4_Markov_Decision_Process.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Markov Decision Process (MDP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ransalu Senanayake"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import copy\n",
    "import timeit\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as pl\n",
    "%matplotlib inline\n",
    "from ipywidgets import interactive\n",
    "import ipywidgets as widgets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the following grid world.\n",
    "\n",
    "**States:** A 10x10 grid\n",
    "\n",
    "**Actions:** Up, Down, Left, Right\n",
    "\n",
    "**Tranistion probabilities:** \n",
    "* 0.7 in the direction of action\n",
    "* 0.1 in the three other directions\n",
    "* The robot bounces back to the same state near edges\n",
    "\n",
    "**Rewards:**\n",
    "* (7,8) has a reward +10\n",
    "* (2,7) has a reward +3\n",
    "* (4,3) has a reward -5\n",
    "* (7,3) has a reward -10\n",
    "* No reward in other states\n",
    "\n",
    "This example is based on Decision Making Under Uncertainty by M.J. Kochenderfer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Let's define MDP paras\n",
    "def createGrid10World():\n",
    "    def xy2s(y, x):\n",
    "        x = max(x, 0)\n",
    "        y = max(y, 0)\n",
    "        x = min(x, 9)\n",
    "        y = min(y, 9)\n",
    "        out = np.ravel_multi_index(np.array([x,y]), (10,10))\n",
    "        return out\n",
    "\n",
    "    def s2xy(s):\n",
    "        x, y = np.unravel_index(s, (10,10))\n",
    "        return y, x\n",
    "\n",
    "    def gridPlot(ax, im, title='', cmap='Blues'):\n",
    "        pl.imshow(im, interpolation='none', cmap=cmap, origin='lower')\n",
    "        pl.colorbar()\n",
    "        ax.set_xticks(np.arange(0, 10, 1));\n",
    "        ax.set_yticks(np.arange(0, 10, 1));\n",
    "        ax.set_xticklabels(np.arange(0, 10, 1));\n",
    "        ax.set_yticklabels(np.arange(0, 10, 1));\n",
    "        ax.set_xticks(np.arange(-.5, 10, 1), minor=True);\n",
    "        ax.set_yticks(np.arange(-.5, 10, 1), minor=True);\n",
    "        ax.grid(which='minor', color='w', linestyle='-', linewidth=1)\n",
    "        pl.title(title);\n",
    "        return \n",
    "    \n",
    "    A = ['left', 'right', 'up', 'down']\n",
    "    S = np.arange(100)\n",
    "    T = np.zeros((len(S), len(A), len(S)))\n",
    "    R = np.zeros((len(S), len(A)))\n",
    "    for s in S:\n",
    "        x, y = s2xy(s)\n",
    "        if x == 2 and y == 7:\n",
    "            R[s, :] = 3\n",
    "        elif x == 7 and y == 8:\n",
    "            R[s, :] = 10\n",
    "        else:\n",
    "            if x == 7 and y == 3:\n",
    "                R[s, :] = -10\n",
    "            elif x == 4 and y == 3:\n",
    "                R[s, :] = -5\n",
    "            elif x == 0:\n",
    "                if y == 0 or y == 9:\n",
    "                    R[s, :] = -0.2\n",
    "                else:\n",
    "                    R[s, :] = -0.1\n",
    "                R[s, 0] = -0.7\n",
    "            elif x == 9:\n",
    "                if y == 0 or y == 9:\n",
    "                    R[s, :] = -0.2\n",
    "                else:\n",
    "                    R[s, :] = -0.1\n",
    "                R[s, 1] = -0.7\n",
    "            elif y == 0:\n",
    "                if x == 0 or x == 9:\n",
    "                    R[s, :] = -0.2\n",
    "                else:\n",
    "                    R[s, :] = -0.1\n",
    "                R[s, 3] = -0.7\n",
    "            elif y == 9:\n",
    "                if x == 0 or x == 9:\n",
    "                    R[s, :] = -0.2\n",
    "                else:\n",
    "                    R[s, :] = -0.1\n",
    "                R[s, 2] = -0.7\n",
    "                \n",
    "            for a in A:\n",
    "                if a == 'left':\n",
    "                    T[s, 0, xy2s(x - 1, y)] += 0.7\n",
