batch_ys, keep_prob: 0.5})\n",
        "        avg_loss_sgd[epoch] = loss\n",
        "\n",
        "        if epoch % display_step == 0:\n",
        "            train_accuracy = accuracy.eval(feed_dict={x:batch_xs, y_:batch_ys, keep_prob: 1.0})\n",
        "            print(\"Epoch %04d, training accuracy %.2f\"%(epoch, train_accuracy))\n",
        "    #end for\n",
        "    print(\"test accuracy %g\" %accuracy.eval(feed_dict={x: mnist.test.images, y_: mnist.test.labels, keep_prob: 1.0}))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "training with SGD optimizer...\n",
            "Epoch 0000, training accuracy 0.10\n",
            "Epoch 0100, training accuracy 0.78\n",
            "Epoch 0200, training accuracy 0.76\n",
            "Epoch 0300, training accuracy 0.84\n",
            "Epoch 0400, training accuracy 0.98\n",
            "test accuracy 0.8902\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RAMvXyCBgvjG",
        "colab_type": "code",
        "outputId": "5614f11b-ef99-455f-e7db-04315b702d2f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 137
        }
      },
      "source": [
        "with tf.Session() as sess2:\n",
        "    sess2.run(init)\n",
        "\n",
        "    print(\"training with momentum optimizer...\")\n",
        "    avg_loss_momentum = np.zeros(training_epochs)\n",
        "    for epoch in range(training_epochs):\n",
        "        batch_xs, batch_ys = mnist.train.next_batch(batch_size)\n",
        "\n",
        "        _, loss = sess2.run([train_step2, cross_entropy], \n",
        "                            feed_dict={x: batch_xs, y_: batch_ys, keep_prob: 0.5})\n",
        "        avg_loss_momentum[epoch] = loss\n",
        "\n",
        "        if epoch % display_step == 0:\n",
        "            train_accuracy = accuracy.eval(feed_dict={x:batch_xs, y_:batch_ys, keep_prob: 1.0})\n",
        "            print(\"Epoch %04d, training accuracy %.2f\"%(epoch, train_accuracy))\n",
        "    #end for\n",
        "    print(\"test accuracy %g\" %accuracy.eval(feed_dict={x: mnist.test.images, y_: mnist.test.labels, keep_prob: 1.0}))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "training with momentum optimizer...\n",
            "Epoch 0000, training accuracy 0.14\n",
            "Epoch 0100, training accuracy 0.90\n",
            "Epoch 0200, training accuracy 0.92\n",
            "Epoch 0300, training accuracy 0.94\n",
            "Epoch 0400, training accuracy 0.98\n",
            "test accuracy 0.9498\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NsrIfUJ4gvjK",
        "colab_type": "code",
        "outputId": "c90b9ceb-633e-490e-d45d-4efa0e4f279f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 137
        }
      },
      "source": [
        "with tf.Session() as sess3:\n",
        "    sess3.run(init)\n",
        "\n",
        "    print(\"training with RMSProp optimizer...\")\n",
        "    avg_loss_rmsprop = np.zeros(training_epochs)\n",
        "    for epoch in range(training_epochs):\n",
        "        batch_xs, batch_ys = mnist.train.next_batch(batch_size)\n",
        "\n",
        "        _, loss = sess3.run([train_step3, cross_entropy], \n",
        "                            feed_dict={x: batch_xs, y_: batch_ys, keep_prob: 0.5})\n",
        "        avg_loss_rmsprop[epoch] = loss\n",
        "\n",
        "        if epoch % display_step == 0:\n",
        "            train_accuracy = accuracy.eval(feed_dict={x:batch_xs, y_:batch_ys, keep_prob: 1.0})\n",
        "            print(\"Epoch %04d, training accuracy %.2f\"%(epoch, train_accuracy))\n",
        "    #end for\n",
        "    print(\"test accuracy %g\" %accuracy.eval(feed_dict={x: mnist.test.images, y_: mnist.test.labels, keep_prob: 1.0}))\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "training with RMSProp optimizer...\n",
            "Epoch 0000, training accuracy 0.08\n",
            "Epoch 0100, training accuracy 0.94\n",
            "Epoch 0200, training accuracy 1.00\n",
            "Epoch 0300, training accuracy 1.00\n",
            "Epoch 0400, training accuracy 1.00\n",
            "test accuracy 0.9807\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zl_eYb2OgvjO",
        "colab_type": "code",
        "outputId": "506ccb31-0a97-4be1-9871-063798a5c667",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 137
        }
      },
      "source": [
        "with tf.Session() as sess4:\n",
        "    sess4.run(init)\n",
        "\n",
        "    print(\"training with Adam optimizer...\")\n",
        "    avg_loss_adam = np.zeros(training_epochs)\n",
        "    for epoch in range(training_epochs):\n",
        "        batch_xs, batch_ys = mnist.train.next_batch(batch_size)\n",
        "\n",
        "        _, loss = sess4.run([train_step4, cross_entropy], \n",
        "                            feed_dict={x: batch_xs, y_: batch_ys, keep_prob: 0.5})\n",
        "        avg_loss_adam[epoch] = loss\n",
        "\n",
        "        if epoch % display_step == 0:\n",
        "            train_accuracy = accuracy.eval(feed_dict={x:batch_xs, y_:batch_ys, keep_prob: 1.0})\n",
        "            print(\"Epoch %04d, training accuracy %.2f\"%(epoch, train_accuracy))\n",
        "    #end for\n",
        "    print(\"test accuracy %g\" %accuracy.eval(feed_dict={x: mnist.test.images, y_: mnist.test.labels, keep_prob: 1.0}))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "training with Adam optimizer...\n",
            "Epoch 0000, training accuracy 0.22\n",
            "Epoch 0100, training accuracy 0.98\n",
            "Epoch 0200, training accuracy 0.96\n",
            "Epoch 0300, training accuracy 1.00\n",
            "Epoch 0400, training accuracy 0.98\n",
            "test accuracy 0.978\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aCq1J-QZ2NUc",
        "colab_type": "text"
      },
      "source": [
        "**Упражнение**. Нарисуйте графики убывания лосса. Сделайте выводы по результатам экспериментов. Какие методы показали себя лучше?\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dPto10uygvjT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# нарисовать графики сходимости\n",
        "# ВАШ КОД ЗДЕСЬ\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9u6Np6yHgvjV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}