Ads_Optimization.ipynb

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        "<a href=\"https://colab.research.google.com/github/roshank1605A04/Ads-Optimization/blob/master/Ads_Optimization.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "id": "YivLDteVfuP0",
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      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns"
      ],
      "execution_count": 0,
      "outputs": []
    },
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      "cell_type": "code",
      "source": [
        "data = pd.read_csv('drive/My Drive/super/Reinforcement Learning/Ads_CTR_Optimisation.csv')\n",
        "\n",
        "data.shape"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 10)"
            ]
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          "metadata": {
            "tags": []
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      "cell_type": "code",
      "source": [
        "data.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
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          "data": {
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              "      <th></th>\n",
              "      <th>Ad 1</th>\n",
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            "text/plain": [
              "   Ad 1  Ad 2  Ad 3  Ad 4  Ad 5  Ad 6  Ad 7  Ad 8  Ad 9  Ad 10\n",
              "0     1     0     0     0     1     0     0     0     1      0\n",
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      "source": [
        "data.describe()"
      ],
      "execution_count": 0,
      "outputs": [
        {
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              "  <thead>\n",
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              "      <th>Ad 1</th>\n",
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              "      <th>Ad 10</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>10000.000000</td>\n",
              "      <td>10000.000000</td>\n",
              "      <td>10000.000000</td>\n",
              "      <td>10000.000000</td>\n",
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              "      <td>10000.00000</td>\n",
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              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>0.170300</td>\n",
              "      <td>0.129500</td>\n",
              "      <td>0.072800</td>\n",
              "      <td>0.119600</td>\n",
              "      <td>0.269500</td>\n",
              "      <td>0.012600</td>\n",
              "      <td>0.111200</td>\n",
              "      <td>0.209100</td>\n",
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              "      <td>0.04890</td>\n",
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              "      <td>0.335769</td>\n",
              "      <td>0.259821</td>\n",
              "      <td>0.324509</td>\n",
              "      <td>0.443722</td>\n",
