Gridworld.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problems Six -- Ten: Q-Learning in Gridworld\n",
    "\n",
    "This is an experiment with Reinforcement Learning a Grid World, a simple\n",
    "problem in which a single agent moves around a 2D grid in search of a goal state where\n",
    "a reward sits waiting.\n",
    "\n",
    "In general, it \"costs\" 1 unit to move, so that many cells may have an immediate reward of -1.\n",
    "There are also \"holes\" where the game terminates and the immediate reward is -100.\n",
    "The start state has a reward of 0 and the goal state has a reward of 100. The trial\n",
    "terminates at holes and in the goal state. \n",
    "\n",
    "The next two cells show how each world is created as an object with a grid of rewards, \n",
    "a start state, and terminal states (where the current trial will end). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "code_folding": [
     0
    ]
   },
   "outputs": [],
   "source": [
    "# Each grid world has a 2d matrix of rewards (which also gives the dimensions of the matrix),\n",
    "# a start state, and a list of terminal states, where a trial will terminate\n",
    "\n",
    "\n",
    "class GridWorld:\n",
    " \n",
    "    # constructor\n",
    "    def __init__(self, reward_grid, start_state, terminal_states):\n",
    "        self.reward_grid = reward_grid\n",
    "        self.terminal_states = terminal_states\n",
    "        self.start_state = start_state\n",
    "        self.num_rows = len(reward_grid)\n",
    "        self.num_cols = len(reward_grid[0])\n",
    "    \n",
    "    # rewards in each state\n",
    "    \n",
    "    def R(self,state):\n",
    "        (r,c) = state\n",
    "        return self.reward_grid[r][c]\n",
    "    \n",
    "    # print out the rewards in text form\n",
    "    \n",
    "    def print_rewards(self):\n",
    "        print(\"Rewards\")\n",
    "        width = 5\n",
    "        hrule = ('-------'*self.num_cols)+'-'\n",
    "\n",
    "        print(hrule)\n",
    "        for r in range(self.num_rows):\n",
    "            print('|',end='')\n",
    "            for c in range(self.num_cols):  \n",
    "                if (r,c) == self.start_state:\n",
    "                    print(f\"{0:{width}} |\",end='')\n",
    "                else:\n",
    "                    print(f\"{self.reward_grid[r][c]:{width}} |\",end='')\n",
    "            print('\\n'+hrule)\n",
    "    \n",
    "    # Display the grid with colors and show the start and goal\n",
    "    \n",
    "    def display_heat_map(self):\n",
    "        fig = plt.figure()\n",
    "        ax = fig.add_subplot(111)\n",
    "        ax.set_title('Grid World')\n",
    "        ax.xaxis.set_ticks(range(20))             # assumes that no more than 20 rows or columns\n",
    "        ax.yaxis.set_ticks(range(20))\n",
    "        for tick in ax.xaxis.get_major_ticks():\n",
    "            tick.tick1line.set_visible(False)\n",
    "            tick.tick2line.set_visible(False)\n",
    "            tick.label1.set_visible(False)\n",
    "            tick.label2.set_visible(False)\n",
    "        for tick in ax.yaxis.get_major_ticks():\n",
    "            tick.tick1line.set_visible(False)\n",
    "            tick.tick2line.set_visible(False)\n",
    "            tick.label1.set_visible(False)\n",
    "            tick.label2.set_visible(False)\n",
    "        ax.imshow(self.reward_grid,extent=(0,self.num_cols,0,self.num_rows))\n",
    "        (r,c) = self.start_state\n",
    "        ax.scatter(c+0.5,self.num_rows-r-0.5,color='r',marker='o')\n",
    "        ax.grid(True)\n",
    "        plt.show()\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "code_folding": [
     0
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "World 0 \n",
      "\n",
      "Rewards\n",
      "---------------\n",
      "|    0 |   -1 |\n",
      "---------------\n",
      "|   -1 |  100 |\n",
      "---------------\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal states: [(1, 1)]\n",
      "\n",
      "\n",
      "World 1 \n",
      "\n",
      "Rewards\n",
      "----------------------\n",
      "|   -1 |   -1 |   -1 |\n",
      "----------------------\n",
      "|    0 | -100 |  100 |\n",
      "----------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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AQHJiAACSEwMAkJwYAIDkxAAAJCcGACA5MQAAyYkBAEhODABAcmIAAJITAwCQnBgAgOTEAAAkJwYAIDkxAADJiQEASE4MAEByYgAAkhMDAJCcGACA5MQAACQnBgAgOTEAAMmJAQBITgwAQHIVXZlULpcPTv6/PT26GOiqiihEa2trRP+2iHJfrwYO2t5SEa2trbG9pSIqSgf6ejkQP+04eJhvP44fTaF8vBkRsXXr1hg5cmT3rAwA6FVbtmyJESNGHHW8SzHQ1tYWTU1NUVVVFYVCoVsXCAD0jHK5HLt27YqampooFo9+Z0CXYgAA+MflBkIASE4MAEByYgAAkhMDAJCcGACA5MQAACQnBgAguf8Hx2kkCZ4WlIIAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal states: [(1, 1), (1, 2)]\n",
      "\n",
      "\n",
      "World 2 \n",
      "\n",
      "Rewards\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|    0 | -100 | -100 | -100 | -100 | -100 | -100 | -100 | -100 | -100 | -100 |  100 |\n",
      "-------------------------------------------------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal states: [(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (3, 11)]\n",
      "\n",
      "\n",
      "World 3 \n",
      "\n",
      "Rewards\n",
      "------------------------------------------------------------------------------\n",
      "|   -1 |   -1 |   -1 | -100 |   -1 |   -1 |   -1 | -100 |   -1 |   -1 |   -1 |\n",
      "------------------------------------------------------------------------------\n",
      "|   -1 | -100 |   -1 | -100 |   -1 | -100 |   -1 | -100 |   -1 | -100 |   -1 |\n",
      "------------------------------------------------------------------------------\n",
      "|   -1 | -100 |   -1 | -100 |   -1 | -100 |   -1 | -100 |   -1 | -100 |   -1 |\n",
      "------------------------------------------------------------------------------\n",
      "|    0 | -100 |   -1 |   -1 |   -1 | -100 |   -1 |   -1 |   -1 | -100 |  100 |\n",
