Complex Time Behaviour.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "import gym, recogym\n",
    "from copy import deepcopy\n",
    "from recogym import env_1_args\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib notebook\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "plt.rcParams['figure.figsize'] = [8, 4]\n",
    "\n",
    "NumberOfUsers = 1\n",
    "NumberOfSamples = 20\n",
    "\n",
    "env_1_args['random_seed'] = 777\n",
    "env_1_args['sigma_omega'] = 1 # Set a big value do diversify products.\n",
    "\n",
    "env = gym.make('reco-gym-v1')\n",
    "env.init_gym(env_1_args)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "## Tick-Tack Time\n",
    "\n",
    "The most straightforward time interpretation in _RecoGym_ is tick-tack. Thus, if you look at logs of data, you shall find that time is changed incrementally _`+1`_ at each step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "std_data = deepcopy(env).generate_logs(NumberOfUsers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {}
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   "outputs": [
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       "      <td>5</td>\n",
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       "      <td>6</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>None</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
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       "      <th>10</th>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>None</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>organic</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>12</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
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       "      <td>0.1</td>\n",
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       "      <td>8.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
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       "      <th>15</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
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       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
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       "      <th>17</th>\n",
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       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
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       "      <th>18</th>\n",
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       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
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       "      <td>4.0</td>\n",
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      "text/plain": [
       "      a    c   ps                                               ps-a   t  u  \\\n",
       "0   NaN  NaN  NaN                                               None   0  0   \n",
       "1   NaN  NaN  NaN                                               None   1  0   \n",
       "2   NaN  NaN  NaN                                               None   2  0   \n",
       "3   NaN  NaN  NaN                                               None   3  0   \n",
       "4   NaN  NaN  NaN                                               None   4  0   \n",
       "5   NaN  NaN  NaN                                               None   5  0   \n",
       "6   NaN  NaN  NaN                                               None   6  0   \n",
       "7   NaN  NaN  NaN                                               None   7  0   \n",
       "8   NaN  NaN  NaN                                               None   8  0   \n",
       "9   NaN  NaN  NaN                                               None   9  0   \n",
       "10  NaN  NaN  NaN                                               None  10  0   \n",
       "11  NaN  NaN  NaN                                               None  11  0   \n",
       "12  3.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...  12  0   \n",
       "13  3.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...  13  0   \n",
       "14  8.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...  14  0   \n",
       "15  6.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...  15  0   \n",
       "16  NaN  NaN  NaN                                               None  16  0   \n",
       "17  NaN  NaN  NaN                                               None  17  0   \n",
       "18  NaN  NaN  NaN                                               None  18  0   \n",
       "19  4.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...  19  0   \n",
       "\n",
       "      v        z  \n",
       "0   0.0  organic  \n",
       "1   0.0  organic  \n",
       "2   0.0  organic  \n",
       "3   0.0  organic  \n",
       "4   0.0  organic  \n",
       "5   0.0  organic  \n",
       "6   0.0  organic  \n",
       "7   7.0  organic  \n",
       "8   7.0  organic  \n",
       "9   0.0  organic  \n",
       "10  1.0  organic  \n",
       "11  2.0  organic  \n",
       "12  NaN   bandit  \n",
       "13  NaN   bandit  \n",
       "14  NaN   bandit  \n",
       "15  NaN   bandit  \n",
       "16  8.0  organic  \n",
       "17  0.0  organic  \n",
       "18  0.0  organic  \n",
       "19  NaN   bandit  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std_data[:NumberOfSamples]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data Shape:\n",
      " (111, 8)\n"
     ]
    }
   ],
   "source": [
    "print(\"Data Shape:\\n\", std_data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "*Note:* the column _**`t`**_ represents the time of the event."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "## Normally Distributed Time Changes\n",
    "\n",
    "For the _Normally Distributed Time Changes_, the time is changed incrementally by the value in the range _`[0; 1]`_.\n",
    "\n",
    "By default, _Normally Distributed Time Changes_ uses these values for drawing _Normal Distribution_:\n",