    "                    T[s, 0, xy2s(x + 1, y)] += 0.1\n",
    "                    T[s, 0, xy2s(x, y - 1)] += 0.1\n",
    "                    T[s, 0, xy2s(x, y + 1)] += 0.1\n",
    "                elif a == 'right':\n",
    "                    T[s, 1, xy2s(x + 1, y)] += 0.7\n",
    "                    T[s, 1, xy2s(x - 1, y)] += 0.1\n",
    "                    T[s, 1, xy2s(x, y - 1)] += 0.1\n",
    "                    T[s, 1, xy2s(x, y + 1)] += 0.1\n",
    "                elif a == 'up':\n",
    "                    T[s, 2, xy2s(x, y + 1)] += 0.7\n",
    "                    T[s, 2, xy2s(x, y - 1)] += 0.1\n",
    "                    T[s, 2, xy2s(x - 1, y)] += 0.1\n",
    "                    T[s, 2, xy2s(x + 1, y)] += 0.1\n",
    "                elif a == 'down':\n",
    "                    T[s, 3, xy2s(x, y - 1)] += 0.7\n",
    "                    T[s, 3, xy2s(x, y + 1)] += 0.1\n",
    "                    T[s, 3, xy2s(x - 1, y)] += 0.1\n",
    "                    T[s, 3, xy2s(x + 1, y)] += 0.1\n",
    "\n",
    "    for a, c_x, c_y in [(0,0,0), (0,0,9),(1,9,0),(1,9,9),(2,0,9),(2,9,9),(3,0,0),(3,9,0)]:                \n",
    "        R[xy2s(c_x,c_y),a] = -0.8\n",
    " \n",
    "    discount = 0.9\n",
    "\n",
    "    nextStates = {}\n",
    "    for si in range(len(S)):\n",
    "        for ai in range(len(A)):\n",
    "            nextStates[(si,ai)] = np.where((T[si, ai, :] != 0) == True)[0]\n",
    "    \n",
    "    return {'S':S, 'A':A, 'T':T, 'R':R, 'discount':discount, 'nextStates':nextStates, 'gridPlot':gridPlot, 'xy2s':xy2s, 's2xy':s2xy}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MDP():\n",
    "    def __init__(self):\n",
    "        pass\n",
    "        \n",
    "    def inbuilt_init(self, mdp_dict):\n",
    "        self.S = mdp_dict['S']\n",
    "        self.A = mdp_dict['A']\n",
    "        self.T = mdp_dict['T']\n",
    "        self.R = mdp_dict['R']\n",
    "        self.discount = mdp_dict['discount']\n",
    "        self.nextStates = mdp_dict['nextStates']\n",
    "        self.gridPlot = mdp_dict['gridPlot']\n",
    "        self.xy2s = mdp_dict['xy2s']\n",
    "        self.s2xy = mdp_dict['s2xy']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 216x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Rz6+5eWYziqQXAS+JiKeXmPdYSmbTrG65nbJoZsNXHJG+Ep/GPuP5lMW8PY90Ef19I+L5ko6VNMihtc1mtIj4XJnOWBnFTXhfPohlmXUTEZdGhNwZMzOb+dwhy9uDgF/6VxGz3hX3IjIzMzPLmjtkPZL0BkmXS7pF0hpJ7TdX7XV5D5V0rqTfSbpM0guK599GGt74hZL+KOkVpCF9H1M8/n31tTFJhxbv+zpJ2wyDLekDklYW0y/9vtenaraKI8g/Kj6z3wJvbT+qLOnpxef9B0kflvT99qNekt4n6SZJVxYjxFHc6+oJwIeK/LUPp23TcM7yN4D8vVXSZ1se7yUpJn8YKY4wv1PSzyTdLOlrSvfyswFy1kZrADmaXeyDNkq6Anhm2+sPlLS0+M64TtLi4vm5kjZJ2rV4/CZJWyTdq3j8b5I+WPz9aUmnSPpG0c4LJP3VQN6AMVFLziLCUw8T6caXDyR1Zl8I3Eq6J8zjSff86TQ9vih/LHB+8fdOwNWkkZ/mAPuR7uuyT/H6W4HPttR9d1lPA/ksZwOXk27Ouj3pflL7TDP/K4FPjrrdM3UaULa2FJ/THNK9ilrztitwM/Dc4vUTgTtJ141Nlr+TdH+k2aQbPl/Ln6+1/d7kvJ56+lydswZMA8hf+/5qLyCAOcXj75HupfawYt/35db5PQ3kM3TWRv8ZVM3R8cClpBvH/wVwXluOfgB8mHSfzH1J94h8SstrRxZ/n1NsC4e1vPac4u9Pk25af2CxL/wccNqo37umTHXlzEfIehQRX4qIayPiTxHxReBXwIERcX5E7DLNNNW1X88CroqIT0XEloi4mLST8uAdw3EgsC4iroiIO4DTgCOmmf9o4AtDadkYGlC2ro2I/y7ytKmtimcAqyPizEinAf8X0H59zq8j4mMRcRdwKmlHultNqzwunLMGGPC+rZPPRMSqiLiVdEPpFygNb2+D4ayN2ABy9ALggxFxdUT8Dnjn5LIl7QE8Dnh9RGyOiJWkkUhfXMzyfeCJxVHpR5D2cU+UNBd4FKlTNukrEfGzYl/4OVLnzsqpJWe+xqJHkl4MvIb06x/APUm/vPfjQcBBbYcy5wCf6buBY2T2vR4UsaX9O/efxaYNq4HNLU8tiYglLY93Jx2hnLQeOGiqZUl6ELA38N2+G2zTGlC2rp7mtQe2vh4RIan9XkbXt7x+m6TJdoy1illzzhpgwPu2Tlq3g18D2xV13DDgehrJ+7TmG0COttpPkXLS+trvIuKWttcnir+/D7wf2B+4BDiXdIuIR5M6EL9tKdf6Y+RtjNF+LtecuUPWg+KN/RhwCPCTiLhL0sr0kp4AfHOa4odFxA/bnrsa+H5EPK1kE3yPghaxZRP3eMgLOr6+eeUpmyNiouMMvTkKOKM4cmIDNsBsTZeR64D5LXWq9XEJY5u/IWbNORuBAeXvVmDHlufvP8W8e7T8vSfpFOGNlRo/g3if1mwDytF1bJuTSdcCfyFp55ZO2Z6kU4EBfgw8BHgO6bvlGkl7ks4O+X7F1Zsxcs2ZO2S92Yn0pWwDgKSXks6HpwhSr78wfB14l6S/Ix3yhHTY+I8RsXaK+W8A5kvavjhMOt4kmFXpbJdr2