      "------------------------------------------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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/yn+fzREAADCPH8MBADCOGAAAwDhiAAAA44gBAACMIwYAADCOGAAAwDhiAAAA44gBAACMIwYAADCOGAAAwDhiAAAA44gBAACMIwYAADCOGAAAwDhiAAAA40LJ7OS67tmd/xNP6zAjKSRHXV1dUrhPcrM9TZLCferq6lIoHlev64+hQ47DzBngzeyr61lSKB737Vozc3r58po+9z36dFtIoWBvtqdJyi/tZ5/m3SGuC8cdag9JJ06cUGlp6chMBgAAMur48eMqKSkZdHtSMdDX16dYLKb8/Hw5jjOiAwIAgPRwXVednZ0qLi5WIDD4nQFJxQAAAPj/xQ2EAAAYRwwAAGAcMQAAgHHEAAAAxhEDAAAYRwwAAGAcMQAAgHH/Bb8hULI/ozKfAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal states: [(0, 3), (0, 7), (1, 1), (1, 3), (1, 5), (1, 7), (1, 9), (2, 1), (2, 3), (2, 5), (2, 7), (2, 9), (3, 1), (3, 5), (3, 9), (3, 10)]\n",
      "\n",
      "\n",
      "World 4 \n",
      "\n",
      "Rewards\n",
      "-------------------------------------------------------------------------------------\n",
      "|    0 |-1.04 |-1.13 |-1.31 |-1.51 |-1.64 |-1.68 |-1.84 |-2.42 |-3.45 |-4.52 |-4.98 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.02 |-1.09 | -1.3 | -1.7 |-2.16 | -2.4 |-2.31 |-2.18 |-2.44 |-3.22 |-4.12 |-4.51 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.04 |-1.16 | -1.5 |-2.16 |-2.91 |-3.28 |-3.01 |-2.48 |-2.29 |-2.62 |-3.17 |-3.42 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.05 |-1.19 | -1.6 |-2.37 |-3.27 | -3.7 |-3.34 |-2.57 |-2.03 |-1.98 |-2.18 | -2.3 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.06 |-1.18 |-1.53 | -2.2 | -3.0 |-3.41 |-3.11 |-2.38 |-1.77 |-1.52 |-1.52 |-1.55 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.11 |-1.18 | -1.4 |-1.87 |-2.47 |-2.87 |-2.75 |-2.22 |-1.66 |-1.33 |-1.22 |-1.19 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.27 | -1.3 | -1.4 |-1.71 |-2.25 |-2.77 |-2.87 |-2.46 |-1.85 |-1.37 |-1.14 |-1.07 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.65 |-1.63 |-1.63 |-1.86 |-2.44 |-3.14 |-3.42 | -3.0 | -2.2 |-1.52 |-1.17 |-1.04 |\n",
      "-------------------------------------------------------------------------------------\n",
      "| -2.3 |-2.21 |-2.06 |-2.14 |-2.66 |-3.39 |-3.72 |-3.28 |-2.37 | -1.6 |-1.19 |-1.04 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-3.14 |-2.97 |-2.59 |-2.37 |-2.59 |-3.08 |-3.31 |-2.92 |-2.16 | -1.5 |-1.16 |-1.03 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-3.88 |-3.63 |-3.03 |-2.48 |-2.28 |-2.39 |-2.44 |-2.17 | -1.7 | -1.3 |-1.09 |-1.02 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-4.18 |-3.89 |-3.17 |-2.43 |-1.95 |-1.76 |-1.68 |-1.52 |-1.31 |-1.13 |-1.04 |100.0 |\n",
      "-------------------------------------------------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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AADBEAQBgiAIAwASNHBxPBlLUbUfiyaDmYzNsN+M5s839jO0ZlqjWdVgkDMNwsoMKhYIymYxyuZxSqdSUrxsAwK1isahsNqt8Pq90Oj3hcQ3laveWg9KI+2cKHVtXqK/7gMqlip/trv1Ot+PJQB3b2tW3aZ+fc96+Un0b9/rZ3rFKvRue8bLdufN6r9uub/Ox29v1/du2t7X73fb5mOJhu95nCg1FoVyqOI/C+G3nN+L47WH327522W6u7WY8Z9v2+ZjiertaXxR4oxkAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCACRo5OJ4MpKjbjsSTQc3HZthuxnNmm/sZ2zMsUa3rsEgYhuFkBxUKBWUyGeVyOaVSqSlfNwCAW8ViUdlsVvl8Xul0esLjGsrV7i0HpRH3zxQ6tq5QX9d+lUsV99vb2p1v2+6mfX7OeftK9W3c62d7xyr1bnjGy3bnzuu9bru+zcdub6/3M59/rrsP+NneusLLdr3PFBqKQrlUcR6F8dvlYcc3ouftZjxntrmfOd12/cDsc7taXxR4oxkAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCACRo5OJ4MpKjbjsSTQc3HZthuxnNmm/sZ2zMsUa3rsEgYhuFkBxUKBWUyGeVyOaVSqSlfNwCAW8ViUdlsVvl8Xul0esLjGsrV7q88J424f6bQsa1dfV37VS5VmmLbdjft83PO21eqb+NeP9s7Vql3/R4v2509q9W77ik/2w+vcX7eY+fs82vt9c919wE/21tXeNmu95lCQ1EolyrSST9vQ5RLFZWHHd+Inreb8ZzZ5n7mdNv1A7PP7Wp9UeCNZgCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCAIQoAAEMUAAAmaOTgeDKQom47Ek8GNR+bYbsZz5lt7mdsz7BEta7DImEYhpMdVCgUlMlklMvllEqlpnzdAABuFYtFZbNZ5fN5pdPpCY9rKFe7v/QTacT9M4WOHavUt3GvyqWKn+1N+5xux5OBOrav9HrOvRue8bLdufN69a57ys/2w2v8bq/f4/x+1tmz2u+fra79fra3tauv+4Cf7a0rvGzX+0yhoSiUT1akkp+3IcqlisrDjm9Ez9vNeM5scz9zuu36gdnndrW+KPBGMwDAEAUAgCEKAABDFAAAhigAAAxRAAAYogAAMEQBAGCIAgDAEAUAgCEKAABDFAAAhigAAAxRAAAYogAAMEQBAGCIAgDAEAUAgCEKAABDFAAAhigAAAxRAAAYogAAMEQBAGCIAgDAEAUAgCEKAAATNHRwEJUSbjsSxKP2MRz1tR1ROBpxuHtqK55s6MszLcY2vW63JqSI26/1WbGdiktRd/ezs+JrzbY7iWpdh0XCMAwnO6hQKCiTySiXyymVSk35ugEA3CoWi8pms8rn80qn0xMe11CuHtu8Txpx/11UZ89q9a7fo3Kp4md7wzNOt+PJQJ07r1ffxr1ezrljxyrn5zy23bnzer9fa+5nzrY7dqxSX9d+P9vb2tXXfcDP9tYVXrbrfabQUBTKJytSyc/bEOVSReVhxzei5+1mPGe2uZ853Xb9wOxzu1pfFHijGQBgiAIAwBAFAIAhCgAAQxQAAIYoAAAMUQAAGKIAADBEAQBgiAIAwBAFAIAhCgAAQxQAAIYoAAAMUQAAGKIAADBEAQBgiAIAwBAFAIAhCgAAQxQAAIYoAAAMUQAAGKIAADBEAQBgiAIAwASNHBxvCaSI247Ek0HNx2bYbsZzZpv7GdszLFGt67BIGIbhZAcVCgVlMhnlcjmlUqkpXzcAgFvFYlHZbFb5fF7pdHrC4xrK1a6uZ6STjp8ptAa67Yc3qnfdUyqXKm63k4E6H16j3vV7nG7Hk4E6e1arb+NeL+fcsWMV202wbbub9vk55+0r1de138/2tnb1dR/ws711hZftep8pNBSFcmlUKtX3iadbuVRRedjxjeh5uxnPmW3uZ063XT8w+9yu1vfYzRvNAABDFAAAhigAAAxRAAAYogAAMEQBAGCIAgDAEAUAgCEKAABDFAAAhigAAAxRAAAYogAAMEQBAGCIAgDAEAUAgCEKAABDFAAAhigAAAxRAAAYogAAMEQBAGCIAgDAEAUAgCEKAABDFAAAhigAAEzQyMHxZEyKuO1IvDX453ZDV3V6tpN+tn3tst1c2814zs28rUS1rsMiYRiGkx1UKBSUyWSUy+WUSqWmfN0AAG4Vi0Vls1nl83ml0+kJj2soV7s2PS2ddP9M4bZHbtKjtz+p8nDF/fYPb1Tv+j0ql9xtx5OBOntWq2/jXqe7Y9sdO1apb9M+P9vbV/rd7trvZ3tbu/NtX7s1290H/GxvXeF1+3OX/qeC2Emn20eP1fdw31AUyqVRqVTfU5DpVh6uOI+CbZf8bPvaZbu5tr2fs+MH5rNhO4idVDxwG4UgNlrXcbzRDAAwRAEAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAQBQCAIQoAAEMUAACGKAAADFEAABiiAAAwRAEAYIgCAMAE9RwUhuGp/9NSlfOOtFRVLBZPbY9dD9fbiaoUVt3tJjztvnO7yvb7ersZz/ks2T56LFAQG3U6/Xb+1MN9OMnjaCSc7AhJhw8f1vz586fnmgEAvHn99dd1wQUXTHh5XVGoVqsaHBzU7NmzFYlEpvUKAgBmXhiGOn78uObNm6dodOJXfOqKAgCgOfBGMwDAEAUAgCEKAABDFAAAhigAAAxRAAAYogAAMP8HnkvLJ8nBYWgAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal states: [(11, 11)]\n",
      "\n",
      "\n",
      "World 5 \n",
      "\n",
      "Rewards\n",
      "-----------------------------------------------------------------------\n",
      "|    0 | -2.8 | -4.0 | -4.6 | -5.8 | -3.5 | -5.6 | -1.1 | -0.4 | -6.2 |\n",
      "-----------------------------------------------------------------------\n",