              "      <td>0.111546</td>\n",
              "      <td>0.314395</td>\n",
              "      <td>0.406686</td>\n",
              "      <td>0.293506</td>\n",
              "      <td>0.21567</td>\n",
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              "      <th>min</th>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
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              "    <tr>\n",
              "      <th>50%</th>\n",
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              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
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              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
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              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
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              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1.000000</td>\n",
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              "      <td>1.000000</td>\n",
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              "               Ad 1          Ad 2          Ad 3          Ad 4          Ad 5  \\\n",
              "count  10000.000000  10000.000000  10000.000000  10000.000000  10000.000000   \n",
              "mean       0.170300      0.129500      0.072800      0.119600      0.269500   \n",
              "std        0.375915      0.335769      0.259821      0.324509      0.443722   \n",
              "min        0.000000      0.000000      0.000000      0.000000      0.000000   \n",
              "25%        0.000000      0.000000      0.000000      0.000000      0.000000   \n",
              "50%        0.000000      0.000000      0.000000      0.000000      0.000000   \n",
              "75%        0.000000      0.000000      0.000000      0.000000      1.000000   \n",
              "max        1.000000      1.000000      1.000000      1.000000      1.000000   \n",
              "\n",
              "               Ad 6          Ad 7          Ad 8          Ad 9        Ad 10  \n",
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              "mean       0.012600      0.111200      0.209100      0.095200      0.04890  \n",
              "std        0.111546      0.314395      0.406686      0.293506      0.21567  \n",
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        "data.isnull().any().any()"
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        }
      },
      "cell_type": "code",
      "source": [
        "data['Ad 10'].value_counts()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    9511\n",
              "1     489\n",
              "Name: Ad 10, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "metadata": {
        "id": "ucQZKq4zhvtw",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Implementing UCB\n",
        "\n",
        "import math\n",
        "\n",
        "N = 10000\n",