Pofvvn8+R+2dkcBr6hSmU1r0NmayjdIg3I8m5S945n6S2MnN5DOGR8/1bLmnOVvEPlbCby++AL4B+CNU8xzjKT/Jd1Y+mTcIdia92lNN4gcnQ68StLXST9y3D1gRERcLenHwDsl/T/gwcDLgBcVr98m6ULS5zo5GMiPSfu6l1Veu5ki05z5GrIeRMQa4D+An5C+nD0c+FGF5d0CPJ30gV1LOoT8buAeHYp8F1gNXC/JvyoCaFbnqbvlwEJJe0vanvQ5LN2minSD1vuQPnerwaCz1aGOjaTrM99DuqB5H2AFcHvJRfwn8DylERj/a5Bta4T+s+acZW4Q+YuIc4EvAr8ALiT96NHuM6QBBa4nDUrwqr4bPVN5n9ZYA9qPfQw4mzRQxEXAmW2vH006HfJa4CvAWyLi2y2vf590KvDPWh7vzNbXj1mGOZscPcyscWbtdP+4x/85puPrm5f/x4XdDjtLegbwQdKoOZ+MiHdIOhlYERFLi3neCsyNiG2GNrXmkjSLdO73iyLivFG3J2dVs+acmaTvkUZV/Pio25Ir79PM6pdrznzKojWXqHrYmYg4Czir7bmT2h6/tVIllg1JfwNcAGwC/pm0Ff10pI1qgopZc87MSvA+zax+mebMHTJrMKVzgc3KewzwedK9Q9YAz55ieHzbhrNmVj/nzKx+eebMHTJrtoq/cth4KX6xeuuIm9FMzppVEBFPGnUbGsE5M6tfhjlzh8waTGUvwDSzSpw1s/o5Z2b1yzNnA+2QSVoELNp5550XP/jBDx7kom3MXHXVVWzcuHH6Y8oDOA+4iZwzG5RSOYOxzJpzZoN04YUXboyIedPONIY5A2fNBqfJ3x0H2iGLiGXAsomJicXn/3RFz+XnzoHNW/qru9+yrjPPso87qMw9+fL8laNuTcxZlbKus76y5XIG45i1qjmDZm0L/neh3jp32E6/7j7X+OUMmrlPG5c6q5TNd5+WZ858yqI1l4DZ+f3KYTbjOGtm9XPOzOqXac7cIbMGq3y3dTMrxVkzq59zZla/PHNW6pidpBMlrZK0WtKr626UWWlS56lhnDPLmrNmVj/nzKx+Geasa4dM0sOAxcCBwCOBZ0laUHfDzLpS8StHp6lBnDPLmrNmVj/nzKx+measzBGyvwYuiIjbImIL8H3gufU2y6wkzeo8NYtzZnlz1szq55yZ1S/DnJWpeRXwBEn3lbQj8Axgj3qbZVZGnr9y9Mk5s4w5a2b1c87M6pdnzroO6hERayW9GzgHuBVYCdzVPp+k44DjAPbcc88BN9OsgwaeVz8V58yyN0ZZc85sZMYoZ+Cs2YhkmLNSx+Yi4hMRcUBEHAzcBPxyinmWRMREREzMmzf9vQ/NBkKCWXM6Tw3jnFm2xixrzpmNxJjlrJjHWbPhyjRnpWqWdL+IuFHSnqRzgB9db7PMSmreaRwdOWeWNWfNrH7OmVn9MsxZ2avXvixpDbAMeEVE/L7GNpmVV3HoUkmHSrpM0jpJb+gwzwskrSmG7v38QNu/NefM8lUha5nlDJw1y5X3aWb1yzBnpY6QRcQTSrXQbJgmhy7tu7hmA6cATwPWA8slLY2INS3zLATeCDwuIm6SdL+Kre7IObNsVchabjkDZ80y5X2aWf0yzVnjxlE1ayWp41TCgcC6iLgiIu4ATgOOaJtnMXBKRNwEEBE3DnQFzBqiQtacM7OSvE8zq1+OOXOHzBpLAs1Sx6mE3YGrWx6vL55r9WDgwZJ+JOmnkg4dUPPNGqNi1pwzsxK8TzOrX645G+hwIpIWAYsWLFjA3D6X3G+5KmVdZ75lp9f114xdJa1oebwkIpb0WMkcYCHwJGA+8ANJDx/lufBNzVmVsq6z3rLd1Z61GZkzaNa24H8X6q2zO+/TxmVbaFKdVcrmuU/LM2cDXd2IWAYsm5iYWLx5S+/l586BfspVKes68y1bxqxZ0x7k3RgRE9O8fg1b36hyfvFcq/XABRFxJ3ClpF+SQra8j+YORBNzVqWs66y3bFkVsjaWOYNmbQv+d6HeOsvyPq338k3bFppUZ5WyOe/TcsyZT1m05qp+2Hk5sFDS3pK2B44ClrbN81XSLxxI2pV0GPqKwa2EWQNUy5pzZlaG92lm9cs0Z6U6ZJL+qRi2cZWkL0iaW6acWZ1E54syy1yYGRFbgBOAs4G1wOkRsVrSyZIOL2Y7G/htMXTvecA/R8Rva1kf58wyVSVrueUMnDXLk/dpZvXLNWddT1mUtDvwKmCfiNgk6XRSb/DTXVttVrMuh527ioizgLPanjup5e8AXlNMtXHOLHdVspZLzsBZs7x5n2ZWvxxzVvYasjnADpLuBHYEri1bgVmdSg5R2hTOmWXLWTOrn3NmVr8cc9a1ixgR1wDvA34DXAf8ISLOqbthZl1VPw84G86ZZc1ZM6ufc2ZWv0xz1rVDJuk+pBue7Q08ENhJ0jFTzHecpBWSVmzYsGHwLTVrU/U84Jw4Z5azccuac2ajMG45K+Zz1myocs1ZmZMonwpcGREbiuEbzwQe2z5TRCyJiImImJg3b96g22k2pRx/5eiTc2ZZG6esOWc2KuOUM3DWbDRyzFmZa8h+Azxa0o7AJuAQYMX0RcyGQNUvzMyIc2b5ctbM6uecmdUv05x17ZBFxAWSzgAuArYAFwO93rHarBZNO42jE+fMcuesmdXPOTOrX445KzXKYkS8BXhLzW0x64lo5GkcHTlnlitnzax+zplZ/XLNWdlh783yozx/5TCbcZw1s/o5Z2b1yzRn7pBZo+V4HrDZTOSsmdXPOTOrX445G2iHTNIiYNGCBQuY2+eS+y1XpazrzLdsV/n9yFG7puasSlnXWW/ZUsYsa4PIGTRrW/C/C/XWWcqY5Qyau08blzqrlM12n5Zhzga6uhGxDFg2MTGxePOW3svPnQP9lKtS1nXmW7YbSVn+ylG3JuasSlnXWW/ZMsYxa1VzBs3aFvzvQr11ljGOOYNm7tPGpc4qZXPdp+WaM5+yaI2WY6jMZiJnzax+zplZ/XLMmTtk1mwZHnY2m5GcNbP6OWdm9cswZ127iJIeImlly3SzpFcPo3Fm0ypu7tdpahLnzLLmrJnVzzkzq1+mOetac0RcFhH7RsS+wAHAbcBXam+ZWRcCpM5TqWVIh0q6TNI6SW+Y4vVjJW1o2am8fMCrAThnlreqWcslZ+CsWb68TzOrX6456/WUxUOAyyPi1z2WM6uBmFXh5n6SZgOnAE8D1gPLJS2NiDVts34xIk7ov509c84sM/1nLeOcgbNmWfE+zax+eeas12NzRwFf6LGMWW0kdZxKOBBYFxFXRMQdwGnAEbU2uBznzLJTIWu55gycNcuM92lm9csxZ6U7ZJK2Bw4HvtTh9eMkrZC0YsOGDVXbZdaVBLNnq+NUwu7A1S2P1xfPtTtS0i8knSFpj0G0vRPnzHJUMWvZ5Qymz5pzZqPgfZqzZvXLNWe9HCE7DLgoIm6Y6sWIWBIRExExMW/evB4Wa9a/WbPUcQJ2nfyHvpiO66OKZcBeEfEI4Fzg1EG2fwrOmWWp5qwNO2cwTdacMxsV79PM6pdjznq5huxofMjZctL9AsyNETExzevXAK2/WswvnrtbRPy25eHHgff02MpeOWeWn2pZyzFn4KxZbrxPM6tfpjkrdYRM0k6ki9fOLDO/2TAIVR26dDmwUNLexWkVRwFLt6pDekDLw8OBtQNbgTbOmeWqYtayyllRn7Nm2fE+zax+ueas1BGyiLgVuG+Zec2GqewQpVOJiC2STgDOBmYDn4yI1ZJOBlZExFLgVZIOB7YAvwOOrdzozu1xzixb/WYtt5wVbXLWLEvep5nVL8ec9TrsvVk+RKWhSwEi4izgrLbnTmr5+43AGytVYtZ0FbPmnJmV4H2aWf0yzZk7ZNZY6eZ+1UJlZt05a2b1c87M6pdrzgbaIZO0CFi0YMEC5va