    "* $\\mu=0$\n",
    "* $\\sigma=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "from recogym import Configuration\n",
    "\n",
    "from recogym import NormalTimeGenerator\n",
    "\n",
    "normal_time_env_01 = {\n",
    "    **env_1_args,\n",
    "    'time_generator': NormalTimeGenerator(Configuration(env_1_args))\n",
    "}\n",
    "\n",
    "env.init_gym(normal_time_env_01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "data_01 = deepcopy(env).generate_logs(NumberOfUsers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
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       "      <th>4</th>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>2.069776</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
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       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>2.976127</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>3.742363</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>4.568417</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>5.892100</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>7.644545</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>8.646994</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>9.191803</td>\n",
       "      <td>0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>11.086964</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>11.856322</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>13.259417</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>13.891885</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>14.450759</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>15.683990</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>16.123494</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>17.038281</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      a    c   ps                                               ps-a  \\\n",
       "0   NaN  NaN  NaN                                               None   \n",
       "1   NaN  NaN  NaN                                               None   \n",
       "2   NaN  NaN  NaN                                               None   \n",
       "3   NaN  NaN  NaN                                               None   \n",
       "4   NaN  NaN  NaN                                               None   \n",
       "5   NaN  NaN  NaN                                               None   \n",
       "6   NaN  NaN  NaN                                               None   \n",
       "7   NaN  NaN  NaN                                               None   \n",
       "8   NaN  NaN  NaN                                               None   \n",
       "9   NaN  NaN  NaN                                               None   \n",
       "10  NaN  NaN  NaN                                               None   \n",
       "11  NaN  NaN  NaN                                               None   \n",
       "12  3.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "13  3.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "14  8.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "15  6.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "16  NaN  NaN  NaN                                               None   \n",
       "17  NaN  NaN  NaN                                               None   \n",
       "18  NaN  NaN  NaN                                               None   \n",
       "19  4.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "\n",
       "            t  u    v        z  \n",
       "0    0.000000  0  0.0  organic  \n",
       "1    0.468209  0  0.0  organic  \n",
       "2    1.291034  0  0.0  organic  \n",
       "3    1.356414  0  0.0  organic  \n",
       "4    2.069776  0  0.0  organic  \n",
       "5    2.976127  0  0.0  organic  \n",
       "6    3.742363  0  0.0  organic  \n",
       "7    4.568417  0  7.0  organic  \n",
       "8    5.892100  0  7.0  organic  \n",
       "9    7.644545  0  8.0  organic  \n",
       "10   8.646994  0  8.0  organic  \n",
       "11   9.191803  0  2.0  organic  \n",
       "12  11.086964  0  NaN   bandit  \n",
       "13  11.856322  0  NaN   bandit  \n",
       "14  13.259417  0  NaN   bandit  \n",
       "15  13.891885  0  NaN   bandit  \n",
       "16  14.450759  0  8.0  organic  \n",
       "17  15.683990  0  1.0  organic  \n",
       "18  16.123494  0  0.0  organic  \n",
       "19  17.038281  0  NaN   bandit  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_01[:NumberOfSamples]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data Shape:\n",
      " (111, 8)\n"
     ]
    }
   ],
   "source": [
    "print(\"Data Shape:\\n\", data_01.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "For a more significant value of $\\mu$ but small $\\sigma$, we shall see that the time advances faster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "normal_time_env_02 = {\n",
    "    **env_1_args,\n",
    "    'time_generator': NormalTimeGenerator(Configuration({\n",
    "        **env_1_args,\n",
    "        'normal_time_mu': 10,\n",
    "        'normal_time_sigma': 0,\n",
    "    }))\n",
    "}\n",
    "\n",
    "env.init_gym(normal_time_env_02)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "data_02 = deepcopy(env).generate_logs(NumberOfUsers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "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>a</th>\n",
       "      <th>c</th>\n",
       "      <th>ps</th>\n",
       "      <th>ps-a</th>\n",
       "      <th>t</th>\n",
       "      <th>u</th>\n",
       "      <th>v</th>\n",
       "      <th>z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>20.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>30.0</td>\n",