        "d = 10\n",
        "\n",
        "ads_selected = []\n",
        "numbers_of_selections = [0] * d\n",
        "sums_of_rewards = [0] * d\n",
        "total_reward = 0\n",
        "\n",
        "for n in range(0, N):\n",
        "    ad = 0\n",
        "    max_upper_bound = 0\n",
        "    for i in range(0, d):\n",
        "        if (numbers_of_selections[i] > 0):\n",
        "            average_reward = sums_of_rewards[i] / numbers_of_selections[i]\n",
        "            delta_i = math.sqrt(3/2 * math.log(n + 1) / numbers_of_selections[i])\n",
        "            upper_bound = average_reward + delta_i\n",
        "        else:\n",
        "            upper_bound = 1e400\n",
        "        if upper_bound > max_upper_bound:\n",
        "            max_upper_bound = upper_bound\n",
        "            ad = i\n",
        "    ads_selected.append(ad)\n",
        "    numbers_of_selections[ad] = numbers_of_selections[ad] + 1\n",
        "    reward = data.values[n, ad]\n",
        "    sums_of_rewards[ad] = sums_of_rewards[ad] + reward\n",
        "    total_reward = total_reward + reward\n",
        "    \n",
        "    \n",
        "    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "2POakggqiykX",
        "colab_type": "code",
        "outputId": "88024926-36dc-4571-d694-3280113005fb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 395
        }
      },
      "cell_type": "code",
      "source": [
        "# Visualising the results\n",
        "\n",
        "plt.hist(ads_selected, color = 'pink')\n",
        "plt.title('Histogram of ads selections')\n",
        "plt.xlabel('Ads')\n",
        "plt.ylabel('Number of times each ad was selected')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0,0.5,'Number of times each ad was selected')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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mcunSJXJyckhOTqZz58706tWLnTt3ArBv3z66devmqKgiIiIux2Ez+Ntuu41BgwYxatQo\nAGbPnk27du2IjIxk06ZNNGjQgLCwMDw9PYmIiGDixIlYLBamTJmCr68vQ4YM4dChQ4wdOxar1cqi\nRYscFVVERMTlWIyK7Ny+QVT3phpt/nEOjXP5Ar5Mq+kIpjLublnTEWoV/U07h8a5hjbRi4iISM1R\nwYuIiLggFbyIiIgLUsGLiIi4IBW8iIiIC1LBi4iIuCAVvIiIiAtSwYuIiLggFbyIiIgLUsGLiIi4\nIBW8iIiIC1LBi4iIuCAVvIiIiAtSwYuIiLggFbyIiIgLUsGLiIi4IBW8iIiIC1LBi4iIuCAVvIiI\niAtSwYuIiLggFbyIiIgLUsGLiIi4II+yfnDmzJlyX9igQYNqDyMiIiLVo8yCHzt2LBaLBcMwSE9P\nx8fHh+LiYnJzc2ncuDG7du1yZk4RERG5DmUW/IEDBwBYsGABQ4cO5e677wYgJSWFbdu2OSediIiI\nVIrpPvgvv/zSXu4AHTp04MSJEw4NJSIiIlVT5gz+V25ubkRHR9OpUycsFgv/+c9/KCgocEY2ERER\nqSTTGfyyZctwc3Pj3XffZePGjdhsNpYtW+aMbCIiIlJJpjN4f39/HnnkEU6fPk27du0oKSnBzU1n\n14mIiNRmpk29fft2Ro8ezaxZswCYP38+mzdvdngwERERqTzTgn/zzTf597//Tf369QGIjIzkvffe\nc3gwERERqTzTgvf19eXmm2+2P/by8sLT09OhoURERKRqTPfB169fnw8++ICCggKOHTvGhx9+iJ+f\nnzOyiYiISCWZzuD/9re/kZqaSk5ODrNnz6agoIAFCxY4I5uIiIhUkukM/uDBgzz//POllm3cuJGx\nY8c6LJSIiIhUTZkF/+WXX3Ls2DHWrl1LXl6efXlRURExMTEqeBERkVqszIK/6aabOH/+PJcvX+bz\nzz+3L7dYLMyYMcN0xUlJSTz11FM0b94cgBYtWvDYY48xY8YMiouLCQgIYMmSJVitVuLi4li3bh1u\nbm6MGjWKkSNHYrPZmDlzJmfOnMHd3Z2FCxfSqFGjanjLIiIirq/Mgg8KCiIoKIju3btz11134ePj\nA0BmZia33nprhVbetWtXVqxYYX88a9YswsPDuf/++1m6dCmxsbGEhYURExNDbGwsnp6ejBgxgtDQ\nUPbt20fdunWJjo7mk08+ITo6WlfQExERqSDTg+yOHTtWasb+zDPP8Pbbb1fqlyUlJdG/f38A+vXr\nR0JCAikpKbRr1w5fX1+8vLwICQkhOTmZhIQEQkNDAejZsyfJycmV+p0iIiK/R6YFHxcXV2oWvnbt\nWrZv316hlZ84cYJJkyYxduxYPv30U/Ly8rBarcAvl8DNyMggMzOz1Gl3fn5+Vy13c3PDYrFQWFh4\nXW9ORETk98r0KPri4mI8PP7vaRaLBcMwTFfctGlTpk6dyv3338+pU6cYP348xcXF9p+XtY7rXf5b\n9et74+Hhbvq86xEQ4Fut65Nr0zjf2PT5XU1j4hwa57KZFvx9993HmDFj6NSpEyUlJSQmJjJw4EDT\nFd92220MGTIEgMaNG3PrrbeSmppKfn4+Xl5enDt3jsDAQAIDA8nMzLS/Lj09neDgYAIDA8nIyKBV\nq1bYbDYMw7DP/suSlZVrmut6BAT4kpFxuVrXKVfTOJcvoKYDVIA+v9L0N+0cGufyv+CYbqKfPHky\nzz77LP7+/gQGBjJ37lyeeOIJ018aFxfHmjVrAMjIyOD8+fMMGzaM+Ph4AHbt2kWfPn3o0KEDqamp\nXLp0iZycHJKTk+ncuTO9evVi586dAOzbt49u3bpV6M2KiIhIBWbwAFeuXMFqtTJu3Dh+/PFHDMPA\nYrGU+5r77ruPZ599lj179mCz2Zg3bx6tW7cmMjKSTZs20aBBA8LCwvD09CQiIoKJEydisViYMmUK\nvr6+DBkyhEOHDjF27FisViuLFi2qljcsIiLye2AxTHZuL1myhB9++IEzZ87w/vvvExMTw4ULF5gz\nZ46zMlZYdW+q0eYf59A4ly/gy7SajmAq4+6WNR2hVtHftHNonKu4if7w4cO89tpr1KlTB4ApU6Zw\n7Nix6ksnIiIi1c604G+66SYA+yb54uLiUkfDi4iISO1jug8+JCSEWbNmkZ6ezptvvsmuXbvo2rWr\nM7KJiIhIJZkW/F//+ld27tyJl5cXZ8+e5dFHH63QaXIiIiJSc8os+FOnTtn/3aZNG9q0aVPqZ7rx\ni4iISO1VZsFPmDDhqqvW/frYYrGwZ88epwQUERGR61dmwe/du9eZOURERKQamR5F/9NPPzFt2jQe\nfvhhADZv3szJkycdnUtERESqwLTg58yZw5/+9Cf7pvqmTZvWyovciIiIyP8xLXibzUb//v3t58F3\n6dLF4aFERESkakwLHuDSpUv2gv/mm28oKChwaCgRERGpGtPz4KdMmcKoUaPIyMjgoYceIisriyVL\nljgjm4iIiFSSacF3796drVu38vXXX2O1WmnWrJn98rUiIiJSO5luoj969CgJCQm0b9+eHTt28D//\n8z8cOXLEGdlERESkkkwL/sUXX6RZs2YcOXKE1NRU5syZw4oVK5yRTURERCqpQneTa9q0KXv27GHU\nqFHcdddduLlV6Ng8ERERqSGmTZ2Xl8eOHTvYvXs3vXv3Jjs7m0uXLjkjm4iIiFSSacFHRESwbds2\n/vrXv+Lj48P69et55JFHnBBNREREKsv0KPpu3brRrVs3++Mnn3zSoYFERESk6rQzXURExAWp4EVE\nRFxQhQr+ypUrAGRmZnLkyBFKSkocGkpERESqxrTg58+fz44dO8jOzmbMmDGsX7+eefPmOSGaiIiI\nVJZpwX/55ZeMHDmSHTt2MHToUJYvX84PP/zgjGwiIiJSSaYF/+t94Pfv3899990HQGFhoWNTiYiI\nSJWYFnyzZs0YMmQIOTk5tG7dmq1bt1KvXj1nZBMREZFKMj0P/sUXX+Trr78mKCgIgLvuuovJkyc7\nPJiIiIhUnmnBA6Snp5OWlgb8snl+1apV7N2716HBREREpPJMC3769OlcvHiRtLQ0QkJCSElJ0dXs\nREREajnTffBnz55lzZo1NGvWjBUrVrBhwwZSU1OdkU1EREQqqcJXsisqKqKgoICGDRty4sQJR2YS\nERGRKjLdRN+9e3dWr17NgAEDGDZsGA0bNtSV7ERERGo504KfOnUqAG5ubnTs2JHz58/Tq1cvhwcT\nERGRyjMt+H79+tGhQwd69+5N7969CQkJcUYuERERqQLTgt+7dy+pqakkJSUxZ84csrKy6NSpE889\n95wz8omIiEglmBa8u7s7bdq0oaioiJKSEj777DOSk5OdkU1EREQqybTgH3nkEdzc3GjTpg2dO3dm\n3Lhx+Pr6Vmjl+fn5PPjgg0yePJkePXowY8YMiouLCQgIYMmSJVitVuLi4li3bh1ubm6MGjWKkSNH\nYrPZmDlzJmfOnMHd3Z2FCxfSqFGjKr9ZERGR3wvT0+Rat26NzWbj+PHjpKWl8e2331JcXFyhlb/+\n+uv269avWLGC8PBwNmzYQJMmTYiNjSU3N5eYmBjeeust1q9fz7p168jOzmb79u3UrVuXjRs3MmnS\nJKKjo6v2LkVERH5nTAs+MjKS9evXs3TpUoKCgli1ahVdunQxXfG3337LiRMnuPfeewFISkqif//+\nwC8H7iUkJJCSkkK7du3w9fXFy8uLkJAQkpOTSUhIIDQ0FICePXtql4CIiMh1Mt1E//XXX3P48GGO\nHDliv+lMZGSk6YoXL17MnDlz2Lp1KwB5eXlYrVYA/P39ycjIIDMzEz8/P/tr/Pz8rlru5uaGxWKh\nsLDQ/noREREpn2nBz58/n169evHoo4/Srl07LBaL6Uq3bt1KcHBwmfvNf73HfFWX/7f69b3x8HCv\n