55H7LVSnrOvMt203VXzmaqKk5q1LWddZbtoxxy9ogcgbN2hb870K9dZYxbjmD5u7TxqXOKmVz3aflmLOBrm5ELAOWTUxMLN68pffyc+dAP+WqlJ07B351w2191blwtx37rnMU6znsOquW7WoAh52bqIk5myzbT9b6zdlknU15j7LNGYxl1qrmDEa3Leyw3wk9l9t08YcatY9oWp2ljGHOoJn7tHH57lilbLb7tExz5lMWrbHSYedRt8Js5nPWzOrnnJnVL9ecuUNmDaYsf+Uwm3mcNbP6OWdm9cszZ2XvQ7aLpDMkXSppraTH1N0wszIkdZyaxjmznDlrZvVzzszql2POyh4h+0/gWxHxvOImaDvW2CazUpTpecAVOGeWJWfNrH7OmVn9cs1Z1w6ZpHsDB1Pc1Cwi7gDuqLdZZuU08VfDqThnljtnzax+zplZ/XLMWZlTFvcGNgCfknSxpI9L2ql9JknHSVohacWGDRsG3lCzqcyapY5TwzhnlrVxyppzZqMyTjkDZ81GI8eclemQzQH2Bz4SEfsBtwJvaJ8pIpZExERETMwGPqvnAAAayUlEQVSbN2/AzTTbltQ5UA3ceTlnlq1xy5pzZqMwbjkDZ82GL9eclemQrQfWR8QFxeMzSCEzGzmp89QwzpllzVkzq59zZla/HHPWtUMWEdcDV0t6SPHUIcCaWltlVtLsWeo4NYlzZrlz1szq55yZ1S/HnJUdZfGVwOeKUXKuAF5aX5PMykm/ZjRrJ9WFc2ZZctbM6uecmdUv15yV6pBFxEpgoua2mPWsab8aTsc5s5w5a2b1c87M6pdjzsoeITPLUoY/cpjNSM6aWf2cM7P65ZizgXbIJC0CFi1YsIC5fS6533JVyi7crf97FTZpPUdRZ9Wy0xEwu2KqJB1KunnlbODjEfGuDvMdSboo+VERsaJSpRU1NWfQf9bGJS855gyqZ21ccwaj2RY2XfyhodfZtPdoFHV2431as/Zp4/LdsUrZHPdpueZsoKsbEcuAZRMTE4s3b+m9/Nw50E+5ybI77HdCz+U2XfyhSnX+6obbei63cLcdK9U5ivd2FGW7kiqdByxpNnAK8DTSiFDLJS2NiDVt8+0MnAhcsO1Shm/UOetnm4f+t/t+sw3953sU23y2OYNKWRvXnEG1bWEUORt2nZP1NiUvOecsFR/PrI1in1Z1m2/Kd8cqZbPdp2WaszLD3ptlSVQeKedAYF1EXBERdwCnAUdMMd+/Ae8GNg+s8WYNUjFrzplZCd6nmdUv15y5Q2aN1uXmfrtKWtEyHddWfHfg6pbH64vn7iZpf2CPiPhGrStilrkKWXPOzEryPs2sfjnmrNQpi5KuAm4B7gK2RIRHzbGRK3ETv41VtlVJs4D3A8f2u4we67sK58wyVGfWhp2zos6rcNYsM96nmdUv15z1cg3ZkyNiYy8LN6tbxQszrwH2aHk8v3hu0s7Aw4DvFecb3x9YKunwGi+Cds4sSxWylmPOwFmzDHmfZla/HHPmYe+t0Sre3G85sFDS3qQwHQX87eSLEfEHYNeWur4H/L9Rj0hlNgoVsuacmZXkfZpZ/XLMWdlryAI4R9KFU5xLaTYSUueLMstcmBkRW4ATgLOBtcDpEbFa0smSDq+5+VM2CefMMlQlaxnmDJw1y5D3aWb1yzVnZY+QPT4irpF0P+BcSZdGxA9aZyjCdhzAnnvu2W97zHpS9eZ+EXEWcFbbcyd1mPdJ1WrryjmzbFXJWmY5gy5Zc85sVLxPM6tfjjkrdYQsIq4p/n8j8BXSkI/t8yyJiImImJg3b16ZxZpVMoChS7PinFmuxi1rzpmNwrjlrHjNWbOhyjVnXTtkknYqbm6GpJ2ApwOr6m6YWRmzpI5Tkzhnljtnzax+zplZ/XLMWZlTFncDvlJcADcH+HxEfKvWVpmVING4ndQ0nDPLlrNmVj/nzKx+ueasa4csIq4AHjmEtpj1bFYDT+OYinNmuXPWzOrnnJnVL8ecedh7a7QMf+Qwm5GcNbP6OWdm9csxZ+6QWWNNDl1qZvVy1szq55yZ1S/XnA20QyZpEbBowYIFzO1zyf2WA9h08YeGXufC3XYcep2jeG9HVbabijf3a6RR56zfbb5Kvf1mu0qd45TRMsYta4PIGfT/uYwiZ6Oos0rZptVZxrjlDJq7T2tanU3Ly7h9dxzo6kbEMmDZxMTE4s1bei8/dw70U65K2blz4Fc33NZXnQt327HvOkexnsOus2rZbgTMzjBUdWtizibL9pO1fnM2WWdT3qNccwbjmbWqOYPRbQtNyVmVsk2rs4xxzBk0c582dw7ssN8JfdW56eIPNWabr1I2131arjnzKYvWaHNK3UnPzKpy1szq55yZ1S/HnLlDZo0l5XnY2WymcdbM6uecmdUv15yV7pBJmg2sAK6JiGfV1ySz8mZn+CtHFc6Z5WomZc05s1zNpJyBs2Z5yjFnvRwhOxFYC9yrpraY9UTkeXO/ipwzy84MzJpzZtmZgTkDZ80yk2vOSvURJc0Hngl8vN7mmPVmtjpPTeOcWc5mStacM8vZTMkZOGuWrxxzVvag3QeB1wF/6jSDpOMkrZC0YsOGDQNpnNl0JDFrmqmBnDPL0gzLmnNmWZphOQNnzTKUa866dsgkPQu4MSIunG6+iFgSERMRMTFv3ryBNdBsOrNndZ7KkHSopMskrZP0hileP17SJZJWSjpf0j6DXoeiHufMslYla86ZWTnep5nVL8eclan6ccDhkq4CTgOeIumz5ZpsVh8Bs2ep49S1fLrY+BTgMGAf4OgpQvP5iHh4ROwLvAd4/4BXY5JzZtmqkjXnzKwc79PM6pdrzrp2yCLijRExPyL2Ao4CvhsRx3RtsVndBLOmmUo4EFgXEVdExB2kncYRrTNExM0tD3cCYlDNb6vHObN8Vcuac2ZWhvdpZvXLNGe+D5k11gDutr47cHXL4/XAQdvUI70CeA2wPfCUKhWaNVHFrDlnZiV4n2ZWv1xz1tNI/BHxPd9HwnLS5VeOXScvFi6m4/qpIyJOiYi/Al4P/OsAm9+pPufMslN31pwzM+/TzIYhx5z5CJk11uR5wNPYGBET07x+DbBHy+P5xXOdnAZ8pHQDzWaIillzzsxK8D7NrH655izDe1WblSTQNFMJy4GFkvaWtD3pPPelW1UhLWx5+EzgV4NqvlljVMuac2ZWhvdpZvXLNGcDPUImaRGwaMGCBcztc8n9lqtSduFuOw69zlGs5yjqrFp2OgLmlLwCcyoRsUXSCcDZwGzgkxGxWtLJwIqIWAqcIOmpwJ3ATcBLqre8mqbmDPrP2rjkJcecQbWsjXPOYDTbQpNyVqVs0+rsxvu0Zu3TNl38oaHX6YxWl2vOBrq6EbEMWDYxMbF485bey8+dA/2Uq1LWdeZbtjtVvTCTiDgLOKvtuZNa/j6xUgU1aGLOqpR1nfWWLada1sYxZ9CsbcH/LtRbZznep43DttCkOquUzXeflmfOfA2ZNZYofXjZzCpw1szq55yZ1S/XnHXtkEmaC/wAuEcx/xkR8Za6G2bWlaodds6Jc2ZZc9bM6uecmdUv05yVOUJ2O/CUiPijpO2A8yV9MyJ+WnPbzKaV668cfXLOLFvOmln9nDOz+uWas64dsogI4I/Fw+2KqZY7u5v1qsvQpY3hnFnunDWz+jlnZvXLMWelhr2XNFvSSuBG4NyIuKDeZpl1J9IG3GlqGufMcuWsmdXPOTOrX645K1V3RNwVEfuSbn52oKSHtc8j6bjJu1pv2LBh0O0025ZgltRxahrnzLI1Zllzzmwkxixn4KzZCGSas546gxHxe+A84NApXlsSERMRMTFv3rxBtc+sIwGzpY5TUzlnlptxy5pzZqMwbjkrXnPWbKhyzVnXDpmkeZJ2Kf7eAXgacGndDTMro+Ld1rPhnFnunDWz+jlnZvXLMWdlRll