CMAB - CUCB Disjoint Window, Dependency v1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import random\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "%matplotlib inline\n",
    "from matplotlib.pyplot import figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "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>Probability</th>\n",
       "      <th>Arm1</th>\n",
       "      <th>Arm2</th>\n",
       "      <th>Arm3</th>\n",
       "      <th>Arm4</th>\n",
       "      <th>Arm5</th>\n",
       "      <th>Arm6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.23</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.52</td>\n",
       "      <td>0.50</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.62</td>\n",
       "      <td>0.60</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.81</td>\n",
       "      <td>0.79</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.45</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.90</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Probability  Arm1  Arm2  Arm3  Arm4  Arm5  Arm6\n",
       "0          0.2  0.00  0.15  0.23  0.21  0.00  0.30\n",
       "1          0.2  0.10  0.24  0.52  0.50  0.10  0.48\n",
       "2          0.2  0.15  0.34  0.62  0.60  0.15  0.68\n",
       "3          0.2  0.30  0.40  0.81  0.79  0.30  0.80\n",
       "4          0.2  0.40  0.45  1.00  0.98  0.40  0.90"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1 = {'Probability': np.ones(5)*0.2,\n",
    "        'Arm1': [0, 0.1, 0.15, 0.3, 0.4],\n",
    "        'Arm2': [0.15, 0.24, 0.34, 0.4, 0.45],\n",
    "        'Arm3': [0.23, 0.52, 0.62, 0.81, 1],\n",
    "        'Arm4': [0.21, 0.50, 0.60, 0.79, 0.98], #arm4 has similar prob dist to arm3\n",
    "        'Arm5': [0, 0.1, 0.15, 0.3, 0.4], #arm5 has same prob dist as arm1\n",
    "        'Arm6': [0.30, 0.48, 0.68, 0.8, 0.9] #arm6 is dependent on arm2, it's double arm2\n",
    "       }\n",
    "\n",
    "df1 = pd.DataFrame(data1)\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Distribution of Rewards for Each Arm')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.boxplot(x=\"variable\", y=\"value\", data=pd.melt(df1[['Arm1','Arm2','Arm3','Arm4','Arm5','Arm6']]))\n",
    "plt.title(\"Distribution of Rewards for Each Arm\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#e.g. trying arms with different types of distributions\n",
    "arr = np.arange(0.01, 1.01, 0.01) #probability dist values\n",
    "np.random.choice(arr)     #one random value within probability dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 , 0.11,\n",
       "       0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21, 0.22,\n",
       "       0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32, 0.33,\n",
       "       0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43, 0.44,\n",
       "       0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54, 0.55,\n",
       "       0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65, 0.66,\n",
       "       0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77,\n",
       "       0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87, 0.88,\n",
       "       0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99,\n",
       "       1.  ])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(0.01, 1.01, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "arm1R = [] #arm1 rewards list\n",
    "arm2R = [] #arm2 rewards list\n",
    "arm3R = [] #arm3 rewards list\n",
    "arm4R = [] #arm4 rewards list\n",
    "arm5R = [] #arm5 rewards list\n",
    "arm6R = [] #arm6 rewards list\n",
    "\n",
    "#arm1 dist\n",