      "| -2.1 | -4.7 | -4.3 | -0.7 | -9.3 | -9.1 | -9.8 | -1.7 | -2.2 | -1.3 |\n",
      "-----------------------------------------------------------------------\n",
      "| -0.2 | -2.0 | -5.4 | -2.2 | -8.8 | -3.6 | -8.6 | -0.6 | -4.8 | -5.9 |\n",
      "-----------------------------------------------------------------------\n",
      "| -7.4 | -2.3 | -5.4 | -4.3 | -9.8 | -3.8 | -3.9 | -3.8 | -0.6 | -3.2 |\n",
      "-----------------------------------------------------------------------\n",
      "| -6.4 | -5.6 | -3.0 | -9.4 | -3.3 | -3.3 | -7.9 | -8.7 | -6.8 | -6.4 |\n",
      "-----------------------------------------------------------------------\n",
      "| -4.3 | -5.6 | -0.1 | -9.0 | -7.9 | -8.4 | -3.5 | -7.5 | -5.3 | -7.6 |\n",
      "-----------------------------------------------------------------------\n",
      "| -8.4 | -8.9 | -3.4 | -8.6 | -8.0 | -6.3 | -1.8 | -9.0 | -1.6 | -9.0 |\n",
      "-----------------------------------------------------------------------\n",
      "| -0.2 | -5.3 | -0.2 | -4.0 | -2.6 | -9.6 | -7.2 | -8.8 | -7.0 | -8.8 |\n",
      "-----------------------------------------------------------------------\n",
      "| -6.8 | -5.9 | -9.4 | -3.1 | -4.3 | -7.3 | -4.8 | -9.1 | -4.2 | -0.7 |\n",
      "-----------------------------------------------------------------------\n",
      "| -6.8 | -3.3 | -8.7 | -2.8 | -7.1 | -8.2 | -4.1 | -9.8 | -1.7 |100.0 |\n",
      "-----------------------------------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal states: [(9, 9)]\n",
      "\n",
      "\n",
      "World 6 \n",
      "\n",
      "Rewards\n",
      "-------------------------------------------\n",
      "|    0 | -100 | -100 |   -1 |   -1 |   -1 |\n",
      "-------------------------------------------\n",
      "|   -1 |   -1 |   -1 | -100 |   -1 |  -10 |\n",
      "-------------------------------------------\n",
      "| -100 |   -1 | -100 |   -1 |   -1 |   -1 |\n",
      "-------------------------------------------\n",
      "| -100 |   -1 |   -1 |   -1 | -100 |   -1 |\n",
      "-------------------------------------------\n",
      "|   -1 |   -1 | -100 |   -1 | -100 |   -1 |\n",
      "-------------------------------------------\n",
      "| -100 | -100 |   -1 |   -1 |  100 |   -1 |\n",
      "-------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal states: [(0, 1), (0, 2), (1, 3), (2, 0), (2, 2), (3, 0), (3, 4), (4, 2), (4, 4), (5, 0), (5, 1), (5, 4)]\n",
      "\n",
      "\n",
      "World 7 \n",
      "\n",
      "Rewards\n",
      "-------------------------------------------\n",
      "|    0 | -100 | -100 |   -1 |   -1 |   -1 |\n",
      "-------------------------------------------\n",
      "|   -1 |   -1 |   -1 | -100 |   -1 | -100 |\n",
      "-------------------------------------------\n",
      "| -100 |   -1 | -100 |   -1 |   -1 |   -1 |\n",
      "-------------------------------------------\n",
      "| -100 |   -1 |   -1 |   -1 | -100 |   -1 |\n",
      "-------------------------------------------\n",
      "|   -1 |   -1 | -100 |   -1 | -100 |   -1 |\n",
      "-------------------------------------------\n",
      "| -100 |   -1 |   -1 | -100 |  100 |   -1 |\n",
      "-------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal states: [(0, 1), (0, 2), (1, 3), (1, 5), (2, 0), (2, 2), (3, 0), (3, 4), (4, 2), (4, 4), (5, 0), (5, 3), (5, 4)]\n",
      "\n",
      "\n",
      "World 8 \n",
      "\n",
      "Rewards\n",
      "-------------------------------------------------------------------------------------\n",
      "|    0 |    0 | -100 |   -1 |   -1 | -100 |   -1 |   -1 |   -1 | -100 | -100 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 | -100 |   -1 | -100 |   -1 | -100 |   -1 | -100 |   -1 |   -1 |   -1 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 | -100 |   -1 | -100 |   -1 | -100 |   -1 | -100 |   -1 | -100 | -100 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 |   -1 |   -1 | -100 |   -1 |   -1 |   -1 | -100 |   -1 |   -1 |   -1 | -100 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 | -100 |   -1 | -100 | -100 | -100 |   -1 |   -1 | -100 | -100 |   -1 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "| -100 |   -1 |   -1 | -100 |   -1 |   -1 | -100 |   -1 |   -1 |   -1 | -100 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 | -100 |   -1 | -100 |   -1 |   -1 |   -1 | -100 |   -1 | -100 |   -1 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 |   -1 |   -1 | -100 |   -1 | -100 | -100 |   -1 |   -1 | -100 |   -1 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 | -100 |   -1 | -100 |   -1 |   -1 |   -1 |   -1 | -100 | -100 | -100 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 |   -1 |   -1 |   -1 |   -1 | -100 | -100 | -100 |   -1 | -100 |   -1 |   -1 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|   -1 | -100 |   -1 |   -1 | -100 |  100 |   -1 |   -1 |   -1 |   -1 |   -1 | -100 |\n",
      "-------------------------------------------------------------------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Terminal states: [(0, 2), (0, 5), (0, 9), (0, 10), (1, 1), (1, 3), (1, 5), (1, 7), (2, 1), (2, 3), (2, 5), (2, 7), (2, 9), (2, 10), (3, 3), (3, 7), (3, 11), (4, 1), (4, 3), (4, 4), (4, 5), (4, 8), (4, 9), (5, 0), (5, 3), (5, 6), (5, 10), (6, 1), (6, 3), (6, 7), (6, 9), (7, 3), (7, 5), (7, 6), (7, 9), (8, 1), (8, 3), (8, 8), (8, 9), (8, 10), (9, 5), (9, 6), (9, 7), (9, 9), (10, 1), (10, 4), (10, 5), (10, 11)]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Grid worlds initialization\n",
    "\n",
    "World = []          #   room for 10 example grid worlds\n",
    "\n",
    "# return a list of all states which have rewards which only occur in terminal states\n",
    "\n",
    "def get_terminal_states(grid,terminal_rewards=[-100,100]):\n",
    "    TS = []\n",
    "    for r in range(len(grid)):\n",
    "        for c in range(len(grid[0])):\n",
    "            if grid[r][c] in terminal_rewards:\n",
    "                TS.append((r,c))\n",
    "    return TS\n",
    "\n",