       "      <td>0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>40.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>60.0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>70.0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>90.0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>100.0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>110.0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>120.0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>130.0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>140.0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>150.0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>160.0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>170.0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>180.0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>190.0</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      a    c   ps                                               ps-a      t  \\\n",
       "0   NaN  NaN  NaN                                               None    0.0   \n",
       "1   NaN  NaN  NaN                                               None   10.0   \n",
       "2   NaN  NaN  NaN                                               None   20.0   \n",
       "3   NaN  NaN  NaN                                               None   30.0   \n",
       "4   NaN  NaN  NaN                                               None   40.0   \n",
       "5   NaN  NaN  NaN                                               None   50.0   \n",
       "6   NaN  NaN  NaN                                               None   60.0   \n",
       "7   NaN  NaN  NaN                                               None   70.0   \n",
       "8   NaN  NaN  NaN                                               None   80.0   \n",
       "9   NaN  NaN  NaN                                               None   90.0   \n",
       "10  NaN  NaN  NaN                                               None  100.0   \n",
       "11  NaN  NaN  NaN                                               None  110.0   \n",
       "12  3.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...  120.0   \n",
       "13  3.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...  130.0   \n",
       "14  8.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...  140.0   \n",
       "15  6.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...  150.0   \n",
       "16  NaN  NaN  NaN                                               None  160.0   \n",
       "17  NaN  NaN  NaN                                               None  170.0   \n",
       "18  NaN  NaN  NaN                                               None  180.0   \n",
       "19  4.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...  190.0   \n",
       "\n",
       "    u    v        z  \n",
       "0   0  0.0  organic  \n",
       "1   0  0.0  organic  \n",
       "2   0  0.0  organic  \n",
       "3   0  9.0  organic  \n",
       "4   0  0.0  organic  \n",
       "5   0  7.0  organic  \n",
       "6   0  7.0  organic  \n",
       "7   0  7.0  organic  \n",
       "8   0  7.0  organic  \n",
       "9   0  8.0  organic  \n",
       "10  0  8.0  organic  \n",
       "11  0  8.0  organic  \n",
       "12  0  NaN   bandit  \n",
       "13  0  NaN   bandit  \n",
       "14  0  NaN   bandit  \n",
       "15  0  NaN   bandit  \n",
       "16  0  8.0  organic  \n",
       "17  0  8.0  organic  \n",
       "18  0  8.0  organic  \n",
       "19  0  NaN   bandit  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_02[:NumberOfSamples]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data Shape:\n",
      " (111, 8)\n"
     ]
    }
   ],
   "source": [
    "print(\"Data Shape:\\n\", data_02.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "Here, you shall find yet another extreme when $\\mu$ is quite small, but $\\sigma$ is big."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "normal_time_env_03 = {\n",
    "    **env_1_args,\n",
    "    'time_generator': NormalTimeGenerator(Configuration({\n",
    "        **env_1_args,\n",
    "        'normal_time_mu': 0.1,\n",
    "        'normal_time_sigma': 10,\n",
    "    }))\n",
    "}\n",
    "\n",
    "env.init_gym(normal_time_env_03)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "data_03 = deepcopy(env).generate_logs(NumberOfUsers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
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       "      <td>organic</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>12.710336</td>\n",
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       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>13.264138</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
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       "    <tr>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>20.297757</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>organic</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>29.461266</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>37.223633</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>45.584174</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>58.721001</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>76.145447</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>86.269937</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>91.818032</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>110.869641</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>118.463216</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>132.394175</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>138.618850</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>144.107586</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>156.339900</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>160.634936</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>169.882808</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      a    c   ps                                               ps-a  \\\n",
       "0   NaN  NaN  NaN                                               None   \n",
       "1   NaN  NaN  NaN                                               None   \n",
