TDn-StepbySampling-Copy1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With Constant Step Size\n",
      "\n",
      "\n",
      "MDP with 10 states and 2 actions\n",
      "discounting factor gamma = 0.95, step size alpha = 0.01\n",
      "\n",
      "Running  100 episodes\n",
      "\n",
      "The Policy is (state,action) = target probability    behavior probability\n",
      "(0,0) = 0.4835164835164835      0.4351851851851852  (0,1) = 0.5164835164835165      0.5648148148148148  \n",
      "(1,0) = 0.48854961832061067      0.423728813559322  (1,1) = 0.5114503816793893      0.576271186440678  \n",
      "(2,0) = 0.881578947368421      0.5714285714285714  (2,1) = 0.11842105263157894      0.42857142857142855  \n",
      "(3,0) = 0.7980769230769231      0.1  (3,1) = 0.20192307692307693      0.9  \n",
      "(4,0) = 0.2926829268292683      0.49382716049382713  (4,1) = 0.7073170731707317      0.5061728395061729  \n",
      "(5,0) = 0.4430379746835443      0.2824427480916031  (5,1) = 0.5569620253164557      0.7175572519083969  \n",
      "(6,0) = 0.88      0.42168674698795183  (6,1) = 0.12      0.5783132530120482  \n",
      "(7,0) = 0.4715447154471545      0.1  (7,1) = 0.5284552845528455      0.9  \n",
      "(8,0) = 0.30952380952380953      0.8636363636363636  (8,1) = 0.6904761904761905      0.13636363636363635  \n",
      "(9,0) = 0.34328358208955223      0.3401360544217687  (9,1) = 0.6567164179104478      0.6598639455782312  \n"
     ]
    },
    {
     "data": {
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ZWTtCIvgyYcmhxIq31Qk/IFWUBiT1xkYjLjYizCutKEsJr121FAlh3i/NI5JrmjMoUjk9SJgov7+ZbVNCu2MIXxSmk3rITpw+jK67JO+Ihjl1TGqXiaIiBbsnzR0plrt/QEgk+kZfqLoAr3u8VTJLU1SNMDFJL5pDk6qHqWiYVFm+HO+evMHCWoHleZ2y5VxCb8fEDF6vxHmDXYG3Er7kjyX0Cp9IKHqR7nzBkp77yi7V678F4fNlpq+ujJmL93Vpz+s/gY9TJILVE+6vvCYQvjOV1KOe2La+ZWGpkJJEiU1RVdCiz4AW0fWziYlgpD1rDp/NpTXOGcKw+GpU7OfFh4TOj3Yp9q2x7ItIoVEyKFIJuftXhDluNYHnzGzr5DZRefdbCV+kTi5miEyc/kfowTvCzHZJ2ncmoSLeS0mFGdLi7t8TCtU0Aa63pIk7ZlbbUq/1dTchqRhB+HJ1T6b3nU0W1k5b47WN9u1O+GK1nL/PhSnqwVpjCLG7TyAU8TnYzPol74+Ou4OZ1Uuxq4eZ9UzadhphvuCrZXmdysvM1jGziwlFNpZF8aRrIiGZPoCw9Epiwlc03+38pL9LU+xzXwWcEfWyAX8lWjcQ3icPJLTLxfu6tOd1NtDSEtYwjN7zlxNe22y4Pbq+OSpQ9TdJBXFujq6HFtO2tpntms6dRkW4mhWz7xBCxeMfgU+jzbOi6y5JbTdJeAwV5RJLWNcw+mHu6ujPB1LfJCeKht1fFf0gURTPRpRhZIZIVaNhoiKV1yBgPcIckKlm9jKhamdNwgT6XQlD3w5192wWv8gKD+u9HQs8AbxlZk8RJv+3IZRmn0soglBWJxOGTv0b6GZmrxDWLducUIihF2sWD3gCuIkwvHQ+obJknI4CrjOzzwgJ3zzCa74tYYijAae5e+K8l7HAGcD9ZvY/whCpnxKGhf5f1OZBMzud0Iv6MyFxbk14znYhFM5JNAoYZWYjCXOydiQ8jz8S1o/LtWPMrDvhMdcm9AbtRhhy9h3Q393Hp3uwqPjNm4T12CAhGXT3L81sNiFxWcHf17YryaeEOXGHm9lKwvnswEOJlTgrqfGEz5nEdQa3IyTVNxU1ytH7urTn9RbCEjJTovNzBaH3e0vgecLaeeXi7i9GhZzOAz43s6J1BhsSepfeIgwzx91fMbOLCMNXZ5jZaOBrwnnbnNVrvqYT15nAxWb2IaHAy0LCfLs2hM/4FcAAd18etR9P+Kw42MyaEKYHNCQsjfExFTdHbiXhc+LjhNdkP+AfwLP8fR3PXHuAUExnT2CamY0i9JD2JXz+tSDMLxUpSEoGRSqpqKfvTDN7gvBlfDfCkLeVhF+HbwIGu/uc2IIshbv/z8w6EXpgehGKUHxP6KG7IurhK+uxfzSz9oTE6GDCHMCVhGI39xGGzibf5g8z+y8hgRyW8AUrLkcRkpWiuW0NCV+C5wKPAXcll+939xfM7BzCgspnEL70fAncFe3/Jlpi4lRCr9jhhFEi8whfugezupch0ZPAUELhmn8REusRhDXmZmbvIRerqELtSkKCO49QLORFYISnXkS7NGMJz+8i1hy2NpYwzPr9YqoWriFKMPcnrAn5f4TCFQDjSG8ZmHw2kPCF+jhCQrOAkIRdmlxgKdvv69KeV3e/08x+J/QM9ycsRP4mYaH6Q8lCMhjFcX5UPXcg4T2wHuFHo/dZvQRDUdurzOwtwvusI2GB9sWEBPIewvqv6ehN+NFlt+jfmxBGA3xL+By7zd0/TrjflWb2L8KSCb2i+59DWB7nSsK6ehXlQEIRnUMJc0W/i/6+NqqUXCHcfZWZ7Uso1nUE4TmZC9xP+Ezbj9VzXkUKjlXg+1FEJO9Fpe87AP9096/jjiduUZGK+wiLuT9SWnupWszsEcIPBpvl8w9Lkj+iz9B27p73HQ5m1ovwg9KV7n5x3PGIxEFzBkVEImbWgfAr/gtKBEVEqgYza5RiWz3gmujPpys2IpH8kfe/2oiI5JqZnUyYJ9ifMAxxUKwBiYhINt0WFeMaTxjivBlhGO1GwJ1RNWmRgqRkUEQkzINrCMwEznD3yTHHIyIi2TMSqEeY67khYV3Kj4Gh7j4szsBE4qY5gyIiIiIiIgVIcwZFREREREQKUJUeJlqvXj1v3rx53GGIiIiIiIjEYvLkyQvdvX6qfVU6GWzevDmTJk2KOwwREREREZFYmNns4vZpmKiIiIiIiEgBUjIoIiIiIiJSgJQMioiIiIiIFCAlgyIiIiIiIgVIyaCIiIiIiEgBUjIoIiIiIiJSgJQMioiIiIiIFCAlgyIiIiIiIgVIyaCIiIiIiEgBUjJYwUaPhvHj445CREREREQKnZLBCuQOF18MnTvDhx/GHY2IiIiIiBQyJYMVyAxGjYL11oMuXeDKK2HlyrijEhERERGRQqRksIJtuilMmBCSwYsvhiuuiDsiEREREREpREoGY9CqFTz7LHTsGJLBSZPijkhERERERAqNksEYPfccbLQRHHUUzJ8fdzQiIiIiIlJIlAzGqG5duP9++Oor2Gcf+O67uCMSEREREZFCoWQwZvvuCw88AFOmQOvW8PbbcUckIiIiIiKFQMlgHjj00JAM1qkTCss8/njcEYmIiIiISFWnZDBPbLUVTJ0K7drB4YfDXXfFHZGIiIiIiFRlSgbzSJ06MHo09O4Np5wCxxwDM2fGHZWIiIiIiFRFSgbzTJ068MQTcNhh8Nhj0KkTvPde3FGJiIiIiEhVo2QwD627Ljz6KEyeDLVqQY8ecPLJsGhR3JGJiIiIiEhVoWQwj22zTaguuvvucPfd4XrFirijEhERERGRqkDJYJ5r2jQsTn/HHTBtGowcGXdEIiIiIiJSFSgZrCROOAE22QRuugnc445GREREREQqOyWDlUSNGvCf/8DEidC+PXz1VdwRiYiIiIhIZaZksBI5+2wYMiQMF23dGl58Me6IRERERESkslIyWImYwfHHw6efQvPm0Lcv/PJL3FGJiIiIiEhlpGSwEmrWDO65B37/PSxMv3x53BGJiIiIiEhlo2SwkurQAa68MlQX3X9/WLo07ohERERERKQyUTJYiV14Idx1F7z0EnTvDp9/HndEIiIiIiJSWSgZrOROOglGjIApU6BVq9Bj+OuvcUclIiIiIiL5LtZk0MxOMbOPzOyX6DLezPok7DczG2Rmc83sdzMbZ2bbxBlzPtpvv7DUxMCBMH48HHCACsuIiIiIiEjJ4u4ZnAOcC+wEtAFeA54xs+2j/ecAZwIDgV2A+cCrZlYnhljzWqNGcNttcMst8Npr0LEjLFkSd1QiIiIiIpKvYk0G3f1Zdx/t7jPd/Qt3vxBYArQ3MwNOB65195Hu/jHQD6gDHBZj2Hnt9NPh6afhk09g111DYigiIiIiIpIs7p7Bv5hZdTP7P6A28C6wOdAQeKWojbv/DrwJdIglyEpi771h1Kiw9ES3bnDYYbB4cdxRiYiIiIhIPok9GTSz7cxsKbAMuAfY392nERJBgB+SbvJDwr5UxxtgZpPMbNKCBQtyEnNl0KdPWJz+vPPgySdh++3h5ZfBPe7IREREREQkH8SeDALTgdZAO+Bu4CEz2zZhf3L6Yim2rW7sPsTd27h7m/r162c92MpknXXgmmvg7behZk3o2RPatYOJE+OOTERERERE4hZ7Mujuf0ZzBie5+/nAFOAMYF7UJLkXsAFr9hZKCdq1C0tP3HorzJgR5hJedlkYRioiIiIiIoUp9mQwhWrAWsDXhIRwz6IdZrY20Jkwp1AyULs2nHoqzJ4NBx8MgwZBmzbw1ltxRyYiIiIiInGIe53Ba82ss5k1j+YOXgN0AR51dwcGA+eZ2QHR0NEHgaXAY7EFXcnVqQOPPw6jR8OcOdCrF3z7bdxRiYiIiIhIRYu7Z7Ah8Ahh3uBYwlqCvdx9dLT/euBm4E5gErAp0MPdtYJeOfXsCa++CsuWwU47heUoVFxGRERERKRwmFfhDKBNmzY+adKkuMPIa9OmwRFHwEcfwTbbwIQJYUipiIiIiIhUfmY22d3bpNoXd8+gxGy77UICeOqpYaH6CRPijkhERERERCqCkkFhnXXg0kuhWjU4/3x4910NGRURERERqeqUDAoAdevC1VfDpEnQsSPcf3/cEYmIiIiISC4pGZS/nHtuqDAKcMYZMHgwLF0ab0wiIiIiIpIbSgblbxo3hs8+C2sQnnEGNG8O11wDK1bEHZmIiIiIiGSTkkFZw1Zbweuvh7mD7drBBRdAzZqwcGHckYmIiIiISLYoGZRitW8Pzz8fissAPPJIvPGIiIiIiEj2KBmUUl10UbhevDjeOEREREREJHuUDEqpatSAOnXgjTc0d1BEREREpKooMRk0s+0rKhDJb/37h3mEW20V5hKKiIiIiEjlVlrP4BQzm2Bmx5jZuhUSkeSlwYNh5EhYtgw6dQpDR1VQRkRERESk8iotGZwBtAXuA743s7vNbKfchyX5xgwOOACmToVDD4WrrgrLTjzzTNyRiYiIiIhIWZSYDLp7S6AL8BhQEzgBmGhmE83seDOrnfsQJZ/UrQuPPgoffAC1aoUE8bjj4o5KREREREQyVWoBGXd/092PBDYFTgWmATsD9wBzzWyIme2S2zAl3+y4I8ycCU2bwv33w223hSGkIiIiIiJSOaRdTdTdF7v7He7emjB09H7AgeOACWb2oZmdZGbr5yhWyTN168Lo0WEI6WmnQceOsGBB3FGJiIiIiEg6yrS0hLtPcvcBhN7C44H3gR2AO4Dvshee5LtWreCHH+CGG+Cjj8LfI0fGHZWIiIiIiJSmXOsMuvtv7n4/YfjoW4ABqjpaYOrXh7POgg8/hMaNoW/f0Ft47rnw559xRyciIiIiIqmUORk0sw3M7BQzmwJMADoDSwnDR6UAbbMNTJoE114b/r7++pAYaqF6EREREZH8k3EyaGa7mdlwYC5wG7A98AFwItAoGj4qBapmzdAj6A5XXw2jRsGJJ8YdlYiIiIiIJKuRTiMzqw8cDRwLbEEYDroEGAIMcfcPcxWgVF7nnw8zZoRqo716wYEHxh2RiIiIiIgUKbFn0Mz2MrMRwBzgWmBLYCKhguim7n6SEkEpyeWXh+u+fWGDDeA7lRcSEREREckLpQ0THQ0cAPwG3AXs4O7t3H2Yu/+W8+ik0mvSBD7/HI44An75Bdq3h3nz4o5KRERERERKSwYnAP0JvYAD3X1aBcQkVUzLlvDww/DSS/Djj9CuHbz4YtxRiYiIiIgUthKTQXfv4O4PufsfFRWQVF177QVjxkCtWtCnD9x7b9wRiYiIiIgUrnKtMyiSqfbtYfJkaNAAhg2LOxoRERERkcKlZFAqXJ060KNHSArffDPuaERERERECpOSQYlFv36wciXsvjt8+mnc0YiIiIiIFB4lgxKL7t1h7Njw7+uuizcWEREREZFCpGRQYtO1KxxwAAwfDh99FHc0IiIiIiKFRcmgxOqkk6B6ddhpJzj+eFi1Ku6IREREREQKQ5mTQTPb3cwuyWYwUni6d4dvvglzCIcODdVGH3kE3OOOTERERESkaitPz2AX4NIsxSEFrFGjkAjedht8/z0ceSRccQWsWBF3ZCIiIiIiVVesw0TN7Hwzm2hmv5jZAjMbZWbbJrV50Mw86TIhrpglN8xg4ED48kvYeWe49FLYcUf46qu4IxMRERERqZrinjPYBbgL6AB0BVYAY8ysblK7McCmCZfeFRijVKCaNWH8eLjvPvjiC2jTBu68E379Ne7IRERERESqlliTQXffy90fcPeP3X0acCRQH+iY1HSZu89LuPxU8dFKRalZE447DqZNg2bN4N//DnML582LOzIRERERkaqjPMngLODNLMVRpA4hpkVJ2zuZ2Xwz+8LM7jOzBlm+X8lDW24JkyfDtdfClCmwyy6wZEncUYmIiIiIVA1lTgbd/SF33yObwQC3AlOA8QnbXgKOAroBZwJtgdfMbK0s37fkoWrV4Nxz4dFHYc4cuPjiuCMSEREREakaasQdQBEzuxnoBHRy95VF29398YRm08xsMjAb6AP8L8VxBgADAJo2bZrTmKXiHHAAtGqlgjIiIiIiItkSdwEZAMzsFuBQoKu7l/h1393nAnOALYrZP3Po0S4AACAASURBVMTd27h7m/r162c/WInNFlvACy/AoEHwk2aNioiIiIiUS+zJoJndChxGSAQ/T6N9PaAx8H2uY5P8csMN0LkzXH457LADjBoVd0QiIiIiIpVX3OsM3gn0J/QKLjKzhtGldrS/tpndaGbtzay5mXUBRgHzgadjC1xiseWWMG4cvPIKrLsu7LMP7L03PPdc3JGJiIiIiFQ+cfcMnkyoIDqW0NNXdDkr2r8S2A54FvgCeAiYDrR3d9WVLFDdu4fqomeeGYaN7rsv9OkTFqwXEREREZH0mLvHHUPOtGnTxidNmhR3GJJDCxeG4aP33gt//AFnnBHmFK6lWrMiIiIiIpjZZHdvk2pfVnsGzayFmfXI5jFFSlKvHlx3HYwfH3oHr70WDjkEqvBvHCIiIiIiWZF2MmhmK82stFXeBgCjyxeSSOZatYKRI8PC9M8+CxdeGHdEIiIiIiL5LZN1Bg3Y38w2L2b/uoS1/zSXT2LzxhvQsydccw1MnAjHHQcHHwxmcUcmIiIiIpJfMl10vnV0KcntZYxFpNzWWQdGj4aLL4abb4YxY+Dhh+GCC6BDh7ijExERERHJH2kXkDGzVcBw4OFimiwHZrv77CzFVm4qIFPYpk8PPYTPPgs//wx9+8L558NOO8UdmYiIiIhIxSipgEymPYNfufvYLMQkknMtW8KDD8Jvv4WKo9dfDyNGwG67we23w/bbxx2hiIiIiEh84l5nUCTn1l0XLr0UZswIlUc/+QR22AFuvDHuyERERERE4qNkUApGo0Zwzjnw2Wdh4fqzz4YPP4w7KhERERGReGQ6TPQYM+teSht3993LGpBIrtWvD0OHQvPmYf7gb7+FwjMiIiIiIoUk02SwaXQpiZb7lrzXrBmcdhrceiucd16YT7jWWnFHJSIiIiJScTJNBgcDt+YiEJGKdtNNMHcu3HYbvPZaGDJaI9N3hIiIiIhIJZXJV9/LgNfzaekIkfKoXh2efDIkg6edBpttBpMmQePGcUcmIiIiIpJ7JRaQMbNTzWwjAHe/zN3frJiwRCrOwIGwzz4wbx4cckjc0YiIiIiIVIzSqokOBr4zs+Fm1qkiAhKpaGZhYfpLL4V33oH99oMvvog7KhERERGR3CotGbwfWA4cAbxhZp+a2RlmtnHuQxOpWOefD5ddBq+8Ehas32IL+PnnuKMSEREREcmNEpNBdz8e2BQ4HpgIbAXcCMwxs0fNrEvOIxSpIGutBZdcAh98ALvuCjNnwsEHw7JlcUcmIiIiIpJ9pS467+6/ufv97t4O2A64A/gVOBQYa2bTzewsM6uf41hFKsRWW8G778Luu8Orr0LbtjB1atxRiYiIiIhkV6nJYCJ3/8TdTwMaEQ0dBVoA1wPfmtkTaSxKL5L3qlWDceNCtdFvv4Wdd4ZTTwXXKpoiIiIiUkVklAwWcfc/3f0xd+8KbAFcC/wEHAS8lMX4RGJ10EFhuGifPnD77dCrF0yeHHdUIiIiIiLlV6ZkMMkSYBGwNPrbsnBMkbxRty48/DAccQSMHRvmE15xBXz9ddyRiYiIiIiUXZmTQTPby8yeAr4l9Ay2AN4EjsxSbCJ5Y/31Q0I4Zw706BEKzfzjH9CtGyxZEnd0IiIiIiKZyygZNLMmZnaJmX0NvAgcCPwC3Axs5e5d3P2xHMQpkhc22QReeAGefhr69oXXXoOOHWH8+LgjExERERHJTKnJoJlVN7P9zOwF4GvgUqApMI5QUbSxu5/t7lqmWwqCWViY/qmn4Kab4KuvoHPnMHR01aq4oxMRERERSU+JyaCZXQPMAUYCvYAfgRuALd29m7s/4e7Lcx+mSH76z39g9mzYf/8wdHS77eD11+OOSkRERESkdKX1DJ4LNADGECqFNnH389z9y5xHJlJJbLwxPPEE3HUXzJoFXbuGOYYTJ8YdmYiIiIhI8UpLBq8B/unue7n7SHdfURFBiVQ21arBSSeFNQlvuSUUlWnbFv73P61NKCIiIiL5qcRk0N0vdPdZFRSLSKVXty6cfjq8+CK0agUHHgjHHQd//hl3ZCIiIiIif5eNdQZFJEmvXjB1Khx8MAwbBk2awNChsFwzbEVEREQkTygZFMmRmjXh8cdh9Gho3hyOPx7OOy/uqEREREREAiWDIjlkBj17wnvvQcOG8KVKL4mIiIhInlAyKFIBzKBlS3j2WXj5ZRWVEREREZH4FZsMmtn6ZlarIoMRqcr69QtVR3v2hLXXhgsugF9/jTsqERERESlUJfUMLiKsMwiAmQ0zs31yH5JI1dS/P8yfD4MHh+qi11wDvXurl1BERERE4lFSMuhJ+48GWmfzzs3sfDObaGa/mNkCMxtlZtsmtTEzG2Rmc83sdzMbZ2bbZDMOkYqy8cZw2mkhATz5ZHjzTejbF556ChYtijs6ERERESkkJSWD3wMtcnz/XYC7gA5AV2AFMMbM6ia0OQc4ExgI7ALMB141szo5jk0kp666KgwX/d//whIUjRuHNQonT4a5c+OOTkRERESquhol7HsNONzM6hESQ4D9zKx5Kcd0dz82nTt3970S/zazI4HFQEdglJkZcDpwrbuPjNr0IySEhwH3pnM/Ivloww1h8eLQOzhhAnzwAdx1F9x6a9i/776w//5wyCEhaRQRERERySbzYiYsmdkmwENAd0IPogOWxjHd3auXKRizTYG5QGd3f9vM/gF8CbR194kJ7V4AFrp7v5KO16ZNG580aVJZQhGJxZdfwk03wSefwIwZ8H30M8wff8Baa8Ubm4iIiIhUPmY22d3bpNpXbM+gu/8A9DSzmsCmwCxgMHBrLoKM3ApMAcZHfzeMrn9IavcD0DjVAcxsADAAoGnTpjkIUSR3/vnP0DsIsGoV7LQTTJ0KW28NQ4ZAt27xxiciIiIiVUep6wy6+3J3/waYDcxy99mlXcoSiJndDHQCDnT3lclhJDdPsa0o3iHu3sbd29SvX78soYjkhWrVYMoUGDUKli+H7t3hoIPglVdg4cK4oxMRERGRyi7tRefdfXN3vy0XQZjZLcChQFd3/yph17zoumHSTRqwZm+hSJW0994hKbzgAhgxAvbaC+rXD8Vm/vwz7uhEREREpLJKOxlMZGadzGygmV1sZqeaWaeyBmBmtxKKwXR198+Tdn9NSAj3TGi/NtAZeLes9ylS2dStG6qPTp0KRx8NPXqEQjMdO8L48VqrUEREREQyV1I10TWY2U7AI0DLok1EwzXNbDpwlLunXbHFzO4EjgT2AxaZWVEP4FJ3X+rubmaDgQvN7HPgC+AiYCnwWCaxi1QF228PDzwQkr+HHw5rFXboAFtsAbvuCvffD7VqxR2liIiIiFQGafcMmlkLwnITWwHvAFcAJ0XXb0fbXzWzLTK4/5OBOsBYwvIVRZezEtpcD9wM3AlMIhSz6eHuSzK4H5EqxQyOOgpmzQoFZ9ZeGx55JFzvvDPceCOsWBF3lCIiIiKSz4pdWmKNhmYPAYcDh7r7Uyn29wUeBx4tbcmHiqKlJaSQXHIJ3HMPLFgQ/t5tN3jjjXhjEhEREZF4lbS0RCZzBrsDz6RKBAHcfQTwbNRORCrY5ZfD/PlhCGnr1mEx++uvjzsqEREREclXmSSD9YDkAi/JPo/aiUiMXn4Z1lsPzj0Xxo6NOxoRERERyUeZJIMLgK1LabMVoBXQRGLWoAHMmAEtWoT1Ce+7L+6IRERERCTfZJIMvgbsY2b/l2qnmR0I7AuMyUZgIlI+m24KEybAdtvBaafB9OlxRyQiIiIi+SSTAjItgMlAbcIaf68TKn82BLoAnYAlwC7uPiMXwWZKBWRE4PPPoVUraNIkLFq//fawzjpxRyUiIiIiFaGkAjJprzPo7jPNrDswHOgYXZyw1iDAdKBfviSCIhJstVXoGbzjDmjXLmwbMADatoVevaBRo3jjExEREZF4pN0z+LcbmXUAdgI2ABYDH7r7O1mOrdzUMyiy2nffwXXXwX//Cwujmb0NGsALL0CblL8ViYiIiEhlV1LPYJmSwcpCyaBIasuXw7hx0KNH+LtDBxg2DFq2jDUsEREREcmybK0zKCJVRM2asOee8O674e933w3DSddfH4YPD2sVioiIiEjVpmRQpIC1bx8Sv3nz4MADYckS6NcPjjxSCaGIiIhIVadkUETYZJNQaXTp0jBk9NFHYebMuKMSERERkVxSMigif1lvPXjwwfDvdu3gs89iDUdEREREckjJoIj8zRZbwG23wYoVYfmJCy+EVavijkpEREREsk3JoIisYeDAUG20WTO4+mp47LG4IxIRERGRbNPSEiJSrJUroUYNqFcv9BLutBN06QK77RYqkoqIiIhIfsvqOoNmVg1oDDQBUn4ddPc3Mw0yF5QMipTfCy/AscfCDz+s3la9OkyaBK1bxxeXiIiIiJSupGSwRoYHOhs4C6hXStPqmRxXRPJXnz4wZw68/z40bQpDh8Jll8GOO4ZhpM2awb33hnUKRURERKTySLtn0MwGAZcAPwKjgO+AFanauvtlWYqvXNQzKJIb330HjzwCzzwDEyaEbS1aQI8ecPjhsOuuofdQREREROKVlWGiZvYtsAzY2d0XZzG+nFEyKJJb7vDcc3D00fDzz6u3b7xxGFo6aBCss05c0YmIiIhISclgJtVENwaeqyyJoIjknhnsuy8sWhQSw88/hyuugPbt4frroVOnsE1ERERE8k8myeBMYKNcBSIilV/LlnDRRTBqFNxxB3zwQRg2WoWLFouIiIhUWpkkg3cBe5tZw1wFIyJVxymnQP/+ISF85pm4oxERERGRZGkng+5+D/Aw8I6Z9TOz7cysaapL7sIVkcrkjjvCtabuioiIiOSfTHoGAaYShooOA6YAX6e4fJXNAEWk8lp3XahfH66+Glq1guHD445IRERERIqkvc6gmR0H3EtYTmIcMJdilpYQESnyyiswbFhYiqJfv1BgpnfvsH7hbrvB2mvHHaGIiIhIYcpkaYnPgA2BDu7+dU6jyhItLSGSP5YvD0nhiBEwZkzYVqsW/N//QffusGoVHHVUqFAqIiIiItlR0tISafcMAs2BoZUlERSR/FKzJpxwQrj8+COMHBnmEg4btnr46BdfwFVXxRuniIiISKHIZM7gd0DNXAUiIoVj441hwAAYMgS+/Rbuuitsv/pqOOAAmDhRy1GIiIiI5FomyeBwoLeZ1clVMCJSeDbdFE46CT7+GI4/HkaPhrZtoVq10GO4ZEncEYqIiIhUTZkkg1cD7wNjzKyLkkIRyaZttgk9hZ9/Dn37hm39+sH664d5hGecAc89B4sXxxuniIiISFWRSQGZlUX/BEq6kbt7JnMRc0YFZEQqr2XL4K234KmnQpJYpHp1WLkSRo2CvfeOLz4RERGRyqCkAjKZJIPjKDkJ/Iu775F2dDmkZFCk6li6FN57L1QjveeesG2vveC886BLl1hDExEREclbWUkGc8XMdgPOAnYGGgH93f3BhP0PAv2Sbvaeu7cr7dhKBkWqpvHj4fzzQ3K47rqwcKGWpBARERFJpaRkMO05g2a2m5m1zl5Yf6kNfAycBvxeTJsxwKYJl945iENEKon27WHcuFB99Kef4O67VX1UREREJFOZFJB5HRiQ7QDc/UV3v8DdRwCrimm2zN3nJVx+ynYcIlL5tG8frk85BU48EX77Ld54RERERCqTTJLBhRTfc5drncxsvpl9YWb3mVmDmOIQkTzSrh38/DP8+9+hyMy228Jhh4XKo1qrUERERKRkmSSD44AOOYqjJC8BRwHdgDOBtsBrZrZWDLGISJ7ZYAO4/XZ44gmoUwf++18YPDisVdiqVZhLuOOOcNZZ8OefcUcrIiIikj8ySQYvAlqa2RVmVjNXASVz98fd/Tl3n+buo4BeQEugT6r2ZjbAzCaZ2aQFCxZUVJgiErODD4apU8OSFIsXh3mEf/wR9k2ZAjfdBB07wiuvwC+/xBuriIiISD7IZGmJYUALoCPwAzAVmMeay024ux9bpmDMlgL/TqwmWky7r4F73P26ktqpmqhIYXOHjz6CJk3giCPgzTfDvMLateGhh+Bf/4KaFfbTloiIiEjFK6maaCaLwx+d8O+G0SUVB8qUDKbDzOoBjYHvc3UfIlI1mMEOO4R/jx4NS5bAsGGhCumBB4btderACSdAmzYhOVx33fjiFREREalImfQMNkv3oO4+O+0AzGoTehwB3gWuBZ4Dfooug4CRhOSvOXANsBnQyt2XlHRs9QyKSCorVsDLL8PQofDMM7DWWmF4acOGYW7hgAEhSRQRERGp7PJ90fkuhGUrkj0EnAQ8A+wIbEhICF8HLnb3b0s7tpJBEUnH8uUwfHhIDidMgI02Wj28VERERKQyy8qi87ni7uPc3VJcjnb33919L3dv4O613L1ZtL3URFBEJF01a8Kxx8L48XDRRbBoEcyYEXdUIiIiIrmVcTJoZu3MbKiZTTazL83sg2jtvziWnRARyapevcK1lqEQERGRqi6TAjKY2ZXA+YAl7WoNHGNm17n7BdkKTkSkotWqFa6XL483DhEREZFcS7tn0MwOAi4AvgGOA/4BrBNdHxdtP9fMDs5BnCIiFaJoqQn1DIqIiEhVl8kw0YGE9QV3cfdh7j7L3ZdF18OAXYAFwCm5CFREpCIU9QwqGRQREZGqLpNkcAdghLsvTLUz2v4UYcioiEilpGGiIiIiUigySQZrAL+V0uY3MpyHKCKST4qSwdNPh733hiefhJhX4BERERHJiUySwZnA3maW8jbR9t7Al9kITEQkDo0bh0TQHV54AQ45BHr2hDFj4o5MREREJLsySQb/C7QCnjWzLRJ3mNk/gRHA1sBj2QtPRKRiVasGt9wCCxbAu+/CEUfAq6/CnnvCWWfFHZ2IiIhI9pinOf7JzGoBrwC7AauAucD3QEOgMSGxfBvo7u55UXqhTZs2PmnSpLjDEJFKbskSOOCA0DvYqVNIEHv2hGbN4o5MREREpGRmNtnd26Tal3bPYJTg7QlcCHwNNCFUEN0s+vtCoFu+JIIiItlSpw48+ij85z8wdy6ceCI0bw5m0KMHTJkSd4QiIiIimUu7Z3CNG5rVBjYAFrv70qxGlSXqGRSRbFu1Cj75BEaMgJEjw78B+vSBffaBww6D2rVDb+KiRdC0abzxioiISGErqWewzMlgZaBkUERybf58uOMOePhhmDUL1l8fBgyAd96B8eOhQwfo3Ru22AJ69Qq9jCIiIiIVRcmgiEiOucOECaH4zFNPrd6+5ZbwxRfh3/XqhbmGZ54JO+wQhpmKiIiI5FJW5gxGB9rdzJ43s/lmttzMVqa4rMhO2CIilYcZtG8f1iWcNg2GDg3X06fD4sXw4ovQsiU88gjsuGPoJZw/P+6oRUREpJBlUk20D/AMUB34BvgWSJn4ufse2QqwPNQzKCL5Zvp02GWXMKewZk04/ng45hjYaSf1FIqIiEj2ldQzWCOD4wwClgN93P2VbAQmIlJoWraEr7+Ghx4KS1UMHQp33QX/+Ad07w5HHhmWr3BXcigiIiK5lckw0W2BJ5QIioiUz8Ybh2UqXnwxDBW95x5o1QqGDIHOnaFFi9BruOOOMHx46EUUERERybZMksGlwE+5CkREpBBtsAGccAI8/zz88AOcdBLMng0rV8K330K/ftCoEQwcGKqTrloVd8QiIiJSVWSSDI4F2ucqEBGRQtegQRgyumwZrFgBc+bA00+HYaN33x2WqTjppLijFBERkaoik2TwXOCfZnaRmWayiIjkSrVqUL06rL027LcfjB4NCxeGpHDIEDj0UHjssVClVERERKSsMqkmOgxoDuwOzAamAD+naOrufmy2AiwPVRMVkark5Zfh8svh3XdXb9tlFzj6aOjfH9ZZJ7bQREREJE9lZdF5M0t3poq7e/V0g8slJYMiUhVNmwYzZsAHH8DgwfDrr6EX8fDD4cILYfPN445QRERE8kW2ksFm6d6hu89Ot20uKRkUkarOPfQYPvUUDBsWtrVtC0ccAX37wqabxhufiIiIxCsryWBlpGRQRArJxIlhAfuPPw5/m8GBB4a5hv/+d5iHKCIiIoWlpGQwkwIyIiKSx3bZJQwhXbgQRo0K8whfew1OPz2sWTh2bNwRioiISD4pczJoZpea2YpsBiMiIuW38caw995w//0wdy5ccUVIELt3h1694Jxz4JlnwjqGiVauDENMGzSArbeGWrWgc2e44QaYNy+exyIiIiK5U+ZhomZ2KXBJvhSLSUXDREVEgiVLQjL4/vt/377VVmH5ilNPhXXXhQ03DNu33RYWLAiJ5aefhm1HHQVdu0KfPlCvXsXGLyIiImWjYaIiIgWuTh2YMAHGjYP33guXSy+F9deH666DRo2gSZPQ9p57wnDTefPgk0/C7bp0geHDwzIWDRpA+/YwaNDqtQ7/+ANWaKyIiIhIpaKeQRGRAvfJJ/DcczByJEyeHKqT9uixZrsvv4Tnn4fZs8Nah++9F6qVHn98WP8QYN994aCDoEULaNlydU+jiIiIxCMn1UTNbBAhGczb3kUlgyIimfn1V1hvvfTa3nknDBkCH31UfJvevcNQ1C23DEljtbz9H0NERKRqylUy2Axo7u5vlCe4XFIyKCKSe3Pnht7Egw4KRWdmzgw9jE8/DVOnhkI1y5eHtvvuCzvtBN99B7ffHtqLiIhI7midQRERiY176Bn86aew1uGCBWF7rVpw2WVw3nnxxiciIlKVlZQM1qjoYEREpLCYwYwZq/9euBBuvTXMUbzwwlDpdIMNYK21oFs32Gyz8LeIiIjkVlo9g2a2P9AFWAG85O6vFtOuH9DP3bumHYDZbsBZwM5AI6C/uz+YsN+AS4EBwEbAe8Ap7v5JacdWz6CISP6aOxeOPBLeeCOscVikenXYZBPYbTfYc0/o1Cn0LIqIiEjmytwzGCViTwAHAhZtPt3MXgCOcvefk27SHNg9w/hqAx8Dw6NLsnOAM4GjgenAJcCrZtbS3ZdkeF8iIpInGjWCsWPhl1/C/MLffw9LXXz2GXzxBbz2Gjz+eEgO998fjjsOdtghJIpmpR9fRERESlbaMNH+QF/gW+AeYDnQD9gbeNvMurr7/PIE4O4vAi8CmNmDifuiZPR04Fp3Hxlt6wfMBw4D7i3PfYuISPzWXx/69Vtz+6pV8OqrcM01MGJEuEAYQnrJJXD44SExFBERkbIprch3f+BnYBd3v8bdbwRaAzcDWwNjzKxeDuPbHGgIvFK0wd1/B94EOuTwfkVEJGbVqsFee8Hrr8O0afDCC3DLLaHwzJlnQsOG0KBBqFD6r3+FpS5efRWWLo07chERkcqhtJ7B7YARib1/7r4SOMvMvgEGExLCPdx9