    "# World[0]: simple test case, two paths\n",
    "\n",
    "\n",
    "\n",
    "World.append( GridWorld( [ [0,-1,], \n",
    "                        [-1,100] \n",
    "                      ], \n",
    "                      (0,0), \n",
    "                      [(1,1)] \n",
    "                    )\n",
    "            )\n",
    "\n",
    "# World[1]: short cliff walking\n",
    "\n",
    "World.append( GridWorld( [ [-1,-1,-1], \n",
    "                        [0,-100,100] \n",
    "                      ], \n",
    "                      (1,0), \n",
    "                      [(1,1),(1,2)] \n",
    "                    )\n",
    "            )\n",
    "\n",
    "# World[2]: cliff walking from lecture\n",
    "\n",
    "grid =                   [ [-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],\n",
    "                           [-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],\n",
    "                           [-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],\n",
    "                           [0,-100,-100,-100,-100,-100,-100,-100,-100,-100,-100,100]\n",
    "                         ]\n",
    "\n",
    "World.append( GridWorld( grid, (3,0), get_terminal_states(grid) ) )\n",
    "\n",
    "\n",
    "# World[3]: walking a serpentine path\n",
    "\n",
    "grid =                [ [-1,  -1,-1,-100,-1,  -1,-1,-100,-1,  -1, -1],\n",
    "                        [-1,-100,-1,-100,-1,-100,-1,-100,-1,-100, -1],\n",
    "                        [-1,-100,-1,-100,-1,-100,-1,-100,-1,-100, -1],\n",
    "                        [ 0,-100,-1,  -1,-1,-100,-1,  -1,-1,-100,100]\n",
    "                      ]\n",
    "\n",
    "World.append( GridWorld( grid, (3,0), get_terminal_states(grid) ) )\n",
    "\n",
    "# World[4]: This one has six \"valleys\" and the agent has to find the best path around them.\n",
    "\n",
    "def makeGridTerrain(num_rows,num_cols,Valleys):\n",
    "\n",
    "    W = np.zeros((num_rows,num_cols))\n",
    "    W.fill(-1)\n",
    "    \n",
    "    # Use the PDF of a 2D normal and subtract from the default -1\n",
    "\n",
    "    for V in Valleys:  \n",
    "        var = multivariate_normal(mean=V[0], cov=[[V[1],0],[0,V[2]]])\n",
    "        for r in range(num_rows):\n",
    "            for c in range(num_cols):\n",
    "                W[r][c] -=  var.pdf([r,c])*V[3]*10\n",
    "\n",
    "    # add start and goal states\n",
    "    \n",
    "    W[0][0] = 0\n",
    "    W[num_rows-1][num_cols-1] = 100\n",
    "    \n",
    "    return np.around(W,2)\n",
    "\n",
    "# List of valleys, each a tuple (mean = center, std_rows, std_cols, depth)\n",
    "\n",
    "Valleys = [([0,11], 4, 4, 10),\n",
    "           ([11,0], 5, 5, 10),\n",
    "           ([3,5], 3, 3, 5),\n",
    "           ([8,6], 3, 3, 5),\n",
    "          ]\n",
    "\n",
    "\n",
    "World.append( GridWorld( makeGridTerrain(12,12,Valleys), (0,0), [(11,11)] ) )\n",
    "               \n",
    "\n",
    "# World[5]: This one is completely random!\n",
    "\n",
    "seed(0); grid = np.around(10*rand(10,10)-10,1); grid[0][0] = 0; grid[9][9] = 100\n",
    "\n",
    "World.append( GridWorld( grid, (0,0), [(9,9)]) )\n",
    "\n",
    "# World[6]: Simple maze\n",
    "\n",
    "grid =                [[-1, -100, -100, -1, -1, -1], \n",
    "                       [-1, -1, -1, -100, -1, -10], \n",
    "                       [-100, -1, -100, -1, -1, -1], \n",
    "                       [-100, -1, -1, -1, -100, -1], \n",
    "                       [-1, -1, -100, -1, -100, -1], \n",
    "                       [-100, -100, -1, -1, 100, -1]\n",
    "                      ]\n",
    "\n",
    "World.append( GridWorld( grid, (0,0), get_terminal_states(grid) ) )\n",
    "\n",
    "# World[6]: More difficult maze\n",
    "\n",
    "grid =                [[-1, -100, -100, -1, -1, -1], \n",
    "                       [-1, -1, -1, -100, -1, -100], \n",
    "                       [-100, -1, -100, -1, -1, -1], \n",
    "                       [-100, -1, -1, -1, -100, -1], \n",
    "                       [-1, -1, -100, -1, -100, -1], \n",
    "                       [-100, -1, -1, -100, 100, -1]\n",
    "                      ]\n",
    "\n",
    "World.append( GridWorld( grid, (0,0), get_terminal_states(grid) ) )\n",
    "\n",
    "\n",
    "# World[7]: Hard maze\n",
    "\n",
    "grid =                [[ -1,  0,  -100,-1,  -1, -100,  -1,  -1,  -1,   -100, -100,  -1 ], \n",
    "                       [ -1, -100,  -1, -100,  -1, -100,  -1, -100,  -1,  -1,  -1,  -1 ], \n",
    "                       [ -1, -100,  -1, -100,  -1, -100,  -1, -100,  -1, -100, -100,  -1 ], \n",
    "                       [ -1,  -1,  -1, -100,  -1,  -1,  -1, -100,  -1,  -1,  -1, -100 ], \n",
    "                       [ -1, -100,  -1, -100,   -100, -100,  -1,  -1, -100, -100,  -1,  -1 ], \n",
    "                       [-100,  -1,  -1, -100,  -1,  -1, -100,  -1,  -1,  -1, -100,  -1 ], \n",
    "                       [ -1, -100,  -1, -100,  -1,  -1,  -1, -100,  -1, -100,  -1,  -1 ], \n",
    "                       [ -1,  -1,  -1, -100,  -1, -100, -100,  -1,  -1, -100,  -1,  -1 ], \n",
    "                       [ -1, -100,  -1, -100,  -1,  -1,  -1,  -1, -100, -100,   -100,  -1 ], \n",
    "                       [ -1,  -1,  -1,  -1,  -1, -100, -100, -100,  -1, -100,  -1,  -1 ], \n",
    "                       [ -1, -100,  -1,  -1, -100,  100,  -1,  -1,  -1,  -1,  -1, -100 ]\n",
    "                      ]\n",
    "\n",
    "World.append( GridWorld( grid, (0,0), get_terminal_states(grid) ) )\n",
    "                     \n",
    "\n",
    "# test\n",
    "\n",
    "for N in range(len(World)):\n",
    "    print(\"\\nWorld\",N,'\\n')\n",
    "    World[N].print_rewards()\n",
    "    World[N].display_heat_map()\n",
    "    print(\"Terminal states:\",World[N].terminal_states)\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 911,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rewards\n",
      "----------------------\n",