8AHCqpNmkDtzpEfH1eptl1p0GcHO/jDhnli1nzax+zplZ/XLNWZlRFn8B7DeEtpj1TBmGqh/OmeXOWTOrn3NmVr8cc1bmCJlZnooLM82sZs6aWf2cM7P6ZZozd8issSaHLjWzejlrZvVzzszql2vOBtohk7QIWLRgwQLm9rnkfstVKes68y3bTY6/ctStqTmrUtZ11lu2jHHL2iByBs3aFvzvQr11ljFuOYPm7tPGpc4qZXPdp+WYs4GubkQsA5ZNTEws3ryl9/Jz50A/5aqUdZ35lu1mcujScdPEnFUp6zrrLVvGOGatas6gWduC/12ot84yxjFn0Mx92rjUWaVsrvu0XHOW41E7s9KqDl0q6VBJl0laJ+kNU7z+GklrJP1C0nckPWjQ62DWBFWy5pyZleN9mln9csyZO2TWYJ3vtF7mcHQxHO8pwGHAPsDRkvZpm+1iYCIiHgGcAbxnwCth1gD9Z805MyvL+zSz+uWZszI3ht5D0nlFT2+1pBO7ttZsCNKFmeo4lXAgsC4iroiIO4DTgCNaZ4iI8yLituLhT4H5g1yHSc6Z5axi1rLJGThrli/v08zql2vOylxDtgV4bURcJGln4EJJ50bEmjKtNquNYFa1Y7y7A1e3PF4PHDTN/C8Dvlmpxs6cM8tXtazllDNw1ixX3qeZ1S/TnJW5MfR1wHXF37dIWls0xqGykdP0v2bsKmlFy+MlEbGkr3qkY4AJ4In9lO/GObPcDSNrdecMnDXLm/dpZvXLMWc9jbIoaS/SndcvmOK144DjAPbcc89eFmvWlxIj5WyMiIlpXr8G2KPl8fziua3rkZ4KvAl4YkTc3kdTe+KcWW4qZi3LnBV17sUUWXPObBS8T3PWrH655qz0QTtJ9wS+DLw6Im5ufz0ilkTERERMzJs3r+xizSqpcmEmsBxYKGlvSdsDRwFLW2eQtB/wUeDwiLhx4CvQxjmzXFXIWnY5K+rsmDXnzEbF+zSz+uWYs1JHyCRtRwrU5yLizDJlzOomYFaFW0lExBZJJwBnA7OBT0bEakknAysiYinwXuCewJeUgvqbiDi8atun4pxZrqpkLbecgbNmefI+zax+ueasa4dMaUmfANZGxPv7XwWzASv/a0ZHEXEWcFbbcye1/P3UShWU5JxZ1ipmLZecgbNmGfM+zax+measzCmLjwP+DniKpJXF9IxeKzKrg6aZGsY5s6w5a2b1c87M6pdjzsqMsng+jfy3wGa6EhdmNoZzZjlz1szq55yZ1S/XnPU0yqJZdvLLlNnM5KyZ1c85M6tfhjlzh8warep5wGZWjrNmVj/nzKx+OeZsoB0ySYuARQsWLGBun0vut1yVsq4z37LdZJip2jU1Z1XKus56y5YxblkbRM6gWduC/12ot84yxi1n0Nx92rjUWaVsrvu0HHM20NWNiGXAsomJicWbt/Refu4c6KdclbKuM9+y3aQLMDNMVc2amLMqZV1nvWXLGMesVc0ZNGtb8L8L9dZZxjjmDJq5TxuXOquUzXWflmvOfMqiNZeq3UvCzEpy1szq55yZ1S/TnHUd9l7SJyXdKGnVMBpk1pMcxy7tk7NmWZshWXPOLGvOmVn9MsxZmfuQfRo4tOZ2mPUh3dyv09RAn8ZZsyzNqKx9GufMsuScmdUvz5x17ZBFxA+A3w2hLWY9me4HjsbtunDWLF8zKWvOmeXKOTOrX6458zVk1mhq3q+GZo3krJnVzzkzq1+OOStzymIpko6TtELSig0bNgxqsWbTmqXO00zknNmojFPWnDMblXHKGThrNho55mxgHbKIWBIRExExMW/evEEt1qyzXI8718g5s5EYs6w5ZzYSY5YzcNZsBDLNmU9ZtMYSed5t3WymcdbM6uecmdUv15yVGfb+C8BPgIdIWi/pZfU3y6ycDH/k6JuzZjmbKVlzzixnzplZ/XLMWZlRFo+OiAdExHYRMT8iPjGMhpmVIanjVLL8oZIuk7RO0humeP1gSRdJ2iLpeQNfgRbOmuWsStacM7NyZso+zTmznOWYs4FdQ2Y2ClLnqXtZzQZOAQ4D9gGOlrRP22y/AY4FPj/Ylps1S79Zc87MyvM+zax+OebM15BZo1U8DfhAYF1EXJGWpdOAI4A1kzNExFXFa3+qVJNZw1XImnNmVpL3aWb1yzFnA+2QSVoELFqwYAFz+1xyv+WqlHWd+ZadjtT1wsxdJa1oebwkIpa0PN4duLrl8XrgoAE2sRZNzVmVsq6z3rLdVMza2OYMmrUt+N+Feuvsxvu0Zu3TxqXOKmVz3KflmrOBrm5ELAOWTUxMLN68pffyc+dAP+WqlHWd+ZYto8uPHBsjYqK+2kejiTmrUtZ11lu2rHHLWtWcQbO2Bf+7UG+dZY1bzqCZ+7RxqbNK2Zz3aTnmzKcsWoOVvwCzg2uAPVoezy+eM7OtVMqac2ZWivdpZvXLM2ce1MMarcqFmcByYKGkvSVtDxwFLK2zvWZNVSFrzplZSd6nmdUvx5yV6pB1G97RbBREtVBFxBbgBOBsYC1wekSslnSypMMBJD1K0nrg+cBHJa2ubX2cM8tUlazllrOiPmfNsuN9mln9cs1Z11MWW4Z3fBrpwrXlkpZGxJrpS5rVTxVv4xcRZwFntT13Usvfy0mHo2vlnFnuqmQtl5yBs2Z58z7NrH455qzMEbK7h3eMiDuAyeEdzUZuljpPDeOcWdacNbP6OWdm9csxZ2U6ZFMN77h7Pc0x64Gg6t3WM+KcWb6cNbP6OWdm9cs0ZwMb1EPScZJWSFqxYcOGQS3WrKOq5wE3kXNmozBuWXPObBTGLWfgrNnw5ZqzMh2yUsM7RsSSiJiIiIl58+YNqn1m08rxsHOfnDPL2jhlzTmzURmnnIGzZqORY87KdMg8jKplS9P81zDOmWXNWTOrn3NmVr8cc9Z1lMWI2CJpcnjH2cAnI6LWIYnNypopp3E4Z5Y7Z82sfs6ZWf1yzFnXDhlMPbyj2aiN+nzfQXPOLFfOmln9nDOz+uWas1IdMrNcNXDkKbNGctbM6uecmdUvx5y5Q2aN1sALnc0ayVkzq59zZla/HHM20A6ZpEXAIuC2HbbT2g6z7Qps7PDavYE/9FGuStnpylUp6zqrlV04zTILjbzQubKac1al7Cgy6n8XqtVZImcwjlkrmTOYOduC/12oVme3st6ndeDvjlnXWaWsvzv2IiIGPgFLpnltxaDL1VVnXe0dlzrrbG9EsO9+B8Tvbt3ScerWtqZP3hb870LddU5O45y1HD+XmVJnXe1t2r8Lk9M458zbQp51zrTPJSLfnNV1yuKyIZdznXnWWaVsqXIZngY8TN4WXOfQ6hzjrGX9uTS8ziplZ2SdY5wzyPhzGeM6q5TNts4cc1ZLhywi+noj+y3nOvOss0rZUuUEs3JM1ZB4W3CdQ6tzjLOW9efS8DqrlJ2RdY5xziDjz2WM66xSNts6M83ZKAb1WDLkcqMq6zrrLYuKyaY0LtuC/12ot07AWetiXLYF11lvWedseuOyLbjOestmmzMV51yaNc7+B0zED368vOPrO8+ddWFETEy3DEmHAv9JunHlxyPiXW2v3wP4X+AA4LfACyPiqopNN2uUqllzzsy68z7NrH655mxWqdabZWryBn9TTd3LajZwCnAYsA9wtKR92mZ7GXBTRCwAPgC8e7BrYNYM/WbNOTMrz/s0s/rlmLOhdcgkHSrpMknrJL2hh3KflHSjpFV91LmHpPMkrZG0WtKJJcvNlfQzST8vyr2tx3pnS7pY0td7LHeVpEskrZS0oseyu0g6Q9KlktZKekyJMg8p6pqcbpb06h7q/Kfi/Vkl6QuS5pYsd2JRZnUv9U29rP5DBRwIrIuIKyLiDuA04Ii2eY4ATi3+PgM4RDneUbDFsLM2qpwVyxhq1vrJWVGu76z1m7OibA5Zc862LjfUnBVlG7VPG0XOivLep2Vm2Dkryvq74/RlnLM6cjaMoRxJh/QuB/4S2B74ObBPybIHA/sDq/qo9wHA/sXfOwO/LFMv6fTSexZ/bwdcADy6h3pfA3we+HqP7b0K2LXP9/hU4OXF39sDu/TxGV0PPKjk/LsDVwI7FI9PB44tUe5hwCpgR9I1jN8GFvSzzvvvf0BsujM6TnQfVvV5pEPNk4//DvhQ2zyrgPktjy/v9zMaxjSKrI0qZ0W5oWatas5aPqNSWes3Z8W8WWTNOdum7FBzVszfqH3asHNWzO99WmbTKHJWlPV3x94+I+dsADkb1qAed/cmASRN9ibXdCsYET+QtFc/lUbEdcB1xd+3SFpL2himrTfSu/fH4uF2xVTqYjtJ84FnAu8ghat2ku5N+sfnWIBIPfY7elzMIcDlEfHrHsrMAXaQdCcpJNeWKPPXwAURcRuApO8DzwXe02N7ueiiC8/eYTvtOs0sc9t+LVoSEZUHOMjc0LM2ipzB8LM2oJxB71nrJ2fgrNWpMTkr5m/MPm2EOQPv03Lj74418nfHjkaSs2F1yHYHrm55vB44aEh1A1AEcz/SLxZl5p8NXAgsAE6JiFLlgA8CryP9qtKrAM6RFMBHe9gA9gY2AJ+S9EhSu0+MiFt7qPso4AulGxpxjaT3Ab8BNgHnRMQ5JYquAt4h6b5FuWcAPR1ib2nDof2Ua3ENsEfL4/nFc1PNs17SHNLd439bsd46jTRrQ8wZDD9rg8gZ9JC1CjmDfLLmnA1YrzkryjRlnzb0nIH3aRXrrYu/O5bj7449yDVnYzGoh6R7Al8GXh0RN5cpExF3RcS+pDf6QEkPK1HPs4AbI+LCPpv6+IjYn3Sh4CskHVyy3BzSofmPRMR+wK1AL+dabw8cDnyphzL3If1StTfwQGAnScd0KxcRa0kXN54DfAtYCdxVtt4BWw4slLR38R4cBSxtm2cp8JLi7+cB3y1+BbM2w8pZUdcoslYpZ9B71vrNGWSVNedsgPrJGTRqnzb0nBVlvE+zrfi74/Scs8HmbFgdsjK9yVpI2o4UqM9FxJm9lo+I3wPnAWV61I8DDpd0Fekiv6dI+mwPdV1T/P9G4Cukw/VlrAfWt/wScwYpZGUdBlwUETf0UOapwJURsSEi7gTOBB5bpmBEfCIiDoiIg4GbSOdnD11EbAFOAM4G1gKnR8RqSSdLOryY7RPAfSWtI51G0NMXgxEYSdaGnDMYTdaq5gx6z1rfOYM8suacDU7VnEEj9mmjyBl4n5Yjf3csV5e/Ow5RbTmLPi6I63Ui9cKvIPWIJy/M/D89lN+L/i7MFOk+AB/ssdw8igsbgR2AHwLP6nEZT6KHCzOBnYCdW/7+MXBoD+V/CDyk+PutwHt7KHsa8NIe1+8gYDXp/F+RLgx9Zcmy9yv+vydwKX1csO2p43s79KyNMmdF2aFlrUrOijI9Za1KzoryzloNU5NyVpRt1D5t2Dkrynifltk0ipwV5fzdsVxZ52yA0/AqSud7/pI00sibeij3BdLFlXeSevMv66Hs40nn1v6CdHhzJfCMEuUeAVxclFsFnNTH+vYaqr8s/rH5ebGxln6PivL7ks6n/QXwVeA+JcvtRDqv9d59rOPbilCsAj4D3KNkuR+SLo79OXDIsLbBcZmGnbVR5qxYztCy1m/OirJ9Za3fnBVlnbWapqbkrCjbqH3aKHJWlPU+LbNp2Dkryvq7Y/dyztmAJxUraWZmZmZmZkM2FoN6mJmZmZmZ5cgdMjMzMzMzsxFxh8zMzMzMzGxE3CEzMzMzMzMbEXfIzMzMzMzMRsQdMjMzMzMzsxFxh8zMzMzMzGxE3CEzMzMzMzMbkf8P1N7IJZXOEkMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x216 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Define the MDP\n",
    "mdp = MDP()\n",
    "mdp.inbuilt_init(mdp_dict=createGrid10World())\n",
    "\n",
    "#Plot states\n",
    "pl.figure(figsize=(3,3))\n",
    "mdp.gridPlot(ax=pl.gca(), im=mdp.S.reshape((10,10)), title='States', cmap='Greys')\n",
    "\n",
    "#Plot rewards\n",
    "pl.figure(figsize=(15,3))\n",
    "pl.suptitle('Rewards', fontsize=15)\n",
    "for a in range(4):\n",
    "    pl.subplot(1,4,a+1)\n",
    "    mdp.gridPlot(ax=pl.gca(), im=mdp.R[:,a].reshape((10,10)), title='a='+mdp.A[a], cmap='jet')\n",
    "pl.show()\n",
    "\n",
    "#Plot rewards\n",
    "pl.figure(figsize=(15,3))\n",
    "pl.suptitle('Rewards - clipped larger +ve values for visualizing the edges', fontsize=15)\n",
    "for a in range(4):\n",
    "    pl.subplot(1,4,a+1)\n",
    "    mdp.gridPlot(ax=pl.gca(), im=np.clip(mdp.R[:,a].reshape((10,10)), -1, -0.5), title='a='+mdp.A[a], cmap='jet')\n",
    "pl.show()\n",
    "\n",
    "#Plot rewards\n",
    "s0_x, s0_y = 3, 5\n",
    "s0 = mdp.xy2s(s0_x, s0_y)\n",
    "pl.figure(figsize=(15,3))\n",
    "pl.suptitle('Transition probabilities T(s1|s0=({},{}),a)'.format(s0_x, s0_y), fontsize=15)\n",
    "for a in range(4):\n",
    "    pl.subplot(1,4,a+1)\n",
    "    mdp.gridPlot(ax=pl.gca(), im=mdp.T[s0,a,:].reshape((10,10)), title='a='+mdp.A[a], cmap='Blues')\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "69e5d03e60f646a79ad4dcb17e1c204c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Text(value='4', description='s0_x'), Text(value='5', description='s0_y'), ToggleButtons(…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#An interactive plot of transition probabilities\n",
    "def f(s0_x, s0_y, action):\n",
    "    a = mdp.A.index(action)\n",
    "    s0 = mdp.xy2s(int(s0_x), int(s0_y))\n",
    "    pl.figure(figsize=(6,6))\n",
    "    title = 'Transition probabilities T(s1|s0=({},{}),a={})'.format(int(s0_x),int(s0_y),action)\n",
    "    mdp.gridPlot(ax=pl.gca(), im=mdp.T[s0,a,:].reshape((10,10)), title=title, cmap='Blues')\n",