    "for i in range(1000):\n",
    "    if np.random.choice(arr) < 0.21:  \n",
    "        arm1 = 0    #20% chance\n",
    "    elif np.random.choice(arr) < 0.41:\n",
    "        arm1 = 0.1    #20% chance\n",
    "    elif np.random.choice(arr) < 0.61:\n",
    "        arm1 = 0.15    #20% chance\n",
    "    elif np.random.choice(arr) < 0.81:\n",
    "        arm1 = 0.3    #20% chance\n",
    "    elif np.random.choice(arr) < 1.01:  \n",
    "        arm1 = 0.4    #20% chance\n",
    "    arm1R = np.append(arm1R, arm1)\n",
    "#print(arm1R)\n",
    "\n",
    "#arm2 dist\n",
    "for i in range(1000):\n",
    "    if np.random.choice(arr) < 0.21:  \n",
    "        arm2 = 0.15    #20% chance\n",
    "    elif np.random.choice(arr) < 0.41:\n",
    "        arm2 = 0.24    #20% chance\n",
    "    elif np.random.choice(arr) < 0.61:\n",
    "        arm2 = 0.34    #20% chance\n",
    "    elif np.random.choice(arr) < 0.81:\n",
    "        arm2 = 0.4    #20% chance\n",
    "    elif np.random.choice(arr) < 1.01:  \n",
    "        arm2 = 0.45    #20% chance\n",
    "    arm2R = np.append(arm2R, arm2)\n",
    "\n",
    "#arm3 dist\n",
    "for i in range(1000):\n",
    "    if np.random.choice(arr) < 0.21:  \n",
    "        arm3 = 0.2    #20% chance\n",
    "    elif np.random.choice(arr) < 0.41:\n",
    "        arm3 = 0.5    #20% chance\n",
    "    elif np.random.choice(arr) < 0.61:\n",
    "        arm3 = 0.6    #20% chance\n",
    "    elif np.random.choice(arr) < 0.81:\n",
    "        arm3 = 0.8    #20% chance\n",
    "    elif np.random.choice(arr) < 1.01:  \n",
    "        arm3 = 1    #20% chance\n",
    "    arm3R = np.append(arm3R, arm3)\n",
    "\n",
    "#arm4 dist\n",
    "for i in range(1000):\n",
    "    if np.random.choice(arr) < 0.21:  \n",
    "        arm4 = 0.2    #20% chance\n",
    "    elif np.random.choice(arr) < 0.41:\n",
    "        arm4 = 0.5    #20% chance\n",
    "    elif np.random.choice(arr) < 0.61:\n",
    "        arm4 = 0.6    #20% chance\n",
    "    elif np.random.choice(arr) < 0.81:\n",
    "        arm4 = 0.8    #20% chance\n",
    "    elif np.random.choice(arr) < 1.01:  \n",
    "        arm4 = 1    #20% chance\n",
    "    arm4R = np.append(arm4R, arm4)\n",
    "\n",
    "#arm5 dist\n",
    "for i in range(1000):\n",
    "    if np.random.choice(arr) < 0.21:  \n",
    "        arm5 = 0    #20% chance\n",
    "    elif np.random.choice(arr) < 0.41:\n",
    "        arm5 = 0.1    #20% chance\n",
    "    elif np.random.choice(arr) < 0.61:\n",
    "        arm5 = 0.15    #20% chance\n",
    "    elif np.random.choice(arr) < 0.81:\n",
    "        arm5 = 0.3    #20% chance\n",
    "    elif np.random.choice(arr) < 1.01:  \n",
    "        arm5 = 0.4    #20% chance\n",
    "    arm5R = np.append(arm5R, arm5)\n",
    "    \n",
    "#arm6 dist\n",
    "for i in range(1000):\n",
    "    if np.random.choice(arr) < 0.21:  \n",
    "        arm6 = 0.3    #20% chance\n",
    "    elif np.random.choice(arr) < 0.41:\n",
    "        arm6 = 0.48    #20% chance\n",
    "    elif np.random.choice(arr) < 0.61:\n",
    "        arm6 = 0.68    #20% chance\n",
    "    elif np.random.choice(arr) < 0.81:\n",
    "        arm6 = 0.8    #20% chance\n",
    "    elif np.random.choice(arr) < 1.01:  \n",
    "        arm6 = 0.9    #20% chance\n",
    "    arm6R = np.append(arm6R, arm6)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "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>Round</th>\n",
       "      <th>Arm1 Reward</th>\n",
       "      <th>Arm2 Reward</th>\n",
       "      <th>Arm3 Reward</th>\n",
       "      <th>Arm4 Reward</th>\n",
       "      <th>Arm5 Reward</th>\n",