UQ7iaxhd/5C0/QegcaobmNkAwvxCmjZtmoOQRESkIpnBttuGS+/eMHAgfPhhGGL69tvw3HOh3fPPh+uaNaFt2zAMdY89YNSoUNH09NPD31rOQkREJCgtGazFmokYAO5+m5mtBG4nzOHrnu3gEu8u6W9Lsa0oriHAEAgFZHIYk4iIxKB6dWjTJlzOPTcUopk7F+rXh+nTQw/iyy/DO+/AU0+tvt1LL4Xrrl3h1FOhTx+ooZraIiJSwEr7b/A7oNjuNXe/08xqEoaNvgy8k8XYAOZF1w0J8xaLNKCYJFVERApLo0bhAtCsGfToEf69ahV8/HFIFLfYAu69Fx58EMaNC8VpataEJk3g66/DchZt2oTb16kDm28O228PzZvD/PnQqlVMD05ERCSHSksGpwF7lNTA3Qeb2VrANcCO2Qos8jUhIdwTmAhg9v/t3XmcFPWd//HXZxhgGLkFRG4QlBsUUFEQEVnUjRpEV4052F8Sk7juL8nuZrPZHBLNxjUPNR5RH1lzeOG1mJWoCwoKXkEEFcUDRTlE7vu+Br77x6c63dP0HIwzXTNd7+fjUY+eru+3qqu/1VNdn/5eVgKMBn5Qy68lIiIFpKjIA7rBg/35r37ly/798OST3tR08WIoK4OTToL33oPnnoM9e7xZaaZp02DSpPy/BxERkbpUVTD4v8AXzexvQwjPVJQphHCTmTUBfk4FzTcrYmbNgd7R0yKgm5kNBbaEED41s9uAH5vZEuAj4CfALuDho3kdERER8MntL7/cl1zKymDZMnjnHXjtNbjlFrjpJh/FdNw4TWshIiKFo6pg8E9AI2B3VTsKIdwQDSrT4yiPYTgwJ+P5z6PlfnxuwV8BzYC7SE86/zeaY1BEROpCcbFPcn/iiXDppd5M9MEHYfx4H8F0wgTvbzhqlD9XcCgiIg2Vhey2MAVk+PDhYeHChXEfhoiINHDbt3vT0pkzvSnpli3ptDPPhKuvhosugtat4ztGERGRXMzsjRDC8JxpCgZFRESqr6zMRyqdOhXuvbd82ogRPvjM+ed7kHj//dC7N4wZ4+tFRETyTcGgiIhIHdi71/sgzp0LTzzhU1u8+irs23dk3p49fVTS0lIfxbRFCzjmGG9uOnSo/y0iIlLbKgsGNcOSiIhIDTVr5o/nnOMLwMGDPtH92rXQsqUHek8+6aOVvv++L4cOld+PGfTq5aOaduoExx0HS5fCggU+uunkyXDjjen+ie++C/fc4/s+80zo3z9vb1lERAqIgkEREZFa1LgxXHJJ+XWDBqX/3r3bm5ouXgxNmnjQ+NZbHiR+9BG8/jps2uR5TzrJ02+6ybcZP95rFR94AO6+O73PAQPgqqt8wJs+fer+PYqISGFQM1EREZF6Zt06b37apo03Ob3wQpg9u3ye9u1hxgxf/+tfw/r1vr5zZ58Go00b+Na34LLLoKQk/+9BRETqB/UZFBERaeBWr/baxIcf9v6Go0bBlVem01et8n6Lf/qT/71iRTqtQwfo2tWnxPiHf/D+iaWlmhZDRCQJFAyKiIgkzP798PTT3ldx1SpvivrGG+n0Tp28xrBvX+jRAyZOhLFjoVEjCEGB9Cl6nAAAGd9JREFUoohIoVAwKCIiknAheED4zDPwwgvezHTRIg8at2yBXbugbVvYscP7Pe7d6wPT9Ovn8yc2bZoe9bRrVzj1VF8nIiL1m4JBERERqdCePR4kPv44TJvm67p39+aoZWWwcyds2OAjpaYUFcENN3iz05YtVZMoIlJfKRgUERGRajl4EIqLjwzuDh2CmTN9xNPmzeHqq9NpLVvC6af76KcAv/iFrxMRkfgpGBQREZFa9f77Pg3Gli0+7+GCBf4IPmVGav7DIUPgrLPgxBNVeygiEgdNOi8iIiK1qn//Iye7nzoVrr8ezj8fXnkF7r/f+yKC90fs3BnOPdenyhg2zAewWbcOunXL//GLiIhqBkVERKSOhOCD1Cxc6MHho4/CgQNH5uvfH044AZ56ykc5PeMMr0ns2BEGD4aePX3Am9WrPb20NP/vRUSkoVIzUREREakXNm3y4HDhQm9aunChj1L66quwfbvn6dXL50k8fPjI7UtKvNnpF7/oI5p26OBBY+PGeX0bIiINhoJBERERqddCgK1bvTkp+CimGzfC22/7oDWvveYB4oAB8NJLvi5b164wcCBMmOCjnBarM4yIiIJBERERKRwhwIcf+iA2GzemaxqPPRaWL4dly+Cyy+CSS7y5ae/esGqV1zS2bw/t2ilQFJHkUDAoIiIiiXHxxfDnP1ec3qiRB4lDhsDIkTB7to+M2rcvHHcc9OgBI0bAeef5NBoiIg2ZgkERERFJlF27vFnpBx94reFvfws33ui1iqtXw3vvwZw5sGOH5+/fH9q08ZrG5ct9vsXGjWH8eFi50vsn9uvnI6H27q2aRRFpOBQMioiIiGTZv98Dv5ISrw3MXD9/PkyfDnfd5c8zFRd7/hNOgKIi2LkTunSB4cN98Ju+fX0xg2uvhVmz/O9evTygPOMMaN3a87do4fsA30+LFvl69yKSFAoGRURERGrg4EGvXRw8GN55x0dA/eST9LJ6tQdx7dp5DWJKSYn3YVy92oO9iRM9/5IlsG/fka8zcCC8+65PnXHSSXDmmR6oTp8OrVr5wDo9e8KoUTB5svd9XLkSmjXzEVVFRCqiYFBERESkjm3Y4APVLFrkA9xs3uyB4nXX+Sio4M1Xp0/3JqyLFsG0aV6r2K6dP7/8cpg7F9avT+938mR/Pncu7N0Lxxzjwem8eZ4+caL3dWzVymsfTz3V+0MuW+aD5hx3HLRsmd+yEJH6Q8GgiIiISAOyY4cHc717pwexOXwYnnsOnnjCg80VK9JpGzb4NgcP+vOmTcs3b+3c2QfEmTABxozx/pGg+RlFkkDBoIiIiEiBO3zYm5bOmAFvvAHHH+/9Gjdv9uatzz2XHjCnUSN/HDPGm58OGQJjx3rNYpMm8NhjPqjO4MHpvCLSMFUWDGosLBEREZECUFTkwd+11+ZOP3gQXnoJnn3WR1g9cMBrH194oeJ9tmjhAWGvXvBv/+YBoogUDtUMioiIiCRUCLBliw9G8/jj8NprHvDt2eOD2Myf701SX3nFR1G99FJfdu/2wW4GDPAayEwzZngt5dlne/9GEYmXmomKiIiISI0tXw7jxvljth49fATUIUN8gJs77/T1RUXeBLVXL+/72Ls3fPwxPPSQB5ZnngkjR8L3v++jogJ89hm8+aYPeLN9OwwaBN27p5uqrlzpaS1bqvmqSHUpGBQRERGRz+WDD+D55z0427fPaw0PHfIA7f33feqMsjLPe8MNHtRt3eq1iEuXwrZt6X1dcYXXQq5Y4c9PPdVrJO+778jXbdoUTjvNH2fNSq+/6iro1g1KS72Wcts2P64LLoChQ+uqFEQaHgWDIiIiIlLnysq8iWiTJuXXp5qjfvwxtG7tNYkAf/yjN0FdssRrHdeuhR/8wGshU/M2LloEb73lg+IcPOjNVKdP9+apa9akA9BMnTp5gHnxxb6vrl09KG3WzGssRZJEwaCIiIiI1HsHDhwZSKbs3++BX2Y/xEOHfJs1a3zexaZN/e8FC3ywnFWrPF+/fl6zmTJ5svdpnDhRczBK4VMwKCIiIiKJcviwN2V95BEPFBcu9JrBvXvTeZo189rJY4+FxYu95rFzZxg+3B9T8zj+/vcwbRp84QseQHbqFM97EqkJBYMiIiIikmghgJn/XVYG3/0u3H13xfmLiqBVK+/3mMnMaxoHD4Zzz/W/f/tb6NjRg8cmTXxQnfPO8+1F4qZgUEREREQky7593nx0xQof7fTYY+HFF72p6ebNvr6oCJ56yvsplpT4FByffAJz58KOHRXvu6jIA8U9e3xU1O99DzZt8j6TAwd68GjmtZHFxelAVaS2Nehg0MymANdlrV4fQuhY1bYKBkVERESkLpSVwbJlPmpq584+VcaePd48dd4877P4wAM+XUYuLVv6QDoLFvjz00+HsWPhlFN88Jtu3Xz9wYPQuHHFx7B/v+ZzlMoVQjB4BXB2xupDIYSNVW2rYFBERERE4rRjh9dAzp3r02CUlnptZGp54QUYNsyDvvffT4+O2quXB5vgNZInn+zTbzRrBm3aQPv2cMcdPkJr8+beNPWYY7zmMhVIikDlwWBxvg+mhspCCOviPggRERERkaPRsqUvf/d36XXnnJM77759PpDNnDk+D2OLFvD22zB6tA+As2KF58nux/jVr8K773pt5LBh8I1vwIkn+pQcffp4sNi+PUyYkK5l3LYNXn7ZazVPOEH9G5OqoQSDvcxsNXAAmA/8ewhhWczHJCIiIiJSa0pKYMQIXypz6JD3aVy/3gO50lIfIOcrX/ERVG++Off8i+CB4d69vo9M3bt7bWSrVh5Irljhgenu3Z5eVOS1k1/4gtdYzpzpg+UMHAhDh8IFF3h/yFat1P+xIWkIzUTPB1oAS4AOwE+AvsCAEMLmyrZVM1ERERERSZqDB32Qm08/hQEDfC7GmTO9pnDtWnj+ebjwQm9yetFF8OGHXgO5erUHmZ984sHk6NHe/DQEn7Nx0aLytZIjR3pT123b0usGDPDayR07oGtXaNTI53884wzo0gV27YI//MEH1xkwwPN06QJt2yqIrCsNus9gNjNrDiwD/jOEcGuO9KuBqwG6des2bOXKlXk+QhERERGRhuvQIR8IJ3vgmt27PWjctQtGjUrXSL7zjo/CunMnPPqoN1kFr4UsK/OmrVXp0gXGjfOaxp07vX+kmR9LcTH07AnHHw+33ur9L7t39zwdOniNZOvWfiy//CW0a+d5i4rgmmt8oJ5mzWq9mBqMggoGAcxsDrAkhPCdyvKpZlBEREREJH9CgC1bvKYvZedODxg3bPCmpbt3ezD52Wde47hsmfdffOWV8rWMlenTB5YuzZ3WrZvXiqYUF3tNaNu2XrPZpo0vbdt6zeQpp/j+li/3aUWGDPH0TIcP+8ivLVp4cFlUVL4m86WXfF89e1bv+POpoIJBMysBlgP3hBCuryyvgkERERERkYahrMyDsbIyr31s1MiXAwd81NR16zzQnDzZaxLLymD7dg8gt21LB3rDhvk2S5d6LeXLL/s0Hzt3+uukajT37k2/duPG3rw2pVUrr6ns3t1rH196CWbMSKcXF/sx9Ojhr71oEUyaBNOm5aOkjk6DDgbN7GbgKeBTvM/gT4GzgEEhhErbgCoYFBERERGRw4c9aGve3GsnwYPBjz/2Gr+334YlS3yAnK1b4dVXvTZz1y5fUu67z+eW3LfPg8tPP/Ugct06mDrVazzrm4Y+tUQX4BGgHbAReA04vapAUEREREREBLxZZ2bTVfB+hIMG+VKZPXu8iWvz5t4f8Wtfq7vjzLd6HwyGEK6I+xhERERERCSZSku9OWghKor7AERERERERCT/FAyKiIiIiIgkkIJBERERERGRBFIwKCIiIiIikkAKBkVERERERBJIwaCIiIiIiEgCKRgUERERERFJIAWDIiIiIiIiCaRgUEREREREJIEUDIqIiIiIiCSQhRDiPoY6Y2YbgZVxH0cO7YBNcR9EQqns46Oyj4/KPj4q+3ip/OOjso+Pyj4+9bXsu4cQ2udKKOhgsL4ys4UhhOFxH0cSqezjo7KPj8o+Pir7eKn846Oyj4/KPj4NsezVTFRERERERCSBFAyKiIiIiIgkkILBePxX3AeQYCr7+Kjs46Oyj4/KPl4q//io7OOjso9Pgyt79RkUERERERFJINUMioiIiIiIJJCCQRERERERkQRSMJhHZnaNmS03s31m9oaZjY77mBoSM/uRmS0wsx1mttHMnjKzgVl57jOzkLW8lpWnqZndaWabzGy3mf3ZzLpk5ekW7X93lO8OM2uSj/dZX5nZlBxluy4j3aI8a8xsr5nNNbMBWftoY2YPmtn2aHnQzFpn5RlkZi9G+1htZj8zM8vX+6yPzGxFjrIPZvZMlF7puYny1Mr5KXRmdlZ0TVgdlePkrPS8fc7NbJKZvW9m+6PHiXX2xuuBysrezBqb2U1m9k50XV5rZg+bWbesfczN8b/waFYeXYeyVONzn7fvVjMbY36PtM/MlpnZt+vsjdcD1Sj7XNf+YGZ3ZeTRvU8NWPXuKwv+mq9gME/M7HLgduCXwMnAX4AZ2V9kUqmzgbuBM4BzgDJgtpm1zco3Gzg+Y7kgK/02YBJwJTAaaAk8bWaNAKLHZ4AWUfqVwKXALbX+jhqeDylftoMy0v4V+GfgH4ERwAZglpm1yMjzMHAKcD5wXvT3g6lEM2sJzALWR/v4/8APgH+qm7fTYIygfLmfAgTg8Yw8lZ0bqIXzkxDNgXeB7wJ7c6Tn5XNuZiOBx4CpwNDo8b/N7LTaeJP1VGVlX4qX439EjxcDXYGZZlaclfePlP9f+FZWuq5DR6rqcw95+G41s57A/+L3SCcDNwJ3mtmkz/0O66+qyv74rOXCaP3jWfl073P0zqbq+8rCv+aHELTkYQHmA/dmrVsK3Bj3sTXUBb+AHgIuzFh3H/B0Jdu0Ag4AV2Ws6wocBiZEz8+PnnfNyPNlYB/QMu73HWN5TwHerSDNgLXAjzPWNQN2At+KnvfDA5gzM/KMitadFD3/DrADaJaR5yfAaqIBr7QEgB8D24DSqs5NbZ6fpC3ALmBybZdjdT7n+E3BrKzjmQ08Ene5xFH2FeTpH5XroIx1c4HfVLKNrkM1KHvy9N0K3AQszdr374B5cZdLXGWfI8+9wIdxnJ9CX8i6r0zKNV81g3kQVbEPA57LSnoO/zVCaqYFXru9NWv9KDPbYGYfmdm9ZtYhI20Y0JiMcxFCWAV8QPpcjAQ+iNanPAs0jbZPsl5R84blZvaomfWK1vcEOlK+XPcCL1G+XHfhv/imvArszsrzcrRtyrNAJ6BHLb+XBilqVvJ14KEQwp6MpIrODdTe+Um6fH7OR3Lkd8az6Fxkahk9Zn8HXBE1cXvPzG7O+gVf16Gay8d3a0Wf++Fm1rj23krDZGbNgSvwgDCb7n0+v+z7ykRc8xUM5kc7oBFePZxpPf4hk5q5HVgEzMtYNxP4KjAOr9Y/FXjBzJpG6R3xX302Ze0r81x05MhztSnaLsnnaz4wGf/18Jt4WfzFzI4lXS6VfcY7AhtD9HMXQPT3Biov+/UZaQLj8S+o32Wsq+zcQO2dn6TL5+e8ojw6F/z1R9ZbgKdCCJ9lJD0MXAWMBW7Am8X9KSNd16Gaydd3a0VlX4zfSyXdl/Dg7P6s9br3qR3Z95WJuOZnt7OXupU9qaPlWCfVYGa34tXwo0IIh1LrQwiZAwUsNrM3gJXA31L+huCIXVL+XFR0XhJ7vkIIMzKfR53TlwFfA1Id1av6jOcqv6ryWAXrk+qbwIIQwqLUiirOza0ZSbVxfiR/n3N9Z+QQ9RF8CGgNXJSZFkLInPB5sZktA+ab2SkhhDdT2XLtFl2HKpTn71aVfcW+CTwZQtiYuVL3Pp9fRfeVkYK+5qtmMD8q+mWlA0f+CiBVMLNf4x2bzwkhLKssbwhhDfAZ0CdatQ6vpc3+hTHzXKzjyHNVUe1uYoUQdgHv4WWbGrmyss/4OqBD5uhZ0d/tqbzsU01dEl/2UbOfi8ndROivss4N1N75Sbp8fs4rypPocxEFgo8Ag4FxIYTNVWyyEP/+zfxf0HXoc6rD79aKyr4MqOpcFzQzGwoMp4rrP+je52hVcl+ZiGu+gsE8CCEcAN7Am3dlGk/5NsZSBTO7HW8mcU4IYUk18rcDOuMdgMHPw0EyzoX50Mr9SJ+LeUA/Kz/k8nhgf7S9AGZWAvTFy3Y5fiEbn5U+mvLl2hxvF58yEjgmK8/oaNuU8cAaYEWtv4mGZzL+OXy0skxZ5wZq7/wkXT4/5/PQd0Y5UZ+xx/BAcGwIYV0Vm4CPqtuI9P+CrkO1oA6/W+cB52a93HhgYQjhYG2+hwboavzzN7uqjLr3qb4q7iuTcc2Pc9SeJC3A5fhITt/A//luxzucdo/72BrKAtyFj8Z0Dv7rSWppHqU3B27G/wl74EMGz8N/HWuRsZ978BGczsWHrp6DtxFvFKU3AhYDL0Tp50b574y7DGIu/5uBMXh/tdOAp6Pz0T1K/2H0/BJgIB6wrMkq+xlR2Z4enafFeJ+fVHor/ML7aLSPS6J9/nPc7z/uBW8u8hFZoxJX59zU1vlJwhJdR4ZGyx7gZ9Hf3WqrHKvzOccHDSgDfoQH9j/Cb+ZOi7uM4ih7vFvLk9G1+BTKfwc0i7Y/IdpmOP4dcAE+QMabRNf32jo/hbZUUfZ5+27Fr2G78WkQ+uH3TAeASXGXURxln5GnFNhOxqiWWdvr3qdmZV/pfWWUp+Cv+bGfiCQtwDX4LwCpX1nOivuYGtKCt5vOtUyJ0pvhIy9tiL48VuLDLXfN2k8JcCfe5GQP8FSOPN3wG+o9Ub47gaZxl0HM5Z+6AB6IviCeAPpnpBs+xcFafCjqF4GBWftoi/f12REtDwGts/IMwkfq2hft6zoSMJx7Ncp/bPR5P/Voz01tnp9CX/AbqVzXmftqsxyr8znH5/haEp3XD4BL4i6fuMoev8mt6DtgcrR91+h8bMa/Zz/Gf3htWxfnp5CWKso+r9+t+A9bb0bncDnw7bjLJ66yz8jz93ig0CnH9rr3qXnZV3pfGeUp+Gt+am4LERERERERSRD1GRQREREREUkgBYMiIiIiIiIJpGBQREREREQkgRQMioiIiIiIJJCCQRERERERkQRSMCgiIiIiIpJACgZFRKQgmdlcM9P8SSIiIhVQMCgiIvWamYWjXCbHfcyVMbMSM/sXM5tvZtvN7ICZrTWzN8zsN2Y2Jiv/lOh9nR3TIYuISIEqjvsAREREqvDzHOu+B7QCbge2ZaUtih6/CpTW4XEdNTNrDrwInAKsA54A1gPHAX2Aq4HWUR4REZE6pWBQRETqtRDClOx1Ue1fK+C2EMKKCrb7tE4PrGa+hweCzwEXhhAOZCaaWRugXxwHJiIiyaNmoiIiUpBy9Rk0s7OjJpdTzGy4mc2MmmpuNbMnzKxrlK+XmT1qZhvNbK+ZzTGzIRW8TqmZ/cjMFpnZbjPbZWbzzOzKHNnPiB7vyQ4EAUIIW0MIf8nY9wrguujpnMzmsDU9hqwyGGlms6My2Glmz5rZ8EqKVURECoiCQRERSaIRwMvR3/cCrwOXAM+bWd/oeRfgAeAZYAwwK2rm+Vdm1hp4BfglcAj4A3A/0B542Mx+kfW6m6PHE6t5nLeRbjJ6P95kNrXU9BhSTgPmAvuBu4AZwDjgZTMbXc3jExGRBkzNREVEJIkuAL4cQpiaWmFmvwf+H/AX4JYQwn9kpP0UuB74Ot5PMeU24GTghyGEX2XkLwGeBP7dzKaFEFL9GB8DvgzcYGY98EDzzRDC2lwHGUK4LQr2xgD3hRDm5sh2tMeQch7wjyGE32Rsc3G0zR/M7KQQwuFcxyUiIoVBNYMiIpJEr2QGgpH7o8ftwH9mpT0QPQ5NrTCzY/HAbmFmEAYQQtgH/BAw4EsZ658GvgvsBb4DPA2siUYTnWpmZx3Nm6jJMWT4GLg7a5vpeE1kb0C1gyIiBU41gyIikkQLc6xbEz0uCiEcykpbHT12yVg3AmgEBDObkmN/jaPHcgPChBDuMLPfAePxPoQnR49fAr5kZjeEEH5WzfdRo2OIvFxBzd9cvCbyZDSqqYhIQVMwKCIiSbQ9x7qyitJCCGVmBungCuDY6HFEtFSkefaKEMIeYHq0YGZNgG/iTVB/amb/E0J4q4r38LmOAZ/SIpd10WOrary+iIg0YGomKiIiUjOpoPHXIQSrZBlb1Y5CCAdCCHcBj0SrqtymFo7huAr22TFr3yIiUqAUDIqIiNTM68Bhardv3c7o0TLWpZqsNqrlYxhlZrnuA86OHqtTMykiIg2YgkEREZEaCCFsAKYCw83sp2Z2RNcLMzvBzHpmPP+2mZ2ea3/RlBaXRU9fzkhKTUfRrTaOIUMf4JqsvBfj/QU/zjoGEREpQOozKCIiUnPX4kHV9cBXzOwVvC9eJ3zQlhHAlcDyKP95wD3RZPKvAquAptE+JuB9Eu8IIbye8Rpz8Nq/G81sILAVIISQmj/waI8hZSZwi5mdD7yNjyB6CbAP+LqmlRARKXwKBkVERGoohLDDzMYAV+OjgU4CSvBgbCnwfWBWxib/ite4nQucDkzEv4vX49NM/DGE8FTWa3xgZl8D/gWvySuJkn5Rw2NImY8HkDfgAaUBLwA/DiEsqFmJiIhIQ2IhhLiPQURERPLEzM7Gaxt/HkKYEu/RiIhInNRnUEREREREJIEUDIqIiIiIiCSQgkEREREREZEEUp9BERERERGRBFLNoIiIiIiISAIpGBQREREREUkgBYMiIiIiIiIJpGBQREREREQkgRQMioiIiIiIJJCCQRERERERkQT6P4LJYmAMLQKZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value Function:   [8.98659637 8.75438769 9.21739811 8.88984922 9.14301319 8.83248316\n",
      " 9.1142633  8.89075671 8.85051059 8.78277715]\n",
      "\n",
      "Minimum Delta:   4.578211114318562\n",
      "explored states:  defaultdict(<class 'int'>, {2: 2076, 7: 4618, 4: 3590, 0: 1561, 6: 2961, 8: 1109, 9: 1353, 3: 1028, 1: 815, 5: 889})\n",
      "\n",
      "\n",
      "\n",
      "With Diminishing Step Size\n",
      "MDP with 10 states and 2 actions\n",
      "discounting factor gamma = 0.95, step size alpha = 0.01\n",
      "\n",
      "Running  100 episodes\n",
      "\n",
      "The Policy is (state,action) = target probability    behavior probability\n",
      "(0,0) = 0.4835164835164835      0.4351851851851852  (0,1) = 0.5164835164835165      0.5648148148148148  \n",