    "    pl.show()\n",
    "\n",
    "interactive_plot = interactive(f, s0_x='4', s0_y='5', action=widgets.ToggleButtons(options=['left', 'right', 'up', 'down']))\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Policy evaluation\n",
    "\n",
    "Computing the utility, U.\n",
    "\n",
    "$U^\\pi_k(s) = R(s, \\pi(s)) + \\gamma \\sum_{s'} T(s' \\mid s, \\pi(s))U^\\pi_{k-1}(s')$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def iterativePolicyEvaluation(mdp, policy, numIterations=10):\n",
    "    U = np.zeros(len(mdp.S))\n",
    "    U_old = copy.copy(U)\n",
    "    for t in range(numIterations):\n",
    "        for s0 in range(len(mdp.S)):\n",
    "            U[s0] = mdp.R[s0,policy] + mdp.discount*sum([mdp.T[s0,policy,s1]*U_old[s1] for s1 in mdp.S])\n",
    "            #U = map(s0 -> R(s0, policy(s0)) + discount*sum(s1 -> (T(s0, policy(s0), s1)*U[s1]), S), S)\n",
    "            #U[s0] = mdp['R'][s0,policy] + mdp['discount']*np.sum(mdp['T'][s0,policy,:]*U_old[:])\n",
    "        U_old = copy.copy(U)\n",
    "    return U\n",
    "\n",
    "numIterations = 5\n",
    "pl.figure(figsize=(15,3))\n",
    "pl.suptitle('Utilities', fontsize=15)\n",
    "for a in range(4):\n",
    "    pl.subplot(1,4,a+1)\n",
    "    U = iterativePolicyEvaluation(mdp=mdp, policy=a, numIterations=numIterations)\n",
    "    mdp.gridPlot(ax=pl.gca(), im=U.reshape(10,10), title='a='+mdp.A[a], cmap='jet')\n",
    "pl.show()\n",
    "#print(np.round(U.reshape(10,10),3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "63138a85920247038f38f6121fafd5b9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(ToggleButtons(description='action', options=('left', 'right', 'up', 'down'), value='left…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(action, numIter=1):  \n",
    "    U = iterativePolicyEvaluation(mdp, policy=mdp.A.index(action), numIterations=numIter)\n",
    "    pl.figure(figsize=(3,3))\n",
    "    mdp.gridPlot(ax=pl.gca(), im=U.reshape(10,10), title='Utility', cmap='jet')\n",
    "    pl.show()\n",
    "\n",
    "interactive_plot = interactive(f, action=widgets.ToggleButtons(options=['left', 'right', 'up', 'down']),\n",
    "                               numIter=widgets.IntSlider(min=0, max=20, step=1, value=0))\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Value iteration\n",
    "def valueIteration(mdp, numIterations=1):\n",
    "    U = np.zeros(len(mdp.S))\n",
    "    U_old = copy.copy(U)\n",
    "    for t in range(numIterations):\n",
    "        for s0 in range(len(mdp.S)):\n",
    "            U[s0] = max([mdp.R[s0,a] + mdp.discount*np.sum(mdp.T[s0,a,:]*U_old[:]) for a in np.arange(len(mdp.A))])\n",
    "        U_old = copy.copy(U)\n",
    "    return U\n",
    "\n",
    "def policyExtration(mdp, U):\n",
    "    policy = np.zeros(len(mdp.S))\n",
    "    for s0 in range(len(mdp.S)):\n",
    "        policy[s0] = np.argmax([mdp.R[s0,a] + mdp.discount*np.sum(mdp.T[s0,a,:]*U[:]) for a in np.arange(len(mdp.A))])\n",
    "    return policy\n",
    "\n",
    "U = valueIteration(mdp, numIterations=2)\n",
    "policy = policyExtration(mdp, U=U)\n",
    "pl.figure(figsize=(3,3))\n",
    "mdp.gridPlot(ax=pl.gca(), im=U.reshape(10,10), title='Utility', cmap='jet')\n",
    "for s in range(100):\n",
    "    x, y = mdp.s2xy(s)\n",
    "    if policy[s] == 0:\n",
    "        m='\\u02C2'\n",
    "    elif policy[s] == 1:\n",
    "        m='\\u02C3'\n",
    "    elif policy[s] == 2:\n",
    "        m='\\u02C4'\n",
    "    elif policy[s] == 3:\n",
    "        m='\\u02C5'\n",
    "    pl.text(x-0.5,y-1,m,color='k',size=20)\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ebcda33788ba481ea132eb66d17954c5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='numIter', max=20), Output()), _dom_classes=('widget-inte…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(numIter=1):  \n",
    "    start_time = timeit.default_timer()\n",
