19_upper_confidence_bound.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "QJdrJJQUv3-k"
   },
   "source": [
    "# Upper Confidence Bound (UCB)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2XCjepjJwEv-"
   },
   "source": [
    "## Importing the libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "l_mBkG3YwNTt"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "npqlXjaNwYTv"
   },
   "source": [
    "## Importing the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "HMJfUVLVwcFc"
   },
   "outputs": [],
   "source": [
    "dataset = pd.read_csv('Ads_CTR_Optimisation.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PaSbots_wfoB"
   },
   "source": [
    "## Implementing UCB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "V1K7jgDFwkRd"
   },
   "outputs": [],
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AXftWcjDwsYj"
   },
   "source": [
    "## Visualising the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 2141,
     "status": "ok",
     "timestamp": 1586416167859,
     "user": {
      "displayName": "Hadelin de Ponteves",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GhEuXdT7eQweUmRPW8_laJuPggSK6hfvpl5a6WBaA=s64",
      "userId": "15047218817161520419"
     },
     "user_tz": -240
    },
    "id": "eVyD_EDXwtkK",
    "outputId": "8cb6b886-8482-43be-e4ee-0313c17508c6"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "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()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "authorship_tag": "ABX9TyMz+roSgJuEsprRsPKmwoVD",
   "collapsed_sections": [],
   "name": "Upper Confidence Bound",
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}