      "|   -1 |   -1 |   -1 |\n",
      "----------------------\n",
      "|    0 | -100 |  100 |\n",
      "----------------------\n",
      "['U', 'L']\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "defaultdict(<function __main__.initialize_Actions.<locals>.<lambda>()>,\n",
       "            {(0, 0): ['R', 'D'],\n",
       "             (0, 1): ['R', 'L', 'D'],\n",
       "             (0, 2): ['L', 'D'],\n",
       "             (1, 0): ['U', 'R'],\n",
       "             (1, 1): ['U', 'R', 'L'],\n",
       "             (1, 2): ['U', 'L']})"
      ]
     },
     "execution_count": 911,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# from collections import defaultdict\n",
    "\n",
    "# Actions for each state\n",
    "# These are lists so can use np.random.choice for exploration \n",
    "\n",
    "Moves     = ['U','R','L','D']\n",
    "    \n",
    "def initialize_Actions(W):\n",
    "    actions = defaultdict(lambda: Moves.copy())\n",
    "    \n",
    "    for r in range(W.num_rows):\n",
    "        for c in range(W.num_cols):\n",
    "            current_actions = []\n",
    "            if r > 0:\n",
    "                current_actions.append('U')\n",
    "            if c < W.num_cols - 1:\n",
    "                current_actions.append('R')\n",
    "            if c > 0:\n",
    "                current_actions.append('L')\n",
    "            if r < W.num_rows - 1:\n",
    "                current_actions.append('D')\n",
    "                \n",
    "            actions[(r, c)] = current_actions\n",
    "            \n",
    "    return actions\n",
    "\n",
    "\n",
    "# test for several values of N\n",
    "N = 1\n",
    "World[N].print_rewards()\n",
    "A = initialize_Actions(World[N])\n",
    "\n",
    "print(A[(1,2)])\n",
    "\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 912,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 3)\n",
      "(2, 4)\n",
      "(2, 2)\n",
      "(3, 3)\n"
     ]
    }
   ],
   "source": [
    "# state transitions -- no error checking, will only be called on legal moves\n",
    "    \n",
    "def goto_state(s,a):\n",
    "    dr_dc = {\n",
    "        'U': (-1, 0),\n",
    "        'R': (0, 1),\n",
    "        'L': (0, -1),\n",
    "        'D': (1, 0)\n",
    "    }\n",
    "    r, c = s\n",
    "    dr, dc = dr_dc[a]\n",
    "    return r + dr, c + dc\n",
    "\n",
    "\n",
    "# test\n",
    "\n",
    "for m in Moves:\n",
    "    print(goto_state((2,3),m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q-Table\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 917,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q-Table\n",
      "----------------------------\n",
      "|U:      |U:      |U:      |\n",
      "|L:      |L:-4.551|L:-3.541|\n",
      "|R:-4.512|R:-3.972|R:      |\n",
      "|D:-2.848|D:-5.763|D:-5.624|\n",
      "----------------------------\n",
      "|U:-1.082|        |        |\n",
      "|L:      |        |        |\n",
      "|R:-0.363|        |        |\n",
      "|D:      |        |        |\n",
      "----------------------------\n"
     ]
    }
   ],
   "source": [
    "# Q-Table is dictionary with keys (state,move) = ((row,col),move) mapped to Q-values\n",
    "\n",
    "# Initialize non-terminal states with random default values in range -10..0; but\n",
    "# must initialize all terminal states with 0.0 or else Q-values will not be accurate!\n",
    "\n",
    "seed(0)\n",
    "\n",
    "def initialize_Q_table(W, A):\n",
    "    Q = {}\n",
    "    \n",
    "    for state in A:\n",
    "        for action in A[state]:\n",
    "            if state in W.terminal_states:\n",
    "                Q[(state, action)] = 0.0\n",
    "            else:\n",
    "                Q[(state, action)] = np.random.uniform(-10, 0) # only way i could get it to randomize same as tests\n",
    "    return Q\n",
    "\n",
    "\n",
    "def print_Q_table(W,A,Q):\n",
    "    print(\"Q-Table\")\n",
    "    width = 6\n",
    "    precision = 4\n",
    "\n",
    "    hrule = ('---------'*W.num_cols)+'-'\n",
    "\n",
    "    print(hrule)\n",
    "    for r in range(W.num_rows):\n",
    "        for move in ['U','L','R','D']:\n",
    "            for c in range(W.num_cols):\n",
    "                if (r,c) in W.terminal_states:\n",
    "                    print('|  '+(\" \"*width),end='')\n",
    "                elif move in A[(r,c)]:\n",
    "                    print('|'+move+':'+f\"{np.around(Q[((r,c),move)],3):{width}.{precision}}\",end='')\n",
    "                else:\n",
    "                    print('|'+move+':'+(\" \"*width),end='')\n",
    "\n",
    "            print('|')\n",
    "        print(hrule)\n",
    "\n",
    "# test -- try for several values of N\n",
    " \n",
    "seed(0)\n",
    "N = 1\n",
    "W = World[N]\n",
    "A = initialize_Actions(World[N])\n",
    "Q = initialize_Q_table(W,A)\n",
    "print_Q_table(W,A,Q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determine allowable moves\n",
    "\n",
    "Now we must create functions to determine the best allowable move, given A, Q, and the state,\n",
    "and write an epsilon-greedy version of the strategy `Pi`. \n",
    "\n",
    "The best move is simply the allowable move from the current state with the maximum Q-value. \n",
    "Return the move as a character 'U', 'R', etc. \n",
    "\n",
    "The epsilon-greed strategy will choose a random move from those allowable in the current\n",
    "state with probability `epsilon` or the best move with probability `1-epsilon`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 854,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "# Strategy code for epsilon-greedy Pi\n",
    "\n",
    "# find move with best Q-value in state s\n",
    "def best_move(A,Q,s):\n",
    "    best_q_value = -sys.maxsize\n",
    "    best_action = None\n",
    "    \n",
    "    for action in A[s]:\n",
    "#         print(Q[s, action])\n",
    "        if Q[(s, action)] > best_q_value:\n",
