Finite horizon Beta-Bernoulli bandit problems.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implementation of finite horizon Beta-Bernoulli bandit problems \n",
    "1. Greedy sampling\n",
    "2. Thompson sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def greedy_epsilon_sampling(probabilities, N, T, epsilon):\n",
    "\n",
    "    # initialize\n",
    "    \n",
    "    # define play # holder\n",
    "    K = np.zeros([N+1,T]).astype(int) # no of arms is rows + 1, no of stages is columns\n",
    "    K[0:,0] = 0\n",
    "\n",
    "    # define probability estimate holder\n",
    "    phat = np.zeros([N+1,T]) # no of arms is rows, no of stages is columns\n",
    "    alphas = np.zeros([N+1,T])\n",
    "    betas = np.zeros([N+1,T])\n",
    "\n",
    "    # initialize \n",
    "    alphas[0:,0] = np.array([0,1,1,1]) #np.concatenate(([0], np.random.randint(1,10,N)), axis = 0)\n",
    "    betas[0:,0] = np.array([0,1,1,1]) # np.concatenate(([0], np.random.randint(1,10,N)), axis = 0)\n",
    "\n",
    "\n",
    "    # populate arms with initial estimates\n",
    "    for t in range(T-1):\n",
    "\n",
    "        for i in range(1,N+1):\n",
    "            phat[i,t] = (alphas[i,t])/(alphas[i,t] + betas[i,t]) # assign probabilities to arms\n",
    "\n",
    "        # flip a coin to decide whether to explore or exploit\n",
    "        decider = np.random.binomial(size = 1, n = 1, p = epsilon)\n",
    "        #print(decider)\n",
    "\n",
    "        # choose index of arm to pull\n",
    "        if decider == 1:\n",
    "            # if true play random arm\n",
    "            at = np.random.randint(1,N+1,1)[0]\n",
    "            #print(\"Explore new arm:\", at)\n",
    "        else:\n",
    "            # if false play the arm with the highest probability\n",
    "            at = np.random.choice(np.where(phat[:,t] == np.amax(phat[:,t]))[0]) # tie braker rule: random\n",
    "\n",
    "\n",
    "        # update pulled arm\n",
    "        zt = np.random.binomial(size=1, n=1, p = probabilities[at-1])\n",
    "        alphas[at,t+1] = alphas[at,t] + zt\n",
    "        betas[at,t+1] = betas[at,t] + (1 - zt)\n",
    "        K[at,t] = K[at, t-1] + 1\n",
    "\n",
    "        # update non-pulled arms\n",
    "        for i in range(1,N+1):\n",
    "            if i != at:\n",
    "                alphas[i,t+1] = alphas[i,t]\n",
    "                betas[i,t+1] = betas[i,t]\n",
    "                K[i,t] = K[i, t-1]\n",
    "    \n",
    "    return(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Thompson_sampling(probabilities, N, T):\n",
    "\n",
    "    # initialize\n",
    "    \n",
    "    # define play # holder\n",
    "    K = np.zeros([N+1,T]).astype(int) # no of arms is rows + 1, no of stages is columns\n",
    "    K[0:,0] = 0\n",
    "\n",
    "    # define probability estimate holder\n",
    "    phat = np.zeros([N+1,T]) # no of arms is rows, no of stages is columns\n",
    "    alphas = np.zeros([N+1,T])\n",
    "    betas = np.zeros([N+1,T])\n",
    "\n",
    "    # initialize \n",
    "    alphas[0:,0] = np.array([0,1,1,1]) #np.concatenate(([0], np.random.randint(1,10,N)), axis = 0)\n",
    "    betas[0:,0] = np.array([0,1,1,1]) # np.concatenate(([0], np.random.randint(1,10,N)), axis = 0)\n",
    "\n",
    "\n",
    "    # populate arms with initial estimates\n",
    "    for t in range(T-1):\n",