0HMrKiCgYscbSNVonG9s+vyupjFxDo1z2UwLfv369de90v3793Pq1Cn279/P2bNnsVqteHt7k5+f\nj5eXF+fOnSMwMJDAwEAyMzPtr0tPTyc4OJjAwEAyMjJo1aoVNpsNwzAqNHvPysq97qzlCQjwJSPj\ncrWuU66mcS5fQE0HqAB9fqXpb9o5NM7lf8Gp8LXor8eyZcvYsmUL7733HiNHjmTy5Mn07NmT+Ph4\nAHbt2kWfPn3o0KEDqampXLp0iZycHJKTk+ncuTO9evVi586dAOzbt49u3bo5IqaIiIjLqtD94KvD\nk08+SWRkJJs2baJBgwaEhYXh6elJREQEEydOxGKxMGXKFHx9fRkyZAiHDh1i7NixWK1WFi1a5KyY\nIiIiLsFilLGD+9eD48oSFhbmkEBVUd2barT5xzk0zuUL+DKtpiOYyri7ZU1HqFX0N+0cGufyN9GX\nOYP/9NNPAcjKyuL48eN06NCB4uJivvjiCzp27FgrC15ERER+UWbBL1myBIBp06axe/duvLy8ALhy\n5QqzZ892TjoRERGpFNOD7M6cOWMvdwAfHx/OnDnj0FAiIiJSNaYH2TVv3pwxY8bQsWNH3NzcSElJ\noXHjxs7IJiIiIpVkWvAvvfQShw4d4uuvv8YwDB5//HHuueceZ2QTERGRSjIteIvFQnBwMM2aNQOg\nsLCQkSNHEhsb6/BwIiIiUjmmBb969WreeOMNCgsL8fb2pqCggIceesgZ2URERKSSTA+yi4+P59Ch\nQ3To0IHExEReeeUVmjdv7oxsIiIiUkmmBV+nTh2sVis2mw2A/v37s2fPHocHExERkcoz3URfr149\n4uLiaNGiBbNmzSIoKIj09HRnZBMREZFKMi34xYsXc/78eUJDQ1m3bh1nz55l6dKlzsgmIiIilWRa\n8DfffDN33HEHAJMmTXJ4IBEREak6h9wuVkRERGqWCl5ERMQFVeh+8BcvXuTSpUulljVq1MghgURE\nRKTqTAt+/vz5fPDBB9SvX59fbx1vsVh0qpyIiEgtZlrwn332GYmJiVitVmfkERERkWpgug++WbNm\neHp6OiOLiIiIVJMyZ/DLly8HfrmS3bhx4+jUqRPu7u72nz/11FOOTyciIiKVUmbB/1rmDRs2pGHD\nhk4LJCIiIlVXZsFPnToVgOLiYv7zn//QuXNnAPbu3cu9997rlHAiIiJSOab74OfOncuBAwfsjz/7\n7DOee+45h4YSERGRqjEt+JMnTxIREWF/PHPmTE6fPu3QUCIiIlI1pgWfn59Pdna2/fG5c+coKChw\naCgRERGpGtPz4KdMmcKDDz7I7bffTnFxMenp6SxYsMAZ2URERKSSTAu+X79+7N69mxMnTmCxWLjz\nzjt1P3gREZFazrTgi4uLSUpKIisrC4Bjx46xatUq9u7d6/BwIiIiUjmmBT99+nQuXrxIWloaISEh\npKSk8OSTTzojm4iIiFSS6UF2Z8+eZc2aNTRr1owVK1awYcMGUlNTnZFNREREKqnC94MvKiqioKCA\nhg0bcuLECUdmEhERkSoy3UTfvXt3Vq9ezYABAxg2bBgNGzakpKTEGdlERESkkkwLftq0aRQXF+Pu\n7k7Hjh05f/48vXr1ckY2ERERqSTTgi8sLGTz5s38/PPPPPvss6SkpJS6q5yIiIjUPqb74OfNm8eP\nP/5IUlIS8MtpcjNnznR4MBEREak804L/7rvvmDVrFl5eXgCEh4frQjciIiK1nGnBe3j8shXfYrEA\nkJubS35+vmNTiYiISJWY7oMfPHgwEyZM4PTp07z44ot8/PHHhIeHm644Ly+PmTNncv78eQoKCpg8\neTKtWrVixowZFBcXExAQwJIlS7BarcTFxbFu3Trc3NwYNWoUI0eOxGazMXPmTM6cOYO7uzsLFy6k\nUaNG1fKmRUREXJ1pwY8bN4727dvz2WefYbVaWbp0KW3btjVd8b59+2jbti2PP/44P/30E3/5y18I\nCQkhPDyc+++/n6VLlxIbG0tYWBgxMTHExsbi6enJiBEjCA0NZd++fdStW5fo6Gg++eQToqOjWbZs\nWbW8aREREVdnWvAA7du3p3379te14iFDhtj//fPPP3PbbbeRlJTE3/72N+CXm9isXbuWZs2a0a5d\nO3x9fQEICQkhOTmZhIQEwsLCAOjZsydRUVHX9ftFRER+zypU8FUxZswYzp49y6pVq3j00UexWq0A\n+Pv7k5GRQWZmJn5+fvbn+/n5XbXczc0Ni8VCYWGh/fUiIiJSNocX/LvvvstXX33F9OnTMQzDvvy3\n//6t613+W/Xre+PhUb3n6Af8vP7pAAAU30lEQVQE+Fbr+uTaNM43Nn1+V9OYOIfGuWymBX/x4kXS\n09Np3rw5Bw8e5IsvvmDUqFEEBASU+7qjR4/i7+/P7bffTuvWrSkuLqZOnTrk5+fj5eXFuXPnCAwM\nJDAwkMzMTPvr0tPTCQ4OJjAwkIyMDFq1aoXNZsMwDNPZe1ZWbgXfdsUEBPiSkXG5WtcpV9M4l6/8\n/6XVDvr8StPftHNonMv/gmN6mtz06dNJT0/n5MmTLFq0iFtuuYXnnnvO9JceOXKEtWvXApCZmUlu\nbi49e/YkPj4egF27dtGnTx86dOhAamoqly5dIicnh+TkZDp37kyvXr3YuXMn8MsBe926davQmxUR\nEZEKzODz8vLo1asXq1atYty4cYwdO5bdu3ebrnjMmDE899xzhIeHk5+fz/PPP0/btm2JjIxk06ZN\nNGjQgLCwMDw9PYmIiGDixIlYLBamTJmCr68vQ4YM4dChQ4wdOxar1cqiRYuq5Q2LiIj8HlSo4C9c\nuEB8fDwrV67EMAwuXrxoumIvLy+io6OvWv7mm29etWzw4MEMHjy41LJfz30XERGR62e6if6hhx5i\n4MCBdO/endtvv52YmBhtLhcREanlLEZFDk//jUuXLlG3bl1H5amS6j7YQgdwOIfGuXwBX6bVdART\nGXe3rOkItYr+pp1D41zFg+yOHz/OsGHD7JvQ169fT0pKSvWlExERkWpnWvAvvPACL730kv20uCFD\nhmjfuIiISC1XobvJtWrVyv64WbNm9jvMiYiISO1UoYI/deqU/XaxBw4cqNBV5URERKTmmE7FIyMj\nmTx5Mt9//z2dOnWiYcOGLF682BnZREREpJJMC75ly5Zs27aNCxcuYLVa8fHxcUYuERERqQLTgk9L\nS+P999/n8uXLpTbN60A7ERGR2su04J966ikefPBB7rrrLmfkERERkWpgWvANGzZk6tSpzsgiIiIi\n1cS04P/0pz+xcuVKOnbsWOr0uC5dujg0mIiIiFSeacHHxcXx/fff88knn9iXWSwW3nnnHYcGExER\nkcozLfgLFy6wZ88eZ2QRERGRamJ6oZsuXbrw448/OiOLiIiIVBPTGfynn37K22+/Tf369fHw8MAw\nDCwWC/v373dCPBEREakM04J/4403nJFDREREqlGZBX/gwAH69u1LQkLCNX8+YsQIh4USERGRqimz\n4NPS0ujbty+ff/75NX+ughcREam9yiz4//mf/wGgd+/ePPDAA6V+tnHjRsemEhERkSops+C/+uor\njh49ytq1a8nLy7MvLyoqIiYmhrFjxzoloIiIiFy/MgvearVy/vx5Ll++XGozvcViYcaMGU4JJyIi\nIpVTZsEHBQURFBRE9+7dCQ4OdmYmERERqSLTC92o3EVERG48pgUvIiIiN54yC37Lli0AbN682Wlh\nREREpHqUuQ/+9ddfx2azsW7dOiwWy1U/13nwIiIitVeZBT9jxgwOHDhw1VH0v1LBi4iI1F5lFvzA\ngQMZOHAg8fHxDBo0yJmZREREpIpMbzYTHBxMVFQUqampWCwWgoODefrpp/Hz83NGPhEREakE06Po\n586dS5s2bVi6dCmvvPIKd955J1FRUc7IJiIiIpVkOoPPy8vjz3/+s/1xixYt2Lt3r0NDiYiISNWY\nzuDz8vJIT0+3Pz579iyFhYUODSUiIiJVYzqDnzx5MsOGDSMgIADDMLhw4QILFixwRjYRERGpJNOC\nv/fee9m9ezcnT54EoFmzZtx0002OziUiIiJVYFrwAF5eXrRq1crRWURERKSaVKjgK+vll1/m888/\np6ioiP/3//4f7dq1Y8aMGRQXFxMQEMCSJUuwWq3ExcWxbt063NzcGDVqFCNHjsRmszFz5kzOnDmD\nu7s7CxcupFGjRo6MKyIi4jJMC94wjGteqtZMYmIi33zzDZs2bSIrK4uhQ4fSo0cPwsPDuf/++1m6\ndCmxsbGEhYURExNDbGwsnp6ejBgxgtDQUPbt20fdunWJjo7mk08+ITo6mmXLllXqTYqIiPzemB5F\nP378+EqtuEuXLixfvhyAunXrkpeXR1JSEv379wegX79+JCQkkJKSQrt27fD19cXLy4uQkBCSk5NJ\nSEggNDQUgJ49e5KcnFypHCIiIr9HpjP41q1bs3z5cjp27Iinp6d9eY8ePcp9nbu7O97e3gDExsZy\nzz338Mknn2C1WgHw9/cnIyODzMzMUlfF8/Pzu2q5m5sbFouFwsJC++tFRESkbKYF/9VXXwFw5MgR\n+zKLxWJa8L/avXs3sbGxrF27loEDB9qXG4Zxzedf7/Lfql/fGw8P9wrlqqiAAN9qXZ9cm8b5xqbP\n72oaE+fQOJfNtODXr18PVG5f/MGDB1m1ahX//Oc/8fX1xdvbm/z8fLy8vDh37hyBgYEEBgaSmZlp\nf016ejrBwcEEBgaSkZFBq1atsNlsGIZhOnvPysq9rnxmAgJ8yci4XK3rlKtpnMsXUNMBKkCfX2n6\nm3YOjXP5X3BM98EfP36cYcOGcf/99wMQExNDSkqK6S+9fPkyL7/8Mm+88Qa33HIL8Mu+9Pj4eAB2\n7dpFnz596NChA6mpqVy6dImcnBySk5Pp3LkzvXr1YufOnQDs27ePbt26mb9TERERASowg3/hhRd4\n6aWX7FevGzJkCLNmzeLdd98t93UffvghWVlZPP300/ZlixYtYvbs2WzatIkGDRoQFhaGp6cnERER\nTJw4EYvFwpQpU/D19WXIkCEcOnSIsWPHYrVaWbRoURXfqoiIyO+HacF7eHiUushNs2bN8PAwP31+\n9OjRjB49+qrlb7755lXLBg8ezODBg0st+/XcdxEREbl+ppvoPTw8OHXqlH3/+4EDByp0wJuIiIjU\nHNOpeGRkJJMnT+b7778nJCSEO+64g8WLFzsjm4iIiFSSacG3bNmSbdu2ceHCBaxWKz4+Ps7IJSIi\nIlVgWvAnTpzg1Vdf5cSJE1gsFlq0aMHUqVO58847nZFPREREKsG04GfMmEF4eDjTpk0D4PPPP2f6\n9Ols2bLF4eFERESkckwLvk6dOowYMcL+OCgoyH4uu4iIiNROZR5FX1JSQklJCT169GDXrl1cuXKF\nnJwcdu/eTZcuXZyZUURERK5TmTP4u+++G4vFcs1T4jw8PJg0aZJDg4mIiEjllVnwx48fd2YOERER\nqUam++DPnTtHfHw8ly9fLjWbnzp1qkODiYiISOWZXsnu8ccf56uvvsJms1FUVGT/T0RERGov0xn8\nLbfcomvCi4iI3GBMCz40NJS4uDg6duyIu7u7fXmDBg0cGkxEREQqz7Tg09LS2LZtm/2e7gAWi4X9\n+/c7MpeIiIhUgWnBp6SkcPjwYaxWqzPyiIiISDUwPciubdu2FBQUOCOLiIiIVJMKnSZ33333ERQU\nVGof/DvvvOPQYCIiIlJ5pgWvK9aJiIjceEwLvri42Bk5REREpBqZFvzKlSvt/7bZbJw4cYKQkBB6\n9Ojh0GAiIiJSeaYFv379+lKPz58/T3R0tMMCiYiISNWZHkX/3/z9/fnuu+8ckUVERESqiekMfvr0\n6VgsFvvjn3/+GTe36/5eICIiIk5kWvA9e/a0/9tiseDj40OvXr0cGkpERESqxrTghw4d6owcIiIi\nUo3KLPj77ruv1KZ5wzCwWCwUFhaSmZnJV1995ZSAIiIicv3KLPi9e/detWz37t1ER0czfPhwh4YS\nERGRqjHdRA9w8uRJXnzxRTw9PfnHP/5Bo0aNHJ1LREREqqDcgs/NzSUmJoYDBw4wffp0+vbt66xc\nIiIiUgVlnu+2fft2hg0bRr169fjggw9U7iIiIjeQMmfwzz77LE2bNuXgwYN88skn9uW/Hmz3r3/9\nyykBRURE5PqVWfB79uxxZg4RERGpRmUWfMOGDZ2ZQ0Tkdy3gy7SajmAq4+6WNR1BroOuOSsiIuKC\nVPAiIiIuSAUvIiLighxa8F9//TUDBgzg7bffBn65E93DDz9MeHg4Tz31FIWFhQDExcUxfPhwRo4c\nyebNmwGw2WxEREQwduxYxo0bx6lTpxwZVURExKU4rOBzc3OZP38+PXr0sC9bsWIF4eHhbNiwgSZN\nmhAbG2u/mM5bb73F+vXrWbduHdnZ2Wzfvp26deuyceNGJk2aRHR0tKOiioiIuByHFbzVamX16tUE\nBgbalyUlJdG/f38A+vXrR0JCAikpKbRr1w5fX1+8vLwICQkhOTmZhIQEQkNDgV9uWZucnOyoqCIi\nIi7HYQXv4eGBl5dXqWV5eXlYrVYA/P39ycjIIDMzEz8/P/tz/Pz8rlru5uZmv5OdiIiImKvQzWYc\nwTCMaln+W/Xre+Ph4V6lXP8tIMC3Wtcn16ZxvrHp87uaK45JbXxPtTFTbeHUgvf29iY/Px8vLy/O\nnTtHYGAggYGBZGZm2p+Tnp5OcHAwgYGBZGRk0KpVK2w2G4Zh2Gf/ZcnKyq3WvAEBvmRkXK7WdcrV\nNM7lC6jpABWgz6+0yvxN63O+fvr/jvK/4Dj1NLmePXsSHx8PwK5du+jTpw8dOnQgNTWVS5cukZOT\nQ3JyMp07d6ZXr17s3LkTgH379tGtWzdnRhUREbmhOWwGf/ToURYvXsxPP/2Eh4cH8fHxvPLKK8yc\nOZNNmzbRoEEDwsLC8PT0JCIigokTJ2KxWJgyZQq+vr4MGTKEQ4cOMXbsWKxWK4sWLXJUVBEREZdj\nMSqyc/sGUd2barT5xzk0zuXTNcpvPJXaRK/P+brp/ztq0SZ6ERERcQ4VvIiIiAtSwYuIiLggFbyI\niIgLUsGLiIi4IBW8iIiIC1LBi4iIuCAVvIiIiAuqsZvN3BAOHKn114eubReeEBGR2kEzeBERERek\nghcREXFBKngREREXpIIXERFxQSp4ERERF6SCFxERcUEqeBERERekghcREXFBKngREREXpIIXERFx\nQSp4ERERF6SCFxERcUEqeBEREReku8nd4AK+TKvpCOXS3e5ERGqGZvAiIiIuSDN4+d2r7VtBREQq\nQzN4ERERF6SCFxERcUHaRC8iLq8mdsMEOP03ipSmghcRkQqpjcer/PaLlM7aKU2b6EVERFyQCl5E\nRMQFaRO9OFRFN+lpf6WIVFVt3IXw35y5G0EzeBERERekGbyIVNmNMHMS+b3RDF5ERMQFqeBFRERc\nUK3eRP/SSy+RkpKCxWIhKiqK9u3b13QkERGRG0KtLfjPPvuMH374gU2bNvHtt98SFRXFpk2bajqW\niIjIDaHWbqJPSEhgwIABAAQFBXHx4kWuXLlSw6lERERuDLW24DMzM6lfv779sZ+fHxkZGTWYSERE\n5MZRazfR/zfDMEyfExDgW72/tG/n6l2fiIj8rjnzol61dgYfGBhIZmam/XF6ejoBAbremYiISEXU\n2oLv1asX8fHxABw7dozAwEB8fHxqOJWIiMiNodZuog8JCaFNmzaMGTMGi8XC3LlzazqSiIjIDcNi\nVGTntoiIiNxQau0mehEREak8FbyIiIgLUsGX4aWXXmL06NGMGTOGL774oqbjuKyXX36Z0aNHM3z4\ncHbt2lXTcVxafn4+AwYM4P3336/pKC4rLi6OP/7xjwwbNoz9+/fXdByXlJOTw9SpU3n44YcZM2YM\nBw8erOlItVatPciuJukyuc6RmJjIN998w6ZNm8jKymLo0KEMHDiwpmO5rNdff5169erVdAyXlZWV\nRUxMDFu2bCE3N5dXX32Ve++9t6ZjuZwPPviAZs2aERERwblz55gwYQI7d+6s6Vi1kgr+Gsq6TK5O\n06teXbp0sd9AqG7duuTl5VFcXIy7u3sNJ3M93377LSdOnFDhOFBCQgI9evTAx8cHHx8f5s+fX9OR\nXFL9+vVJS0sD4NKlS6WueCqlaRP9Negyuc7h7u6Ot7c3ALGxsdxzzz0qdwdZvHgxM2fOrOkYLu30\n6dPk5+czadIkwsPDSUhIqOlILumBBx7gzJkzhIaGMm7cOCIjI2s6Uq2lGXwF6ExCx9q9ezexsbGs\nXbu2pqO4pK1btxIcHEyjRo1qOorLy87O5rXXXuPMmTOMHz+effv2YbFYajqWS/n3v/9NgwYNWLNm\nDcePHycqKkrHlZRBBX8Nukyu8xw8eJBVq1bxz3/+E1/far6XgACwf/9+Tp06xf79+zl79ixWq5U/\n/OEP9OzZs6ajuRR/f386duyIh4cHjRs3pk6dOly4cAF/f/+ajuZSkpOT6d27NwCtWrUiPT1du/bK\noE3016DL5DrH5cuXefnll3njjTe45ZZbajqOy1q2bBlbtmzhvffeY+TIkUyePFnl7gC9e/cmMTGR\nkpISsrKyyM3N1f5hB2jSpAkpKSkA/PTTT9SpU0flXgbN4K9Bl8l1jg8//JCsrCyefvpp+7LFixfT\noEGDGkwlUjm33XYbgwYNYtSoUQDMnj0bNzfNoarb6NGjiYqKYty4cRQVFTFv3ryajlRr6VK1IiIi\nLkhfL0VERFyQCl5ERMQFqeBFRERckApeRETEBangRUREXJAKXkRMpaenc/fdd/OPf/zjmj8/dOgQ\nDz/8sJNTiUh5VPAiYmrr1q0EBQXpkqAiNxAVvIiY2rJlC1FRUeTl5ZGcnAz8cg+BBx54gIkTJ7J7\n9277c9etW8fw4cMZN24cjz32GFlZWTUVW+R3TVeyE5FyHT58mKKiIrp3705YWBjvv/8+ISEhvPDC\nC7z55psEBQXx4osv2p+/YsUK4uPjufXWWzl48CDp6em6ZKtIDdAMXkTKFRsby9ChQ7FYLAwbNowd\nO3Zw7tw5CgoKCAoKAqB79+72548YMYLHHnuM119/nTvuuIOWLVvWVHSR3zXN4EWkTFeuXGHXrl3c\nfvvtfPTRRwCUlJSQkJBQ6jaoxcXF9n/PmjWLn376iQMHDjBlyhQiIyPp27ev07OL/N6p4EWkTNu3\nb6dLly6ljp7ftm0b7733Hu7u7pw8eZKmTZty6NAhAC5evMi//vUvpkyZQnh4OIZhkJqaqoIXqQEq\neBEpU2xsLFOmTCm1bNCgQSxatIgJEyYwZcoUGjVqRJMmTQCoV68eOTk5jBgxgrp16+Lh4cGCBQtq\nIrrI757uJiciIuKCdJCdiIiIC1LBi4iIuCAVvIiIiAtSwYuIiLggFbyIiIgLUsGLiIi4IBW8iIiI\nC1LBi4iIuKD/D0NEvdreJyTzAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fae2429c5c0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "YsnnlFySi2rR",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Implementing Thompson sampling\n",
        "\n",
        "import random\n",
        "N = 10000\n",
        "d = 10\n",
        "ads_selected = []\n",
        "numbers_of_rewards_1 = [0] * d\n",
        "numbers_of_rewards_0 = [0] * d\n",
        "total_reward = 0\n",
        "for n in range(0, N):\n",
        "    ad = 0\n",
        "    max_random = 0\n",
        "    for i in range(0, d):\n",
        "        random_beta = random.betavariate(numbers_of_rewards_1[i] + 1, numbers_of_rewards_0[i] + 1)\n",
        "        if random_beta > max_random:\n",
        "            max_random = random_beta\n",
        "            ad = i\n",
        "    ads_selected.append(ad)\n",
        "    reward = data.values[n, ad]\n",
        "    if reward == 1:\n",
        "        numbers_of_rewards_1[ad] = numbers_of_rewards_1[ad] + 1\n",
        "    else:\n",
        "        numbers_of_rewards_0[ad] = numbers_of_rewards_0[ad] + 1\n",
        "    total_reward = total_reward + reward"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "PRZBUJdMjmng",
        "colab_type": "code",
        "outputId": "6cc470f2-c8e8-4f05-d7b8-2fa58f755d63",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 395
        }
      },
      "cell_type": "code",
      "source": [
        "# Visualising the results\n",
        "\n",
        "plt.hist(ads_selected, color = 'orange')\n",
        "plt.title('Histogram of ads selections')\n",
        "plt.xlabel('Ads')\n",
        "plt.ylabel('Number of times each ad was selected')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0,0.5,'Number of times each ad was selected')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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2rN2DAQAA25kW/K+//qpx48apTJkykqSQkBBudAMAQClnWvBubn/uxbdYLJKk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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fae241866d8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "TRLs7XZQj0w6",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}