    "            best_q_value = Q[(s, action)]\n",
    "            best_action = action\n",
    "    return best_action\n",
    "        \n",
    "\n",
    "# epsilon-greedy strategy\n",
    "\n",
    "def Pi(A, Q, s, epsilon):\n",
    "    if random() < epsilon:\n",
    "        return choice(A[s])\n",
    "    else:\n",
    "        return best_move(A, Q, s)\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 918,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "D\n",
      "L\n",
      "\n",
      "R\n",
      "R\n",
      "U\n"
     ]
    }
   ],
   "source": [
    "# Tests:   run this cell repeatedly to test for N == 1 two cells up\n",
    "print(best_move(A,Q,(0,0)))   # 'D' \n",
    "print(best_move(A,Q,(0,2)))   # 'L' \n",
    "print()\n",
    "print(Pi(A,Q,(1,0),0.0))    # 'R' \n",
    "print(Pi(A,Q,(1,0),0.5))    # should give 'R' about 3x as often as 'U'\n",
    "print(Pi(A,Q,(1,0),1.0))    # should give approximately same number of 'U' and 'R'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 920,
   "metadata": {
    "code_folding": [
     0
    ]
   },
   "outputs": [],
   "source": [
    "# Pretty-printing code for Strategy\n",
    "# Uses: best_move\n",
    "        \n",
    "def print_strategy(W,A,Q):\n",
    "    print(\"Strategy Pi\")\n",
    "    width = 6\n",
    "    precision = 4\n",
    "\n",
    "    hrule = ('------'*W.num_cols)+'-'\n",
    "\n",
    "    print(hrule)\n",
    "    for r in range(W.num_rows):\n",
    "        for k in range(3):\n",
    "            for c in range(W.num_cols):\n",
    "                if (r,c) in W.terminal_states:\n",
    "                    print('|     ',end='')\n",
    "                else:\n",
    "                    move = best_move(A,Q,(r,c))\n",
    "                    if k == 0:\n",
    "                        if move in ['L','R']:\n",
    "                            print('|     ',end='')\n",
    "                        elif move == 'U':\n",
    "                            print('|  ^  ',end='')\n",
    "                        else:\n",
    "                            print('|  |  ',end='')\n",
    "                    elif k == 1:\n",
    "                        if move =='R':\n",
    "                            print('|---->',end='')\n",
    "                        elif move == 'L':\n",
    "                            print('|<----',end='')\n",
    "                        else:\n",
    "                            print('|  |  ',end='')                        \n",
    "                    else: \n",
    "                        if move in ['L','R']:\n",
    "                            print('|     ',end='')\n",
    "                        elif move == 'D':\n",
    "                            print('|  v  ',end='')\n",
    "                        else:\n",
    "                            print('|  |  ',end='')                   \n",
    "            print('|')\n",
    "        print(hrule)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiment code\n",
    "\n",
    "In this part we will create the framework for running multiple trials for the agent\n",
    "to learn how to solve the GridWorld problem of maximizing rewards. \n",
    "\n",
    "There are several parameters of interest, as explained in lecture:\n",
    "\n",
    "- epsilon =  for epsilon-greedy strategy, probability of exploration by random move\n",
    "\n",
    "- lam = exponential decrease in epsilon    (can not use \"lambda\" because that is a keyword in Python)\n",
    "\n",
    "- num_trials = number of random trials in this experiment\n",
    "\n",
    "(We also thought about the use of a \"learning rate\" parameter `alpha` and a \"discount\" `gamma` for future rewards, but these seemed to only be a disadvantage in this simple GridWorld scenario.)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1084,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Rewards\n",
      "-------------------------------------------------------------------------------------\n",
      "|    0 |-1.04 |-1.13 |-1.31 |-1.51 |-1.64 |-1.68 |-1.84 |-2.42 |-3.45 |-4.52 |-4.98 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.02 |-1.09 | -1.3 | -1.7 |-2.16 | -2.4 |-2.31 |-2.18 |-2.44 |-3.22 |-4.12 |-4.51 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.04 |-1.16 | -1.5 |-2.16 |-2.91 |-3.28 |-3.01 |-2.48 |-2.29 |-2.62 |-3.17 |-3.42 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.05 |-1.19 | -1.6 |-2.37 |-3.27 | -3.7 |-3.34 |-2.57 |-2.03 |-1.98 |-2.18 | -2.3 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.06 |-1.18 |-1.53 | -2.2 | -3.0 |-3.41 |-3.11 |-2.38 |-1.77 |-1.52 |-1.52 |-1.55 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.11 |-1.18 | -1.4 |-1.87 |-2.47 |-2.87 |-2.75 |-2.22 |-1.66 |-1.33 |-1.22 |-1.19 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.27 | -1.3 | -1.4 |-1.71 |-2.25 |-2.77 |-2.87 |-2.46 |-1.85 |-1.37 |-1.14 |-1.07 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-1.65 |-1.63 |-1.63 |-1.86 |-2.44 |-3.14 |-3.42 | -3.0 | -2.2 |-1.52 |-1.17 |-1.04 |\n",
      "-------------------------------------------------------------------------------------\n",
      "| -2.3 |-2.21 |-2.06 |-2.14 |-2.66 |-3.39 |-3.72 |-3.28 |-2.37 | -1.6 |-1.19 |-1.04 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-3.14 |-2.97 |-2.59 |-2.37 |-2.59 |-3.08 |-3.31 |-2.92 |-2.16 | -1.5 |-1.16 |-1.03 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-3.88 |-3.63 |-3.03 |-2.48 |-2.28 |-2.39 |-2.44 |-2.17 | -1.7 | -1.3 |-1.09 |-1.02 |\n",
      "-------------------------------------------------------------------------------------\n",
      "|-4.18 |-3.89 |-3.17 |-2.43 |-1.95 |-1.76 |-1.68 |-1.52 |-1.31 |-1.13 |-1.04 |100.0 |\n",
      "-------------------------------------------------------------------------------------\n",
      "\n",
      "Q-Table\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U:      |U:      |U:      |U:      |U:      |U:      |U:      |U:      |U:      |U:      |U:      |U:      |\n",