       "      <th>Arm6 Reward</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.48</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Round  Arm1 Reward  Arm2 Reward  Arm3 Reward  Arm4 Reward  Arm5 Reward  \\\n",
       "0      1         0.00         0.40          0.2          0.8         0.00   \n",
       "1      2         0.10         0.24          0.6          0.6         0.15   \n",
       "2      3         0.10         0.34          0.5          0.5         0.30   \n",
       "3      4         0.10         0.24          0.2          0.6         0.00   \n",
       "4      5         0.15         0.34          0.5          0.8         0.15   \n",
       "5      6         0.15         0.15          0.5          0.5         0.10   \n",
       "6      7         0.15         0.40          0.2          0.5         0.10   \n",
       "7      8         0.10         0.15          0.8          0.2         0.30   \n",
       "8      9         0.15         0.34          0.8          0.6         0.10   \n",
       "9     10         0.00         0.24          0.8          0.2         0.15   \n",
       "\n",
       "   Arm6 Reward  \n",
       "0         0.68  \n",
       "1         0.80  \n",
       "2         0.80  \n",
       "3         0.80  \n",
       "4         0.48  \n",
       "5         0.68  \n",
       "6         0.48  \n",
       "7         0.68  \n",
       "8         0.48  \n",
       "9         0.48  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = {'Round': np.arange(1,1001),\n",
    "        'Arm1 Reward': arm1R,\n",
    "        'Arm2 Reward': arm2R,\n",
    "        'Arm3 Reward': arm3R,\n",
    "        'Arm4 Reward': arm4R, \n",
    "        'Arm5 Reward': arm5R,\n",
    "        'Arm6 Reward': arm6R,\n",
    "       }\n",
    "\n",
    "df2 = pd.DataFrame(data2)\n",
    "df2.head(10)  #shows first 10 rounds out of 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k=6\n",
    "K=3\n",
    "\n",
    "math.ceil(k/K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#implementing CUCB, 1000 runs\n",
    "#CUCB for K=2 arms being selected\n",
    "rounds = len(df2.index) # number of rounds; \n",
    "k = 6 # number of arms\n",
    "mu = 0 # initialize to 0, the empirical mean\n",
    "mu_arr = []\n",
    "N = np.zeros(k) # number of times a given arm has been selected before current round; initialize to 0 as no arm selected yet\n",
    "rewardSum = np.zeros(k)\n",
    "hist_UCB_rewards = [] #stores history of UCB CHOSEN rewards\n",
    "alpha = 0.6\n",
    "beta = 0.7\n",
    "r_mu = 0\n",
    "opt_mu = 0\n",
    "\n",
    "for t in range(rounds):\n",
    "    UCB_Values = np.zeros(k) #array holding ucb values. re-initialize to 0 at start of each round \n",
    "    temp_UCB_Values = np.zeros(k)\n",
    "    arm_selected = 0\n",
    "    for a in range(k):\n",
    "        if (N[a] > 0):\n",
    "            #calculate UCB below\n",
    "            mu = rewardSum[a]/N[a]\n",
    "            ucb_value = mu + math.sqrt(3/2*math.log(t)/N[a]) \n",
    "            UCB_Values[a] = ucb_value\n",
    "        elif (N[a] == 0): #i.e. if N is 0 for arm a, then allow exploration of that arm\n",
    "            UCB_Values[a] = 1e500 #infinity\n",
    "        temp_UCB_Values[a] = UCB_Values[a] #this is a copy of UCB_Values[a], to be modified below to find runner-up arms\n",
    "        \n",
    "    arm1_selected = np.argmax(UCB_Values) #NB: argmax gives index of max value in a list/array\n",
    "    temp_UCB_Values[arm1_selected] = 0\n",
    "    arm2_selected = np.argmax(temp_UCB_Values)\n",
    "    \n",
    "    #update Values as of round t\n",