    "\n",
    "        for i in range(1,N+1):\n",
    "            #print(\"alpha\", np.absolute(alphas[i,t]))\n",
    "            #print(\"beta\", np.absolute(betas[i,t]))\n",
    "            phat[i,t] = np.random.beta(np.absolute(alphas[i,t]), np.absolute(betas[i,t]), size = 1) # assign probabilities to arms\n",
    "            \n",
    "                  \n",
    "        # if false play the arm with the highest probability\n",
    "        at = np.random.choice(np.where(phat[:,t] == np.amax(phat[:,t]))[0]) # break ties randomly\n",
    "\n",
    "        # update pulled arm\n",
    "        zt = np.random.binomial(size=1, n=1, p = probabilities[at-1])\n",
    "        alphas[at,t+1] = alphas[at,t] + zt\n",
    "        betas[at,t+1] = betas[at,t] + (1 - zt)\n",
    "        K[at,t] = K[at, t-1] + 1\n",
    "\n",
    "        # update non-pulled arms\n",
    "        for i in range(1,N+1):\n",
    "            if i != at:\n",
    "                alphas[i,t+1] = alphas[i,t]\n",
    "                betas[i,t+1] = betas[i,t]\n",
    "                K[i,t] = K[i, t-1]\n",
    "    \n",
    "    return(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 3\n",
    "T = 1000\n",
    "probabilities = np.array([0.9, 0.6, 0.3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 10000\n",
    "for i in range(M):\n",
    "    np.random.seed(i)\n",
    "    if i == 0:\n",
    "        GE0 = greedy_epsilon_sampling(probabilities, N, T, 0) # greedy\n",
    "        GE001 = greedy_epsilon_sampling(probabilities, N, T, 0.01) # epsilon greedy with 001\n",
    "        GE01 = greedy_epsilon_sampling(probabilities, N, T, 0.1) # espilon greedy with 0.1\n",
    "        TK = Thompson_sampling(probabilities, N, T)\n",
    "        \n",
    "    else:\n",
    "        GE0 = GE0 + greedy_epsilon_sampling(probabilities, N, T, 0) # greedy\n",
    "        GE001 = GE001 + greedy_epsilon_sampling(probabilities, N, T, 0.01) # greedy wiht 0.01\n",
    "        GE01 = GE01 + greedy_epsilon_sampling(probabilities, N, T, 0.1) # epsilon greedy with 0.1\n",
    "        TK = TK + Thompson_sampling(probabilities, N, T)\n",
    "        \n",
    "    #print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "greedy0K = np.true_divide(GE0, M)\n",
    "greedy001K = np.true_divide(GE001, M)\n",
    "greedy01K = np.true_divide(GE01, M)\n",
    "ThompsonK = np.true_divide(TK, M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "greedy0K = np.hstack((np.array([[0,0,0,0]]).T, greedy0K))\n",
    "greedy001K = np.hstack((np.array([[0,0,0,0]]).T, greedy001K))\n",
    "greedy01K = np.hstack((np.array([[0,0,0,0]]).T, greedy01K))\n",
    "ThompsonK = np.hstack((np.array([[0,0,0,0]]).T, ThompsonK))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "greedy0K[0,:] = range(T+1)\n",
    "greedy001K[0,:] = range(T+1)\n",
    "greedy01K[0,:] = range(T+1)\n",
    "ThompsonK[0,:] = range(T+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fietekrutein/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:7: RuntimeWarning: invalid value encountered in true_divide\n",
      "  import sys\n",
      "/Users/fietekrutein/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:8: RuntimeWarning: invalid value encountered in true_divide\n",
      "  \n",
      "/Users/fietekrutein/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:9: RuntimeWarning: invalid value encountered in true_divide\n",