    "    U = valueIteration(mdp, numIterations=numIter)\n",
    "    policy = policyExtration(mdp, U=U)\n",
    "    elapsed = timeit.default_timer() - start_time\n",
    "    print('time=', np.round(elapsed*1000,2))\n",
    "    pl.figure(figsize=(3,3))\n",
    "    mdp.gridPlot(ax=pl.gca(), im=U.reshape(10,10), title='Utility', cmap='jet')\n",
    "    for s in range(100):\n",
    "        x, y = mdp.s2xy(s)\n",
    "        if policy[s] == 0:\n",
    "            m='\\u02C2'\n",
    "        elif policy[s] == 1:\n",
    "            m='\\u02C3'\n",
    "        elif policy[s] == 2:\n",
    "            m='\\u02C4'\n",
    "        elif policy[s] == 3:\n",
    "            m='\\u02C5'\n",
    "        pl.text(x-0.5,y-1,m,color='k',size=20)\n",
    "    pl.show()\n",
    "\n",
    "interactive_plot = interactive(f, numIter=widgets.IntSlider(min=0, max=20, step=1, value=0))\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Policy iteration\n",
    "\n",
    "Policy evaluation can be used in policy iteration:\n",
    "1. Given the current policy, compute U\n",
    "2. Using U, compute a new policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def policyIteration(mdp, numIterations=1):\n",
    "    U_pi_k = np.zeros(len(mdp.S)) #initial values\n",
    "    pi_k = np.random.randint(low=0,high=4,size=len(mdp.S),dtype=int) #initial policy\n",
    "    pi_kp1 = copy.copy(pi_k)\n",
    "    for t in range(numIterations):\n",
    "        #Policy evaluation: compute U_pi_k\n",
    "        U_pi_k_temp = copy.copy(U_pi_k)\n",
    "        pi_k = copy.copy(pi_kp1)\n",
    "        for s0 in range(len(mdp.S)):\n",
    "            U_pi_k[s0] = mdp.R[s0,pi_k[s0]] + mdp.discount*np.sum(mdp.T[s0,pi_k[s0],:]*U_pi_k_temp[:])\n",
    "        #Policy improvement\n",
    "        for s0 in range(len(mdp.S)):\n",
    "            pi_kp1[s0] = np.argmax([mdp.R[s0,a] + mdp.discount*np.sum(mdp.T[s0,a,:]*U_pi_k[:]) for a in np.arange(len(mdp.A))])\n",
    "    return U_pi_k, pi_kp1\n",
    "\n",
    "U_pi_k, pi_kp1 = policyIteration(mdp, numIterations=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cee421beb3234a6c87a0bf2d48a4cdb0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='numIter', max=20), Output()), _dom_classes=('widget-inte…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(numIter=1):  \n",
    "    start_time = timeit.default_timer()\n",
    "    # code you want to evaluate\n",
    "    value, policy = policyIteration(mdp, numIterations=numIter)\n",
    "    elapsed = timeit.default_timer() - start_time\n",
    "    print('time=', np.round(elapsed*1000,2))\n",
    "    pl.figure(figsize=(3,3))\n",
    "    mdp.gridPlot(ax=pl.gca(), im=value.reshape(10,10), title='Utility', cmap='jet')\n",
    "    for s in range(100):\n",
    "        x, y = mdp.s2xy(s)\n",
    "        if policy[s] == 0:\n",
    "            m='\\u02C2'\n",
    "        elif policy[s] == 1:\n",
    "            m='\\u02C3'\n",
    "        elif policy[s] == 2:\n",
    "            m='\\u02C4'\n",
    "        elif policy[s] == 3:\n",
    "            m='\\u02C5'\n",
    "        pl.text(x-0.5,y-1,m,color='k',size=20)\n",
    "    pl.show()\n",
    "\n",
    "interactive_plot = interactive(f, numIter=widgets.IntSlider(min=0, max=20, step=1, value=0))\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Q-learning\n",
    "\n",
    "This is a model-free reinforcement algorithm. \n",
    "\n",
    "Instead of using transition probabilities and rewards, use the observed next state.\n",
    "\n",
    "$Q(s,a) \\leftarrow Q(s,a) + \\alpha \\big( r + \\gamma \\max_{a'}Q(s',a') - Q(s,a) \\big)$\n",
    "\n",
    "1. Choose an action based on $Q$ and some exploration stratergy\n",
    "2. Observe new state and reward\n",
    "3. Update the new $Q$ values using the above equation\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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