    "    reward = df2.values[t, arm1_selected+1] + df2.values[t, arm2_selected+1]\n",
    "    r_mu = reward/2 #reward divide by K\n",
    "    arm3_mean = np.mean([0.23, 0.52, 0.62, 0.81, 1])\n",
    "    arm6_mean = np.mean([0.30, 0.48, 0.68, 0.8, 0.9])\n",
    "    opt_mu = (arm3_mean+arm6_mean)/2 #divide by K\n",
    "    if r_mu < alpha*opt_mu: #superarm S is bad if the reward sum from S is < alpha*mean Reward of Optimal Arm.\n",
    "        #this superarm is a bad superarm\n",
    "        #only increment the simple arm within this superarm that has min N\n",
    "        if N[arm1_selected] < N[arm2_selected]:\n",
    "            N[arm1_selected] += 1\n",
    "        else:\n",
    "            N[arm2_selected] += 1\n",
    "    #else if superarm S is not bad then don't increment N at all for any simple arms within that superarm\n",
    "    \n",
    "    rewardSum[arm1_selected] += df2.values[t, arm1_selected+1]  #will need loop here to do this K times\n",
    "    rewardSum[arm2_selected] += df2.values[t, arm2_selected+1]\n",
    "    hist_UCB_rewards.append(reward)\n",
    "    UCB_cumu_reward = np.cumsum(hist_UCB_rewards)\n",
    "    UCB_cumu_reward_norm = UCB_cumu_reward/2 #UCB_cumu_reward divide by K\n",
    "    UCB_total_reward = sum(hist_UCB_rewards)\n",
    "    UCB_total_reward_norm = UCB_total_reward/2 #UCB_total_reward divide by K\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "524.1150000000016"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "UCB_total_reward_norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.2500e+00, 3.9000e-01, 5.1810e+02, 9.0000e-01, 7.0000e-01,\n",
       "       5.6156e+02])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arm3_mean = np.mean([0.23, 0.52, 0.62, 0.81, 1])\n",
    "arm6_mean = np.mean([0.30, 0.48, 0.68, 0.8, 0.9])\n",
    "opt_mu = (arm3_mean+arm6_mean)/2\n",
    "opt_mu\n",
    "rewardSum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Number of times Each Arm was Selected')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#reward\n",
    "reward_arr1 = UCB_cumu_reward\n",
    "plt.plot(reward_arr1,color = 'g')\n",
    "plt.title(\"Total Reward over Time (Rounds)\")\n",
    "plt.show()\n",
    "\n",
    "#num times arms selected\n",
    "plt.bar(['arm1','arm2','arm3','arm4','arm5', 'arm6'], N) #NB: N calculated according to CUCB (pg 5 in Superarm paper)\n",
    "plt.title(\"Number of times Each Arm was Selected\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'UCB Values for Each Arm')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(['arm1','arm2','arm3','arm4','arm5', 'arm6'], UCB_Values)\n",
    "plt.title(\"UCB Values for Each Arm\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Quantity that Each Arm within Superarm Contributed to Total Reward')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#how much each arm contributed to the reward\n",
    "plt.bar(['arm1','arm2','arm3','arm4','arm5', 'arm6'], rewardSum)\n",
    "plt.title(\"Quantity that Each Arm within Superarm Contributed to Total Reward\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "#implementing CUCB, 1000 runs\n",
    "#CUCB for K=3 arms being selected\n",
    "rounds = len(df2.index) # number of rounds; \n",
    "k = 6 # number of arms\n",
    "mu = 0 # initialize to 0, the empirical mean\n",
    "mu_arr = []\n",
    "N = np.zeros(k) # number of times a given arm has been selected before current round; initialize to 0 as no arm selected yet\n",
    "rewardSum = np.zeros(k)\n",
    "hist_UCB_rewards = [] #stores history of UCB CHOSEN rewards\n",
    "alpha = 1\n",
    "beta = 1\n",
    "r_mu = 0\n",
    "opt_mu = 0\n",