      "(1,0) = 0.48854961832061067      0.423728813559322  (1,1) = 0.5114503816793893      0.576271186440678  \n",
      "(2,0) = 0.881578947368421      0.5714285714285714  (2,1) = 0.11842105263157894      0.42857142857142855  \n",
      "(3,0) = 0.7980769230769231      0.1  (3,1) = 0.20192307692307693      0.9  \n",
      "(4,0) = 0.2926829268292683      0.49382716049382713  (4,1) = 0.7073170731707317      0.5061728395061729  \n",
      "(5,0) = 0.4430379746835443      0.2824427480916031  (5,1) = 0.5569620253164557      0.7175572519083969  \n",
      "(6,0) = 0.88      0.42168674698795183  (6,1) = 0.12      0.5783132530120482  \n",
      "(7,0) = 0.4715447154471545      0.1  (7,1) = 0.5284552845528455      0.9  \n",
      "(8,0) = 0.30952380952380953      0.8636363636363636  (8,1) = 0.6904761904761905      0.13636363636363635  \n",
      "(9,0) = 0.34328358208955223      0.3401360544217687  (9,1) = 0.6567164179104478      0.6598639455782312  \n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value Function:   [8.35497924 8.3117326  8.37202574 8.38142943 8.32736215 8.18794174\n",
      " 8.23435353 8.36316658 8.51156334 8.24232702]\n",
      "\n",
      "Minimum Delta:   6.594643786159993\n",
      "explored states:  defaultdict(<class 'int'>, {0: 1940, 2: 1573, 8: 2675, 9: 2203, 5: 2249, 6: 2941, 1: 2499, 3: 1896, 7: 1255, 4: 769})\n",
      "n =  1\n",
      "Minimum Delta:   0.5350115777267407 \n",
      "\n",
      "\n",
      "n =  2\n",
      "Minimum Delta:   0.6496003083972257 \n",
      "\n",
      "\n",
      "n =  4\n",
      "Minimum Delta:   2.4121258486271033 \n",
      "\n",
      "\n",
      "n =  8\n",
      "Minimum Delta:   1.2992427318527753 \n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import defaultdict\n",
    "import mdptoolbox.example\n",
    "import random\n",
    "\n",
    "\n",
    "class n_StepTDLearner:\n",
    "    \"\"\"\n",
    "    Class that will ues on policy temporal difference\n",
    "    prediction to solve the model free problem with a given policy\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, target_policy, behavior_policy, states, actions, alpha=0.01, gamma=0.95, beta = 0.5, diminish = None, episodes=1000, timesteps = 200,n_step= 5):\n",
    "        #action value function, mapping each state action pair\n",
    "        #initialized to have 0 for every new state action pair\n",
    "        self.value_function = np.zeros(states)\n",
    "\n",
    "        #step size between [0,1]\n",
    "        self.alpha = alpha\n",
    "        self.gamma = gamma\n",
    "\n",
    "        #the mapping of states to actions\n",
    "        self.target_policy = target_policy\n",
    "        self.behavior_policy = behavior_policy\n",
    "\n",
    "        #the amount of states and actions\n",
    "        self.states = states\n",
    "        self.actions = actions\n",
    "        #state space S\n",
    "        self.state_space = np.arange(0,self.states)\n",
    "        #action space A\n",
    "        self.action_space = np.arange(0,self.actions)\n",
    "\n",
    "        #transition probability matrix P, with shape AxSxS'\n",
    "        self.transitionProbabilities, self.rewardMatrix = mdptoolbox.example.rand(states,actions)\n",
    "        \n",
    "        #the reward matrix\n",
    "        self.rewardMatrix = np.random.rand(actions,states,states)\n",
    "\n",
    "        #transition probability matrix under policy pi\n",
    "        self.probabilityMatrix = np.zeros((self.states,self.states))\n",
    "                \n",
    "        \n",
    "        #using behavior policy to forming it into a matrix\n",
    "        self.policyMatrix = []\n",
    "        for a, p in self.behavior_policy.items():\n",
    "            self.policyMatrix.append(p)\n",
    "\n",
    "        \n",
    "        #only for diminishing step size using alpha and beta\n",
    "        self.diminish = diminish\n",
    "        self.step_size = self.alpha\n",
    "        self.beta = beta\n",
    "        \n",
    "        #amount of episodes to run the environment for\n",
    "        self.episodes = episodes\n",
    "        #max time steps in an episode\n",
    "        self.T = timesteps\n",
    "        \n",
    "        #keeps track of the amount of times the states have been visited\n",
    "        self.exploringStates = defaultdict(int)\n",
    "        \n",
    "        #estimated v_pi, using value iteration\n",
    "        self.v_pi = [10.3269891,10.28997413, 10.61215495, 10.47182536, 10.53804012, 10.44741659, 10.58984017, 10.28781177, 10.42280426, 10.27326007]\n",
    "        \n",
    "        #save the difference between v_pi and v\n",
    "        self.difference= []\n",
    "        \n",
    "        #n step trajecrtory you would like to \n",
    "        self.n = n_step\n",
    "    \n",
    "    def setVpi(self,v_pi):\n",
    "        \"\"\"\n",
    "        Set the estimated v_pi to what you found\n",
    "        Must be called before running the environment\n",
    "        Default reward matrix is set to what was found in value iteration\n",
    "        \n",
    "        For this to work\n",
    "        :param v_pi: estimated v_pi, needs to be in length of state space S\n",
    "        :returns: void\n",
    "        \"\"\"\n",
    "        self.v_pi = v_pi  \n",
    "        \n",
    "    \n",
    "    def setRewardMatrix(self,matrix):\n",
    "        \"\"\"\n",
    "        Change the reward matrix to whatever you want with this function\n",
    "        Must be called before running the environment\n",
    "        Default reward matrix is set to random values between [0,1]\n",
    "        \n",
    "        For this to work\n",