       "2   NaN  NaN  NaN                                               None   \n",
       "3   NaN  NaN  NaN                                               None   \n",
       "4   NaN  NaN  NaN                                               None   \n",
       "5   NaN  NaN  NaN                                               None   \n",
       "6   NaN  NaN  NaN                                               None   \n",
       "7   NaN  NaN  NaN                                               None   \n",
       "8   NaN  NaN  NaN                                               None   \n",
       "9   NaN  NaN  NaN                                               None   \n",
       "10  NaN  NaN  NaN                                               None   \n",
       "11  NaN  NaN  NaN                                               None   \n",
       "12  3.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "13  3.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "14  8.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "15  6.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "16  NaN  NaN  NaN                                               None   \n",
       "17  NaN  NaN  NaN                                               None   \n",
       "18  NaN  NaN  NaN                                               None   \n",
       "19  4.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "\n",
       "             t  u    v        z  \n",
       "0     0.000000  0  0.0  organic  \n",
       "1     4.582088  0  0.0  organic  \n",
       "2    12.710336  0  0.0  organic  \n",
       "3    13.264138  0  0.0  organic  \n",
       "4    20.297757  0  0.0  organic  \n",
       "5    29.461266  0  7.0  organic  \n",
       "6    37.223633  0  7.0  organic  \n",
       "7    45.584174  0  7.0  organic  \n",
       "8    58.721001  0  7.0  organic  \n",
       "9    76.145447  0  8.0  organic  \n",
       "10   86.269937  0  8.0  organic  \n",
       "11   91.818032  0  8.0  organic  \n",
       "12  110.869641  0  NaN   bandit  \n",
       "13  118.463216  0  NaN   bandit  \n",
       "14  132.394175  0  NaN   bandit  \n",
       "15  138.618850  0  NaN   bandit  \n",
       "16  144.107586  0  8.0  organic  \n",
       "17  156.339900  0  1.0  organic  \n",
       "18  160.634936  0  1.0  organic  \n",
       "19  169.882808  0  NaN   bandit  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_03[:NumberOfSamples]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data Shape:\n",
      " (111, 8)\n"
     ]
    }
   ],
   "source": [
    "print(\"Data Shape:\\n\", data_03.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "Finally, let's analyse the environment where $\\Omega_{\\sigma}$ is changed _**both**_ for _Organic_ and _Bandit_ events with _Normally Distributed Time Changes_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "normal_time_env_04 = {\n",
    "    **env_1_args,\n",
    "    'change_omega_for_bandits': True,\n",
    "    'time_generator': NormalTimeGenerator(Configuration({\n",
    "        **env_1_args,\n",
    "        'normal_time_mu': 1,\n",
    "        'normal_time_sigma': 1,\n",
    "    })),\n",
    "}\n",
    "\n",
    "env.init_gym(normal_time_env_04)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "data_04 = deepcopy(env).generate_logs(NumberOfUsers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
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       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>1.930224</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>3.836575</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>5.602812</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>7.428866</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>7.752549</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>8.504993</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>10.507442</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>None</td>\n",
       "      <td>12.052252</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>organic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>14.947413</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>15.178055</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>15.581151</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>15.948684</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>16.389810</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>7.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>16.623041</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>17.183538</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...</td>\n",
       "      <td>19.098325</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bandit</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      a    c   ps                                               ps-a  \\\n",
       "0   NaN  NaN  NaN                                               None   \n",
       "1   NaN  NaN  NaN                                               None   \n",
       "2   NaN  NaN  NaN                                               None   \n",
       "3   NaN  NaN  NaN                                               None   \n",
       "4   NaN  NaN  NaN                                               None   \n",
       "5   NaN  NaN  NaN                                               None   \n",
       "6   NaN  NaN  NaN                                               None   \n",
       "7   NaN  NaN  NaN                                               None   \n",
       "8   NaN  NaN  NaN                                               None   \n",
       "9   NaN  NaN  NaN                                               None   \n",
       "10  NaN  NaN  NaN                                               None   \n",
       "11  NaN  NaN  NaN                                               None   \n",