    "\n",
    "for t in range(rounds):\n",
    "    UCB_Values = np.zeros(k) #array holding ucb values. re-initialize to 0 at start of each round \n",
    "    temp_UCB_Values = np.zeros(k)\n",
    "    arm_selected = 0\n",
    "    for a in range(k):\n",
    "        if (N[a] > 0):\n",
    "            #calculate UCB below\n",
    "            mu = rewardSum[a]/N[a]\n",
    "            ucb_value = mu + math.sqrt(3/2*math.log(t)/N[a]) \n",
    "            UCB_Values[a] = ucb_value\n",
    "        elif (N[a] == 0): #i.e. if N is 0 for arm a, then allow exploration of that arm\n",
    "            UCB_Values[a] = 1e500 #infinity\n",
    "        temp_UCB_Values[a] = UCB_Values[a] #this is a copy of UCB_Values[a], to be modified below to find runner-up arms\n",
    "        \n",
    "    arm1_selected = np.argmax(UCB_Values) #NB: argmax gives index of max value in a list/array\n",
    "    temp_UCB_Values[arm1_selected] = 0\n",
    "    arm2_selected = np.argmax(temp_UCB_Values)\n",
    "    temp_UCB_Values[arm2_selected] = 0\n",
    "    arm3_selected = np.argmax(temp_UCB_Values)\n",
    "    \n",
    "    #update Values as of round t\n",
    "    reward = df2.values[t, arm1_selected+1] + df2.values[t, arm2_selected+1] + df2.values[t, arm3_selected+1]\n",
    "    r_mu = reward/3 #reward divide by K\n",
    "    arm3_mean = np.mean([0.23, 0.52, 0.62, 0.81, 1])\n",
    "    arm4_mean = np.mean([0.21, 0.5, 0.6, 0.79, 0.98])\n",
    "    arm6_mean = np.mean([0.30, 0.48, 0.68, 0.8, 0.9])\n",
    "    opt_mu = (arm3_mean+arm4_mean+arm6_mean)/3 #divide by K\n",
    "    if r_mu < alpha*opt_mu: #superarm S is bad if the reward sum from S is < alpha*mean Reward of Optimal Arm.\n",
    "        #this superarm is a bad superarm\n",
    "        #only increment the simple arm within this superarm that has min N\n",
    "        if N[arm1_selected] < N[arm2_selected]:\n",
    "            N[arm1_selected] += 1\n",
    "        else:\n",
    "            N[arm2_selected] += 1\n",
    "    #else if superarm S is not bad then don't increment N at all for any simple arms within that superarm\n",
    "    \n",
    "    rewardSum[arm1_selected] += df2.values[t, arm1_selected+1]  #will need loop here to do this K times\n",
    "    rewardSum[arm2_selected] += df2.values[t, arm2_selected+1]\n",
    "    rewardSum[arm3_selected] += df2.values[t, arm3_selected+1]\n",
    "    hist_UCB_rewards.append(reward)\n",
    "    UCB_cumu_reward = np.cumsum(hist_UCB_rewards)\n",
    "    UCB_cumu_reward_norm = UCB_cumu_reward/3 #UCB_cumu_reward divide by K\n",
    "    UCB_total_reward = sum(hist_UCB_rewards)\n",
    "    UCB_total_reward_norm = UCB_total_reward/3 #UCB_total_reward divide by K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.628"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arm3_mean = np.mean([0.23, 0.52, 0.62, 0.81, 1])\n",
    "arm4_mean = np.mean([0.21, 0.5, 0.6, 0.79, 0.98])\n",
    "arm6_mean = np.mean([0.30, 0.48, 0.68, 0.8, 0.9])\n",
    "opt_mu = (arm3_mean+arm4_mean+arm6_mean)/3\n",
    "opt_mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Number of times Each Arm was Selected')"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#reward\n",
    "reward_arr1 = UCB_cumu_reward\n",
    "plt.plot(reward_arr1,color = 'g')\n",
    "plt.title(\"Total Reward over Time (Rounds)\")\n",
    "plt.show()\n",
    "\n",
    "#num times arms selected\n",
    "plt.bar(['arm1','arm2','arm3','arm4','arm5', 'arm6'], N) #NB: N calculated according to CUCB (pg 5 in Superarm paper)\n",