    "        Matrix needs to be in shape AxSxS\n",
    "        A is the Action space\n",
    "        S is the State space\n",
    "        \n",
    "        :param matrix: the reward matrix of choice\n",
    "        :return: void\n",
    "        \"\"\"\n",
    "        self.rewardMatrix = matrix\n",
    "        \n",
    "    def createProbabilityMatrix(self):\n",
    "        \n",
    "        #to run TD, the transition probability matrix has to be under the policy \n",
    "        #taking the sum of the probabilities of taking that action a under state s and multiplying that by the transition probability value \n",
    "        \n",
    "        for s in range(self.states):\n",
    "            probabilities = np.zeros(self.states)\n",
    "            for a in range(self.actions):\n",
    "                    action_prob = self.behavior_policy[s][a]\n",
    "                    probabilities += self.transitionProbabilities[a][s]*action_prob\n",
    "            self.probabilityMatrix[s] = probabilities\n",
    "            \n",
    "\n",
    "    def getNextState(self, state, action):\n",
    "        \"\"\"\n",
    "        Just return the next state based on the transition probability matrix and the action taken\n",
    "        Using random choice that will use a distribution to give a state\n",
    "        :param state: observation that was previously seen\n",
    "        :param action: action that was take\n",
    "        :return: next state that the agent will go to \n",
    "        \"\"\"\n",
    "            \n",
    "        next_state = np.random.choice(self.state_space,1,p = self.probabilityMatrix[state])\n",
    "        return next_state[0]\n",
    "    \n",
    "    def chooseAction(self, state):\n",
    "        \"\"\"\n",
    "        Using the current state and the given policy find the action  using random choice based on the probabilities\n",
    "        :return: action \n",
    "        \"\"\"\n",
    "        \n",
    "        p = []\n",
    "        for action,prob in sorted(self.behavior_policy[state].items()):\n",
    "            p.append(prob)\n",
    "            \n",
    "        action = np.random.choice(self.action_space, 1, p = p)\n",
    "        \n",
    "        return action[0] \n",
    "\n",
    "    def takeAction(self,state,action):\n",
    "        \n",
    "        \"\"\"\n",
    "        Perform the action on the environment and see the observation\n",
    "        :param state: current state\n",
    "        :param action: the action taken at state \n",
    "        :return: next state S' , reward R\n",
    "        state sucessor and the reward observed\n",
    "        \"\"\"\n",
    "        \n",
    "        next_state = self.getNextState(state,action)\n",
    "        reward = self.rewardMatrix[action][state][next_state]\n",
    "        \n",
    "        return next_state, reward\n",
    "    \n",
    "    def TDupdate(self):\n",
    "        \"\"\"\n",
    "        Need to use episodes because otherwise it doesn't explore since my ploicy is not e-greedy\n",
    "        Using the puesdo-code in Sutton and Barto doing the n-step TD Bootstrapping to predict Vπ\n",
    "        \n",
    "        the V(S) function update is\n",
    "        V(s') = V(s) + αρt:t+n−1[Gt:t+n - V(s)]\n",
    "        \"\"\"\n",
    "        \n",
    "        states = []\n",
    "        rewards = [0]\n",
    "        actions = []\n",
    "        \n",
    "        #starting initial state\n",
    "        state = np.random.randint(0,self.states)\n",
    "        states.append(state)\n",
    "        t = 0\n",
    "        while True:\n",
    "            \n",
    "            if t<self.T:\n",
    "                action = self.chooseAction(states[t])\n",
    "                actions.append(action)\n",
    "                next_state,reward = self.takeAction(states[t],action)\n",
    "                states.append(next_state)\n",
    "                self.exploringStates[next_state]+=1\n",
    "                rewards.append(reward)\n",
    "                \n",
    "                \n",
    "                \n",
    "            tau = t-self.n+1\n",
    "            if tau>=0:\n",
    "                rho = 1\n",
    "                G = 0\n",
    "                #get importance sampling ratio\n",
    "                for i in range(tau+1,min(tau+self.n,self.T)):\n",
    "                    rho*= self.target_policy[states[i]][actions[i]]/ self.behavior_policy[states[i]][actions[i]]\n",
    "                    \n",
    "                #get truncated return value after n steps\n",
    "                G = sum([(self.gamma**(i-tau-1))*rewards[i] for i in range(tau+1,min(tau+self.n+1,self.T+1))])\n",
    "                \n",
    "                if tau+self.n < self.T:\n",
    "                    G += (self.gamma**self.n) * self.value_function[states[tau+self.n]]\n",
    "                    \n",
    "                #update the value function\n",
    "                self.value_function[states[tau]] += self.step_size*rho*(G - self.value_function[states[tau]])\n",
    "                \n",
    "                #calculate the difference\n",
    "                self.difference.append(np.linalg.norm(self.v_pi - self.value_function))\n",
    "                \n",
    "            if tau==self.T-1:\n",
    "                break\n",
    "                \n",
    "            t+=1\n",
    "        \n",
    "\n",
    "    def runEnvironment(self):\n",
    "        \"\"\"\n",
    "        Will run the OpenGym AI environment set using on policy Temporal Difference Learning\n",
    "\n",
    "        :return: difference list between v_pi and v\n",