       "12  3.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "13  4.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "14  8.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "15  2.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "16  9.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "17  7.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "18  3.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "19  4.0  0.0  0.1  [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, ...   \n",
       "\n",
       "            t  u    v        z  \n",
       "0    0.000000  0  0.0  organic  \n",
       "1    0.531791  0  0.0  organic  \n",
       "2    0.708966  0  0.0  organic  \n",
       "3    1.643586  0  0.0  organic  \n",
       "4    1.930224  0  0.0  organic  \n",
       "5    3.836575  0  7.0  organic  \n",
       "6    5.602812  0  8.0  organic  \n",
       "7    7.428866  0  7.0  organic  \n",
       "8    7.752549  0  8.0  organic  \n",
       "9    8.504993  0  8.0  organic  \n",
       "10  10.507442  0  8.0  organic  \n",
       "11  12.052252  0  8.0  organic  \n",
       "12  14.947413  0  NaN   bandit  \n",
       "13  15.178055  0  NaN   bandit  \n",
       "14  15.581151  0  NaN   bandit  \n",
       "15  15.948684  0  NaN   bandit  \n",
       "16  16.389810  0  NaN   bandit  \n",
       "17  16.623041  0  NaN   bandit  \n",
       "18  17.183538  0  NaN   bandit  \n",
       "19  19.098325  0  NaN   bandit  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_04[:NumberOfSamples]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data Shape:\n",
      " (58, 8)\n"
     ]
    }
   ],
   "source": [
    "print(\"Data Shape:\\n\", data_04.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "## Logistic Regression with a Feature Set Built with Time\n",
    "\n",
    "In _[Likelihood Agents](./Likelihood%20Agents.ipynb)_ notebook you can find a study related to a feature set that incorporates the notion _Time_.\n",
    "\n",
    "Now, having a non-linear _Time Generator_, we are going to check how that affects _`Agent`_ performance.\n",
    "\n",
    "To make the study more complecated, we are going to change the state of _RecoGym_ _**both**_ for _Bandit_ and _Organic_ _`Events`_ (by default, only _Organic_ _`Events`_ change the state i.e. $\\omega_{u,t}$).\n",
    "\n",
    "Below, you shall find performance of different _`Agents`_ with different history functions, namely:\n",
    "* $\\frac{1}{1 + t}$\n",
    "* $\\frac{1}{1 + \\ln(1 + t)}$\n",
    "* $e^{-t}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "from recogym import Configuration\n",
    "\n",
    "from recogym.agents import RandomAgent, random_args\n",
    "from recogym.agents import LogregPolyAgent, logreg_poly_args\n",
    "\n",
    "def build_exploration_data(\n",
    "        env,\n",
    "        time_functions,\n",
    "        num_initial_train_users = 10000,\n",
    "        num_step_users = 10000\n",
    "):\n",
    "    time_env = {\n",
    "        **env_1_args,\n",
    "        'change_omega_for_bandits': True,\n",
    "        'time_generator': NormalTimeGenerator(Configuration({\n",
    "            **env_1_args,\n",
    "            'normal_time_mu': 1,\n",
    "            'normal_time_sigma': 1,\n",
    "        })),\n",
    "    }\n",
    "\n",
    "    def test_agents(agents):\n",
    "        for agent_key in agents:\n",
    "            stats = recogym.test_agent(\n",
    "                deepcopy(env),\n",
    "                deepcopy(agents[agent_key]),\n",
    "                10000,\n",
    "                10000\n",
    "            )\n",
    "            print(f\"Agent: {agent_key}\\n\", stats)\n",
    "\n",
    "    print(\"Agents without History Functions\")\n",
    "    test_agents(\n",
    "        {\n",
    "            'Logreg Poly': LogregPolyAgent(Configuration({\n",
    "                **env_1_args,\n",
    "                **logreg_poly_args,\n",
    "            })),\n",
    "            'Logreg Poly IPS': LogregPolyAgent(Configuration({\n",
    "                **env_1_args,\n",
    "                **logreg_poly_args,\n",
    "                'with_ips': True,\n",
    "            })),\n",
    "        }\n",
    "    )\n",
    "\n",
    "    for time_function_key in time_functions:\n",
    "        print(f\"Agents wit History Function: {time_function_key}\")\n",
    "        time_function = time_functions[time_function_key]\n",
    "        test_agents(\n",
    "            {\n",
    "                'Logreg Poly with History': LogregPolyAgent(Configuration({\n",
    "                    **env_1_args,\n",
    "                    **logreg_poly_args,\n",
    "                    'weight_history_function': time_function,\n",
    "                })),\n",
    "                'Logreg Poly IPS with History': LogregPolyAgent(Configuration({\n",
    "                    **env_1_args,\n",
    "                    **logreg_poly_args,\n",
    "                    'with_ips': True,\n",
    "                    'weight_history_function': time_function,\n",
    "                }))\n",
    "            }\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Agents without History Functions\n",
      "Start: Agent Training #0\n",
      "Start: Agent Testing #0\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "build_exploration_data(\n",
    "    env,\n",
    "    {\n",
    "        '1/(1 + t)': lambda t: 1.0 / (1.0 + t),\n",
    "        '1/(1 + ln(1 + t))': lambda t: 1.0 / (1.0 + np.log(1.0 + t)),\n",
    "        'exp(-t)': lambda t: np.exp(-1.0 * t),\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {}
   },
   "source": [
    "# Conclusion\n",
    "\n",
    "The notion _time_ definitely plays an important role in click prediction. Therefore, the ability to define a complex time behaviour in _RecoGym_ allows to simulate more realistic scenarios, as result, it allows to approbate some nontrivial models."
   ]
  }
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