    "plt.title(\"Number of times Each Arm was Selected\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'UCB Values for Each Arm')"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(['arm1','arm2','arm3','arm4','arm5', 'arm6'], UCB_Values)\n",
    "plt.title(\"UCB Values for Each Arm\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Quantity that Each Arm within Opt Superarm Contributed to Total Reward')"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#how much each arm within opt superarm contributed to the reward\n",
    "plt.bar(['arm1','arm2','arm3','arm4','arm5', 'arm6'], rewardSum)\n",
    "plt.title(\"Quantity that Each Arm within Opt Superarm Contributed to Total Reward\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "math domain error",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-12-ad41982fb4a1>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     40\u001b[0m             \u001b[0mmu\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrewardSum\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mN\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     41\u001b[0m             \u001b[0mmu_arr\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmu\u001b[0m \u001b[1;31m#expectation vector being updated\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 42\u001b[1;33m             \u001b[0mucb_value\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmu\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mN\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     43\u001b[0m             \u001b[0mUCB_Values\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mucb_value\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     44\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mN\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m \u001b[1;31m#i.e. if N is 0 for arm a, then set ucb value to infinity to allow exploration of arm a\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: math domain error"
     ]
    }
   ],
   "source": [
    "#implementing CUCB, 1000 runs\n",
    "#CUCB for K arms being selected\n",
    "rounds = len(df2.index) # number of rounds\n",
    "K = 3 # window size, num of arms within a window\n",
    "k = 6 # number of arms\n",
    "mu = 0 # initialize to 0, the empirical mean\n",
    "N = np.zeros(k) # number of times a given arm has been selected before current round; initialize to 0 as no arm selected yet\n",
    "rewardSum = np.zeros(k)\n",
    "hist_UCB_rewards = [] #stores history of UCB CHOSEN rewards\n",
    "mu_arr = np.zeros(k)  #expectation vector; array of mu for each simple arm\n",
    "alpha = 0.6\n",
    "beta = 0.7\n",
    "r_mu = 0     #expected reward from a certain superarm\n",
    "r_mu_arr = []   #array of expected rewards for each superarm S\n",
    "Rt_S = 0      #sum of K arms' rewards in round t\n",
    "opt_mu = 0  #max(r_mu_arr)\n",
    "\n",
    "#initialize all the simple arms in a separate chunk of code from the rest of algorithm, acc. line 2 in pseudocode\n",
    "for i in range(math.ceil(k/K)):\n",
    "    UCB_Values = np.zeros(k) #array holding ucb values. re-initialize to 0 at start of each round\n",
    "    arm_selected = 0\n",
    "    for j in np.arange(K):\n",
    "        #pull superarm consisting of K arms\n",
    "        arm_selected = j\n",
    "        #N[arm_selected] += 1\n",
    "        #reward = df2.values[i, arm_selected+1]\n",
    "        #rewardSum[arm_selected] += reward\n",
    "    N[arm_selected] += 1\n",
    "    reward = df2.values[i, arm_selected+1]\n",
    "    rewardSum[arm_selected] += reward\n",
    "    i = i+K  #disjoint window, shifts right by K simple arms\n",
    "        \n",
    "#suppose CUCB is working\n",
