upper_confidence_bound.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/sunnyy6/first-repo/blob/main/upper_confidence_bound.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QJdrJJQUv3-k"
      },
      "source": [
        "# Upper Confidence Bound (UCB)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2XCjepjJwEv-"
      },
      "source": [
        "## Importing the libraries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l_mBkG3YwNTt"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "npqlXjaNwYTv"
      },
      "source": [
        "## Importing the dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HMJfUVLVwcFc"
      },
      "source": [
        "dataset = pd.read_csv('Ads_CTR_Optimisation.csv')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PaSbots_wfoB"
      },
      "source": [
        "## Implementing UCB"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V1K7jgDFwkRd"
      },
      "source": [
        "import math\n",
        "N = 10000\n",
        "d = 10\n",
        "ads_selected = []\n",
        "numbers_of_selections = [0] * d\n",
        "sums_of_rewards = [0] * d\n",
        "total_reward = 0\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 = dataset.values[n, ad]\n",
        "  sums_of_rewards[ad] = sums_of_rewards[ad] + reward\n",
        "  total_reward = total_reward + reward"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AXftWcjDwsYj"
      },
      "source": [
        "## Visualising the results"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eVyD_EDXwtkK",
        "outputId": "45843b84-4a0f-453f-be68-07cd203a72ae",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        }
      },
      "source": [
        "plt.hist(ads_selected)\n",
        "plt.title('Histogram of ads selections')\n",
        "plt.xlabel('Ads')\n",
        "plt.ylabel('Number of times each ad was selected')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}