    "        \n",
    "        Rough Estimate of the Value Function Limit\n",
    "        [10.3269891,10.28997413, 10.61215495, 10.47182536, 10.53804012, 10.44741659, 10.58984017, 10.28781177, 10.42280426, 10.27326007]\n",
    "\n",
    "        \"\"\"\n",
    "        \n",
    "        #create the transition probability matrix given the policy pi\n",
    "        self.createProbabilityMatrix()\n",
    "        for i in range(self.episodes):\n",
    "            self.TDupdate()\n",
    "                \n",
    "        return self.difference      \n",
    "    \n",
    "    def plot(self):\n",
    "        \"\"\"\n",
    "        Will plot the 2-norm difference found and more information on the results\n",
    "        For debugging purposes\n",
    "        \"\"\"\n",
    "        \n",
    "        #info on the MDP\n",
    "        print(f\"MDP with {self.states} states and {self.actions} actions\\ndiscounting factor gamma = {self.gamma}, step size alpha = {self.step_size}\\n\")\n",
    "        print(\"Running \", self.episodes, \"episodes\")\n",
    "        \n",
    "        #info on the policy\n",
    "        print(\"\\nThe Policy is (state,action) = target probability    behavior probability\")\n",
    "        for s in range(self.states):\n",
    "            for a in range(self.actions):\n",
    "                print(f\"({s},{a}) = {self.target_policy[s][a]}      {self.behavior_policy[s][a]} \",end=\" \")\n",
    "            print()\n",
    "                      \n",
    "        \n",
    "        #plot the difference between v-pi and v\n",
    "        plt.figure(figsize=(15,5))\n",
    "        plt.plot(range(len(self.difference)), self.difference, 'b-')\n",
    "        plt.title(\"Off-Policy n-Step TD with Importance Sampling\",fontsize = 20)\n",
    "        plt.xlabel(\"TimeStep\",fontsize = 20)\n",
    "        plt.ylabel(\"2-norm of Vπ - V\",fontsize = 20)\n",
    "        plt.xticks(fontsize = 14)\n",
    "        plt.yticks(fontsize = 14)\n",
    "        plt.show()\n",
    "        \n",
    "        #info on the value function\n",
    "        print(\"Value Function:  \", self.value_function)\n",
    "        print(\"\\nMinimum Delta:  \", min(self.difference))\n",
    "        print(\"explored states: \", self.exploringStates)\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    \n",
    "    \n",
    "     \n",
    "    \"\"\"\n",
    "    The Main Function to Run your program\n",
    "    Example code given below\n",
    "    All hyperparameters can be adjusted to your liking\n",
    "    \n",
    "    \n",
    "    Policy must be given  \n",
    "    the policy will be in the format of \n",
    "    (state,action) = Probability\n",
    "    \n",
    "    in python code it will be a dictionary inside of a dictionary\n",
    "    {state: {action: probability of that action, action: probabiity, ... } state:{...}}\n",
    "    \"\"\"\n",
    "\n",
    "    np.random.seed(0)\n",
    "    target_policy = {0: {0: 0.4835164835164835, 1: 0.5164835164835165}, 1: {0: 0.48854961832061067, 1: 0.5114503816793893}, 2: {0: 0.881578947368421, 1: 0.11842105263157894}, 3: {0: 0.7980769230769231, 1: 0.20192307692307693}, 4: {0: 0.2926829268292683, 1: 0.7073170731707317}, 5: {0: 0.4430379746835443, 1: 0.5569620253164557}, 6: {0: 0.88, 1: 0.12}, 7: {0: 0.4715447154471545, 1: 0.5284552845528455}, 8: {0: 0.30952380952380953, 1: 0.6904761904761905}, 9: {0: 0.34328358208955223, 1: 0.6567164179104478}}\n",
    "    behavior_policy = {0: {0: 0.4351851851851852, 1: 0.5648148148148148}, 1: {0: 0.423728813559322, 1: 0.576271186440678}, 2: {0: 0.5714285714285714, 1: 0.42857142857142855}, 3: {0: 0.1, 1: 0.9}, 4: {0: 0.49382716049382713, 1: 0.5061728395061729}, 5: {0: 0.2824427480916031, 1: 0.7175572519083969}, 6: {0: 0.42168674698795183, 1: 0.5783132530120482}, 7: {0: 0.1, 1: 0.9}, 8: {0: 0.8636363636363636, 1: 0.13636363636363635}, 9: {0: 0.3401360544217687, 1: 0.6598639455782312}}\n",
    "    states = 10\n",
    "    actions = 2\n",
    "    \n",
    "    \n",
    "    print(\"With Constant Step Size\\n\\n\")\n",
    "    learner = n_StepTDLearner(target_policy = target_policy,behavior_policy = behavior_policy,states = states, actions = actions,episodes = 100, n_step = 3)\n",
    "    learner.runEnvironment()\n",
    "    learner.plot()\n",
    "    \n",
    "    \n",
    "    print(\"\\n\\n\\nWith Diminishing Step Size\")\n",
    "    learner = n_StepTDLearner(target_policy = target_policy,behavior_policy = behavior_policy,states = states, actions = actions,episodes = 100, diminish = lambda a,k,b: a/(k**b), n_step = 3)\n",
    "    learner.runEnvironment()\n",
    "    learner.plot()\n",
    "    \n",
    "    \n",
    "    #running multiple n-steps and plotting them on the same graph\n",
    "    plt.figure(figsize = (15,5))\n",
    "    for n in range(0,4):\n",
    "        learner = n_StepTDLearner(target_policy = target_policy,behavior_policy = behavior_policy,states = 10, actions = 2,episodes = 500, n_step = 2**n)\n",
    "        graph = learner.runEnvironment()\n",
    "        print(\"n = \", 2**n)\n",
    "        plt.plot(range(len(graph)), graph, label = f\"n = {2**n}\")\n",
    "        print(\"Minimum Delta:  \", min(graph),\"\\n\\n\")\n",
    "    plt.xlabel(\"Iteration\",fontsize = 20)\n",
    "    plt.ylabel(\"2-norm of Vπ - V\",fontsize = 20)\n",
    "    plt.title(\"Off-Policy n-Step TD with Importance Sampling\",fontsize = 20)\n",
    "    plt.legend(fontsize = 14)\n",
    "    plt.xticks(fontsize = 14)\n",
    "    plt.yticks(fontsize = 14)\n",
    "    plt.show()\n",
    "\n",
    "\n"
   ]
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