      "|L:      |L: 69.41|L: 69.03|L: 69.77|L:  70.9|L: 72.21|L: 73.72|L: 75.36|L: 77.04|L: 78.64|L: 78.32|L: 76.93|\n",
      "|R: 69.03|R: 69.77|R:  70.9|R: 72.21|R: 73.72|R: 75.36|R: 77.04|R: 78.64|R: 78.32|R: 76.93|R: 76.85|R:      |\n",
      "|D: 69.41|D: 70.07|D: 69.94|D: 70.31|D: 72.01|D: 74.17|D: 76.57|D: 78.88|D: 81.06|D: 81.77|D: 81.45|D: 81.83|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 69.41|U: 69.03|U: 69.77|U:  70.9|U: 72.21|U: 73.72|U: 75.36|U: 77.04|U: 78.64|U: 78.32|U: 76.93|U: 76.85|\n",
      "|L:      |L: 69.41|L: 70.07|L: 69.94|L: 70.31|L: 72.01|L: 74.17|L: 76.57|L: 78.88|L: 81.06|L: 81.77|L: 81.45|\n",
      "|R: 70.07|R: 69.94|R: 70.31|R: 72.01|R: 74.17|R: 76.57|R: 78.88|R: 81.06|R: 81.77|R: 81.45|R: 81.83|R:      |\n",
      "|D: 70.43|D: 71.16|D: 71.24|D: 70.54|D: 71.82|D: 74.73|D: 78.01|D: 81.02|D:  83.5|D: 84.99|D: 85.57|D: 86.34|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 69.41|U: 70.07|U: 69.94|U: 70.31|U: 72.01|U: 74.17|U: 76.57|U: 78.88|U: 81.06|U: 81.77|U: 81.45|U: 81.83|\n",
      "|L:      |L: 70.43|L: 71.16|L: 71.24|L: 70.54|L: 71.82|L: 74.73|L: 78.01|L: 81.02|L:  83.5|L: 84.99|L: 85.57|\n",
      "|R: 71.16|R: 71.24|R: 70.54|R: 71.82|R: 74.73|R: 78.01|R: 81.02|R:  83.5|R: 84.99|R: 85.57|R: 86.34|R:      |\n",
      "|D: 71.47|D: 72.32|D: 72.74|D:  72.7|D: 72.91|D: 76.18|D: 79.88|D: 83.22|D: 85.79|D: 87.61|D: 88.74|D: 89.76|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 70.43|U: 71.16|U: 71.24|U: 70.54|U: 71.82|U: 74.73|U: 78.01|U: 81.02|U:  83.5|U: 84.99|U: 85.57|U: 86.34|\n",
      "|L:      |L: 71.47|L: 72.32|L: 72.74|L:  72.7|L: 72.91|L: 76.18|L: 79.88|L: 83.22|L: 85.79|L: 87.61|L: 88.74|\n",
      "|R: 72.32|R: 72.74|R:  72.7|R: 72.91|R: 76.18|R: 79.88|R: 83.22|R: 85.79|R: 87.61|R: 88.74|R: 89.76|R:      |\n",
      "|D: 72.52|D: 73.51|D: 74.34|D: 75.07|D: 76.14|D: 78.92|D: 82.33|D: 85.44|D: 87.82|D: 89.59|D: 90.92|D: 92.06|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 71.47|U: 72.32|U: 72.74|U:  72.7|U: 72.91|U: 76.18|U: 79.88|U: 83.22|U: 85.79|U: 87.61|U: 88.74|U: 89.76|\n",
      "|L:      |L: 72.52|L: 73.51|L: 74.34|L: 75.07|L: 76.14|L: 78.92|L: 82.33|L: 85.44|L: 87.82|L: 89.59|L: 90.92|\n",
      "|R: 73.51|R: 74.34|R: 75.07|R: 76.14|R: 78.92|R: 82.33|R: 85.44|R: 87.82|R: 89.59|R: 90.92|R: 92.06|R:      |\n",
      "|D: 73.58|D: 74.69|D: 75.87|D: 77.27|D: 79.14|D: 81.61|D: 84.48|D: 87.23|D: 89.45|D: 91.11|D: 92.44|D: 93.61|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 72.52|U: 73.51|U: 74.34|U: 75.07|U: 76.14|U: 78.92|U: 82.33|U: 85.44|U: 87.82|U: 89.59|U: 90.92|U: 92.06|\n",
      "|L:      |L: 73.58|L: 74.69|L: 75.87|L: 77.27|L: 79.14|L: 81.61|L: 84.48|L: 87.23|L: 89.45|L: 91.11|L: 92.44|\n",
      "|R: 74.69|R: 75.87|R: 77.27|R: 79.14|R: 81.61|R: 84.48|R: 87.23|R: 89.45|R: 91.11|R: 92.44|R: 93.61|R:      |\n",
      "|D: 74.41|D: 75.68|D: 76.98|D: 78.38|D: 80.09|D: 82.34|D: 85.11|D: 87.98|D: 90.44|D: 92.29|D: 93.66|D:  94.8|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 73.58|U: 74.69|U: 75.87|U: 77.27|U: 79.14|U: 81.61|U: 84.48|U: 87.23|U: 89.45|U: 91.11|U: 92.44|U: 93.61|\n",
      "|L:      |L: 74.41|L: 75.68|L: 76.98|L: 78.38|L: 80.09|L: 82.34|L: 85.11|L: 87.98|L: 90.44|L: 92.29|L: 93.66|\n",
      "|R: 75.68|R: 76.98|R: 78.38|R: 80.09|R: 82.34|R: 85.11|R: 87.98|R: 90.44|R: 92.29|R: 93.66|R:  94.8|R:      |\n",
      "|D: 73.57|D: 75.22|D: 76.85|D: 78.48|D: 79.64|D: 81.42|D: 84.56|D: 87.98|D: 90.98|D: 93.18|D:  94.7|D: 95.87|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 74.41|U: 75.68|U: 76.98|U: 78.38|U: 80.09|U: 82.34|U: 85.11|U: 87.98|U: 90.44|U: 92.29|U: 93.66|U:  94.8|\n",
      "|L:      |L: 73.57|L: 75.22|L: 76.85|L: 78.48|L: 79.64|L: 81.42|L: 84.56|L: 87.98|L: 90.98|L: 93.18|L:  94.7|\n",
      "|R: 75.22|R: 76.85|R: 78.48|R: 79.64|R: 81.42|R: 84.56|R: 87.98|R: 90.98|R: 93.18|R:  94.7|R: 95.87|R:      |\n",
      "|D: 73.77|D: 76.07|D: 78.28|D: 80.34|D: 82.08|D:  82.7|D: 84.75|D: 88.47|D: 91.75|D: 94.12|D: 95.72|D: 96.91|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 73.57|U: 75.22|U: 76.85|U: 78.48|U: 79.64|U: 81.42|U: 84.56|U: 87.98|U: 90.98|U: 93.18|U:  94.7|U: 95.87|\n",
      "|L:      |L: 73.77|L: 76.07|L: 78.28|L: 80.34|L: 82.08|L:  82.7|L: 84.75|L: 88.47|L: 91.75|L: 94.12|L: 95.72|\n",
      "|R: 76.07|R: 78.28|R: 80.34|R: 82.08|R:  82.7|R: 84.75|R: 88.47|R: 91.75|R: 94.12|R: 95.72|R: 96.91|R:      |\n",
      "|D: 73.78|D: 76.92|D: 79.89|D: 82.48|D: 84.74|D: 86.09|D: 87.57|D: 90.21|D: 93.13|D: 95.29|D: 96.79|D: 97.95|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 73.77|U: 76.07|U: 78.28|U: 80.34|U: 82.08|U:  82.7|U: 84.75|U: 88.47|U: 91.75|U: 94.12|U: 95.72|U: 96.91|\n",
      "|L:      |L: 73.78|L: 76.92|L: 79.89|L: 82.48|L: 84.74|L: 86.09|L: 87.57|L: 90.21|L: 93.13|L: 95.29|L: 96.79|\n",
      "|R: 76.92|R: 79.89|R: 82.48|R: 84.74|R: 86.09|R: 87.57|R: 90.21|R: 93.13|R: 95.29|R: 96.79|R: 97.95|R:      |\n",
      "|D: 74.31|D: 78.19|D: 81.82|D: 84.85|D: 87.33|D: 89.17|D: 90.88|D: 92.83|D: 94.89|D: 96.59|D: 97.89|D: 98.98|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 73.78|U: 76.92|U: 79.89|U: 82.48|U: 84.74|U: 86.09|U: 87.57|U: 90.21|U: 93.13|U: 95.29|U: 96.79|U: 97.95|\n",
      "|L:      |L: 74.31|L: 78.19|L: 81.82|L: 84.85|L: 87.33|L: 89.17|L: 90.88|L: 92.83|L: 94.89|L: 96.59|L: 97.89|\n",
      "|R: 78.19|R: 81.82|R: 84.85|R: 87.33|R: 89.17|R: 90.88|R: 92.83|R: 94.89|R: 96.59|R: 97.89|R: 98.98|R:      |\n",
      "|D: 75.94|D: 80.12|D: 84.01|D: 87.18|D: 89.61|D: 91.56|D: 93.32|D:  95.0|D: 96.52|D: 97.83|D: 98.96|D: 100.0|\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "|U: 74.31|U: 78.19|U: 81.82|U: 84.85|U: 87.33|U: 89.17|U: 90.88|U: 92.83|U: 94.89|U: 96.59|U: 97.89|        |\n",
      "|L:      |L: 75.94|L: 80.12|L: 84.01|L: 87.18|L: 89.61|L: 91.56|L: 93.32|L:  95.0|L: 96.52|L: 97.83|        |\n",
      "|R: 80.12|R: 84.01|R: 87.18|R: 89.61|R: 91.56|R: 93.32|R:  95.0|R: 96.52|R: 97.83|R: 98.96|R: 100.0|        |\n",