    "#remaining rounds, given that math.ceil(k/K) rounds already completed in initialization\n",
    "for t in range(rounds-math.ceil(k/K)):\n",
    "    UCB_Values = np.zeros(k) #array holding ucb values. re-initialize to 0 at start of each round\n",
    "    arm_selected = 0\n",
    "    for a in range(k):\n",
    "        if (N[a] > 0):\n",
    "            mu = rewardSum[a]/N[a]\n",
    "            mu_arr[a] = mu #expectation vector being updated\n",
    "            ucb_value = mu + math.sqrt(3/2*math.log(t)/N[a]) \n",
    "            UCB_Values[a] = ucb_value\n",
    "        elif (N[a] == 0): #i.e. if N is 0 for arm a, then set ucb value to infinity to allow exploration of arm a\n",
    "            #ensures initialization of all k arms\n",
    "            UCB_Values[a] = 1e500 #infinity\n",
    "    arm_selected = np.argmax(UCB_Values)\n",
    "\n",
    "\n",
    "#updates\n",
    "if r_mu < alpha*opt_mu:\n",
    "    #this superarm is a bad superarm\n",
    "    #only increment the simple arm within this superarm that has min N\n",
    "    n_arr = []\n",
    "    for r in range(K):\n",
    "        #find the simple with the min N,increment that simple arm's N value\n",
    "        n_arr = np.append(n_arr, N[r]) #NB: N[K*0+r] = N[r] only for superarm 1. for superarm 2, N[K*1+r]. superarm 3, N[K*2+r]\n",
    "        N[arm_selected] = min(n_arr)+1\n",
    "#else:\n",
    "    #this superarm is not a bad superarm\n",
    "    #do not incremement N for any of the simple arms within this superarm\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#regret = alpha*beta*optimal_superarm_mean_reward*t_rounds - sum of cucb_rewards yielded over t rounds\n",
    "\n",
    "regret = rounds*alpha*beta*opt_mu - UCB_total_reward\n",
    "print(\"Total regret after N rounds: \", regret)\n",
    "\n",
    "regret_arr = alpha*beta*opt_mu*np.arange(rounds) - UCB_cumu_reward\n",
    "regret_arr\n",
    "\n",
    "plt.plot(regret_arr,color = 'b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for t in range(rounds):\n",
    "    UCB_Values = np.zeros(k) #array holding ucb values. re-initialize to 0 at start of each round\n",
    "    arm_selected = 0\n",
    "    for a in range(k):\n",
    "        if (N[a] > 0):\n",
    "            mu = rewardSum[a]/N[a]\n",
    "            mu_arr[a] = mu #expectation vector being updated\n",
    "            ucb_value = mu + math.sqrt(3/2*math.log(t)/N[a]) \n",
    "            UCB_Values[a] = ucb_value\n",
    "        elif (N[a] == 0): #i.e. if N is 0 for arm a, then set ucb value to infinity to allow exploration of arm a\n",
    "            #ensures initialization of all k arms\n",
    "            UCB_Values[a] = 1e500 #infinity\n",
    "        \n",
    "    #update Values as of round t\n",
    "    #superarm S is bad if the reward sum from S is < alpha*opt_mu.\n",
    "    #if superarm S is bad then increment N as follows:\n",
    "    if N[arm1_selected] < N[arm2_selected]:\n",
    "        N[arm1_selected] += 1\n",
    "    else:\n",
    "        N[arm2_selected] += 1\n",
    "    #if superarm S is not bad then don't increment N at all:\n",
    "    reward = df2.values[t, arm1_selected+1] + df2.values[t, arm2_selected+1]\n",
    "    rewardSum[arm1_selected] += df2.values[t, arm1_selected+1]  #will need loop here to do this K times\n",
    "    rewardSum[arm2_selected] += df2.values[t, arm2_selected+1]\n",
    "    hist_UCB_rewards.append(reward)\n",
    "    UCB_cumu_reward = np.cumsum(hist_UCB_rewards)\n",
    "    UCB_total_reward = sum(hist_UCB_rewards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "reward_arr1 = UCB_cumu_reward\n",
    "\n",