      "  if __name__ == '__main__':\n",
      "/Users/fietekrutein/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:21: RuntimeWarning: invalid value encountered in true_divide\n",
      "/Users/fietekrutein/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:22: RuntimeWarning: invalid value encountered in true_divide\n",
      "/Users/fietekrutein/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:23: RuntimeWarning: invalid value encountered in true_divide\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([   0.,    1.,    2., ...,  998.,  999., 1000.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "\n",
    "plt.figure(figsize=[12,5])\n",
    "\n",
    "arm1 = greedy0K[1,:T]/greedy0K[0,:T]\n",
    "arm2 = greedy0K[2,:T]/greedy0K[0,:T]\n",
    "arm3 = greedy0K[3,:T]/greedy0K[0,:T]\n",
    "t = range(T)\n",
    "\n",
    "plot1 = plt.subplot(121)\n",
    "plt.plot(t, arm1, label = 'arm 1')\n",
    "plt.plot(t, arm2, label = 'arm 2')\n",
    "plt.plot(t, arm3, label = 'arm 3')\n",
    "plt.xlabel(\"Stage\")\n",
    "plt.ylabel(\"Fraction of pulls over 10000 reps\")\n",
    "plt.legend(loc=\"center right\")\n",
    "plot1.set_title(\"Evolution of arm pulls for greedy sampling\")\n",
    "\n",
    "arm11 = greedy001K[1,:T]/greedy001K[0,:T]\n",
    "arm21 = greedy001K[2,:T]/greedy001K[0,:T]\n",
    "arm31 = greedy001K[3,:T]/greedy001K[0,:T]\n",
    "# t = range(T)\n",
    "\n",
    "plot2 = plt.subplot(122)\n",
    "plt.plot(t, arm11, label = 'arm 1')\n",
    "plt.plot(t, arm21, label = 'arm 2')\n",
    "plt.plot(t, arm31, label = 'arm 3')\n",
    "plt.xlabel(\"Stage\")\n",
    "plt.ylabel(\"Fraction of pulls over 10000 reps\")\n",
    "plt.legend(loc=\"center right\")\n",
    "plot2.set_title(\"Evolution of arm pulls for epsilon greedy sampling at epsilon = 0.01\")\n",
    "\n",
    "plt.savefig('Q5 Results 1.png', dpi = 800)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "greedy0K[1,:]\n",
    "greedy0K[0,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "\n",
    "plt.figure(figsize=[12,5])\n",
    "\n",
    "arm1 = greedy01K[1,1:T-1]/greedy01K[0,1:T-1]\n",
    "arm2 = greedy01K[2,1:T-1]/greedy01K[0,1:T-1]\n",
    "arm3 = greedy01K[3,1:T-1]/greedy01K[0,1:T-1]\n",
    "t = range(T-2)\n",
    "\n",
    "plot1 = plt.subplot(121)\n",
    "plt.plot(t, arm1, label = 'arm 1')\n",
    "plt.plot(t, arm2, label = 'arm 2')\n",
    "plt.plot(t, arm3, label = 'arm 3')\n",
    "plt.xlabel(\"Stage\")\n",
    "plt.ylabel(\"Fraction of pulls over 10000 reps\")\n",
    "plt.legend(loc=\"center right\")\n",
    "plot1.set_title(\"Evolution of arm pulls for greedy sampling at epsilon = 0.1\")\n",
    "\n",
    "arm11 = ThompsonK[1,1:T-1]/ThompsonK[0,1:T-1]\n",
    "arm21 = ThompsonK[2,1:T-1]/ThompsonK[0,1:T-1]\n",
    "arm31 = ThompsonK[3,1:T-1]/ThompsonK[0,1:T-1]\n",
    "# t = range(T)\n",
    "\n",
    "plot2 = plt.subplot(122)\n",
    "plt.plot(t, arm11, label = 'arm 1')\n",
    "plt.plot(t, arm21, label = 'arm 2')\n",
    "plt.plot(t, arm31, label = 'arm 3')\n",
    "plt.xlabel(\"Stage\")\n",
    "plt.ylabel(\"Fraction of pulls over 10000 reps\")\n",
    "plt.legend(loc=\"center right\")\n",
    "plot2.set_title(\"Evolution of arm pulls for Thompson sampling\")\n",
    "\n",
    "plt.savefig('Q5 Results 2.png', dpi = 800)\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}