    "plt.plot(reward_arr1,color = 'g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Number of times Each Arm was Selected')"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(['arm1','arm2','arm3','arm4','arm5'], N) #NB: N is calculated according to CUCB algorithm (page 5 in Superarm paper)\n",
    "plt.title(\"Number of times Each Arm was Selected\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#regret = alpha*beta*optimal_superarm_mean_reward*t_rounds - sum of cucb_rewards yielded over t rounds\n",
    "\n",
    "regret = opt_mu*rounds - UCB_total_reward\n",
    "print(\"Total regret after N rounds: \", regret)\n",
    "\n",
    "regret_arr = 0.7*np.arange(rounds) - UCB_cumu_reward\n",
    "regret_arr\n",
    "\n",
    "plt.plot(regret_arr,color = 'b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndentationError",
     "evalue": "expected an indented block (<ipython-input-212-dbe3899c7e2f>, line 29)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-212-dbe3899c7e2f>\"\u001b[1;36m, line \u001b[1;32m29\u001b[0m\n\u001b[1;33m    arm1_selected = np.argmax(UCB_Values) #NB: argmax gives index of max value in a list/array\u001b[0m\n\u001b[1;37m    ^\u001b[0m\n\u001b[1;31mIndentationError\u001b[0m\u001b[1;31m:\u001b[0m expected an indented block\n"
     ]
    }
   ],
   "source": [
    "#implementing CUCB, 1000 runs\n",
    "#CMAB for any number K arms selected\n",
    "\n",
    "rounds = len(df.index) # number of rounds; \n",
    "k = 10 # number of arms\n",
    "mu = 0 # initialize to 0, the empirical mean\n",
    "N = np.zeros(k) # number of times a given arm has been selected before current round; initialize to 0 as no arm selected yet\n",
    "rewardSum = np.zeros(k)\n",
    "hist_UCB_rewards = [] #stores history of UCB CHOSEN rewards\n",
    "\n",
    "for t in range(rounds):\n",
    "    UCB_Values = np.zeros(k) #array holding ucb values. re-initialize to 0 at start of each round\n",
    "    arm_selected = 0\n",
    "    for a in range(k):\n",
    "        if (N[a] > 0):\n",
    "            #calculate UCB below\n",
    "            mu = rewardSum[a]/N[a]\n",
    "            ucb_value = mu + math.sqrt(3/2*math.log(t)/N[a]) \n",
    "            UCB_Values[a] = ucb_value\n",
    "        elif (N[a] == 0): #i.e. if N is 0 for arm a, then allow exploration of that arm\n",
    "            UCB_Values[a] = 1e500 #infinity\n",
    "        temp_UCB_Values[a] = UCB_Values[a]\n",
    "    \n",
    "    for i in range(K): #K is the num of arms we are selecting (window size)\n",
    "        for a in range(k): #sort, and take the first K ind\n",
    "            #take the highest K arms in terms of UCB values\n",
    "            #need array with indeces of the K best arms\n",
    "    arm1_selected = np.argmax(UCB_Values) #NB: argmax gives index of max value in a list/array\n",
    "    temp_UCB_Values[arm1_selected] = 0\n",
    "    arm2_selected = np.argmax(temp_UCB_Values)\n",
    "    \n",
    "    #update Values as of round t\n",
    "    N[arm1_selected] += 1 #will need loop here to do this K times\n",
    "    N[arm2_selected] += 1\n",
    "    reward = df.values[t, arm1_selected+1] + df.values[t, arm2_selected+1]\n",
    "    rewardSum[arm1_selected] += df.values[t, arm1_selected+1]  #will need loop here to do this K times\n",
    "    rewardSum[arm2_selected] += df.values[t, arm2_selected+1]\n",
    "    hist_UCB_rewards.append(reward)\n",
    "    UCB_cumu_reward = np.cumsum(hist_UCB_rewards)\n",
    "    UCB_total_reward = sum(hist_UCB_rewards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.11.4"
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 },
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}