      "|D:      |D:      |D:      |D:      |D:      |D:      |D:      |D:      |D:      |D:      |D:      |        |\n",
      "-------------------------------------------------------------------------------------------------------------\n",
      "\n",
      "Strategy Pi\n",
      "-------------------------------------------------------------------------\n",
      "|  |  |  |  |     |     |     |     |     |  |  |  |  |  |  |  |  |  |  |\n",
      "|  |  |  |  |---->|---->|---->|---->|---->|  |  |  |  |  |  |  |  |  |  |\n",
      "|  v  |  v  |     |     |     |     |     |  v  |  v  |  v  |  v  |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|  |  |  |  |  |  |     |     |     |     |     |  |  |  |  |  |  |  |  |\n",
      "|  |  |  |  |  |  |---->|---->|---->|---->|---->|  |  |  |  |  |  |  |  |\n",
      "|  v  |  v  |  v  |     |     |     |     |     |  v  |  v  |  v  |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|  |  |  |  |  |  |  |  |     |     |     |     |  |  |  |  |  |  |  |  |\n",
      "|  |  |  |  |  |  |  |  |---->|---->|---->|---->|  |  |  |  |  |  |  |  |\n",
      "|  v  |  v  |  v  |  v  |     |     |     |     |  v  |  v  |  v  |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|  |  |  |  |  |  |  |  |     |     |     |     |  |  |  |  |  |  |  |  |\n",
      "|  |  |  |  |  |  |  |  |---->|---->|---->|---->|  |  |  |  |  |  |  |  |\n",
      "|  v  |  v  |  v  |  v  |     |     |     |     |  v  |  v  |  v  |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|  |  |  |  |  |  |  |  |  |  |     |     |     |     |  |  |  |  |  |  |\n",
      "|  |  |  |  |  |  |  |  |  |  |---->|---->|---->|---->|  |  |  |  |  |  |\n",
      "|  v  |  v  |  v  |  v  |  v  |     |     |     |     |  v  |  v  |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|     |     |     |     |     |     |     |     |     |     |  |  |  |  |\n",
      "|---->|---->|---->|---->|---->|---->|---->|---->|---->|---->|  |  |  |  |\n",
      "|     |     |     |     |     |     |     |     |     |     |  v  |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|     |     |     |     |     |     |     |     |     |     |     |  |  |\n",
      "|---->|---->|---->|---->|---->|---->|---->|---->|---->|---->|---->|  |  |\n",
      "|     |     |     |     |     |     |     |     |     |     |     |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|     |     |     |  |  |  |  |     |     |     |     |     |     |  |  |\n",
      "|---->|---->|---->|  |  |  |  |---->|---->|---->|---->|---->|---->|  |  |\n",
      "|     |     |     |  v  |  v  |     |     |     |     |     |     |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|     |     |     |  |  |  |  |  |  |     |     |     |     |     |  |  |\n",
      "|---->|---->|---->|  |  |  |  |  |  |---->|---->|---->|---->|---->|  |  |\n",
      "|     |     |     |  v  |  v  |  v  |     |     |     |     |     |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|     |     |     |  |  |  |  |  |  |  |  |     |     |     |     |  |  |\n",
      "|---->|---->|---->|  |  |  |  |  |  |  |  |---->|---->|---->|---->|  |  |\n",
      "|     |     |     |  v  |  v  |  v  |  v  |     |     |     |     |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|     |     |     |     |  |  |  |  |  |  |  |  |     |     |     |  |  |\n",
      "|---->|---->|---->|---->|  |  |  |  |  |  |  |  |---->|---->|---->|  |  |\n",
      "|     |     |     |     |  v  |  v  |  v  |  v  |     |     |     |  v  |\n",
      "-------------------------------------------------------------------------\n",
      "|     |     |     |     |     |     |     |     |     |     |     |     |\n",
      "|---->|---->|---->|---->|---->|---->|---->|---->|---->|---->|---->|     |\n",
      "|     |     |     |     |     |     |     |     |     |     |     |     |\n",
      "-------------------------------------------------------------------------\n",
      "\n",
      "Reward: 69.41\n"
     ]
    }
   ],
   "source": [
    "# Q-Algorithm code\n",
    "\n",
    "\n",
    "def run_experiment(N,epsilon=0.25,lam=1.0,num_trials=1000,display=False):\n",
    "       \n",
    "    # initialize grid world N\n",
    "    W = World[N]\n",
    "       \n",
    "    # use a seed to help with comparing results\n",
    "    seed(0)\n",
    "    \n",
    "    # initialize A\n",
    "    A = initialize_Actions(W)\n",
    "    \n",
    "    # initialize Q\n",
    "    Q = initialize_Q_table(W, A)\n",
    "    \n",
    "    for _ in range(num_trials):\n",
    "    \n",
    "        # initialize the current state s to the start state\n",
    "        s = W.start_state\n",
    "        \n",
    "        # while s is not a terminal state\n",
    "        while s not in W.terminal_states:\n",
    "            #  determine the action a from s using the policy Pi       \n",
    "            a = Pi(A, Q, s, epsilon)\n",
    "            #  determine the next state s1 given the action a\n",
    "            s1 = goto_state(s, a)\n",
    "            #  determine the reward and the best move in s1\n",
    "            reward = W.R(s1)\n",
    "            best_next_move = best_move(A, Q, s1)\n",
    "            #  update Q-Table with the new Q-value for current state s = sum of reward in s1 and \n",
    "            #       Q-value of best move in s1;\n",
    "            Q[(s, a)] = reward + Q[(s1, best_next_move)]\n",
    "\n",
    "            #  update epsilon, reduced in each successive move by lam (if lam < 1 this means\n",
    "            #      you will explore less and less as the trial goes on)\n",
    "            epsilon *= lam\n",
    "            #  update current state to s1\n",
    "            s = s1\n",
    "            \n",
    "#     print(W.start_state)\n",
    "#     print(s)\n",
    "    # calculate the cumulative reward of the path given by the strategy implied by the Q-table\n",
    "    \n",
    "    s = W.start_state\n",
    "    cumulative_reward = 0\n",
    "    visited = set()\n",
    "    \n",
    "    cycle = False\n",
    "    while s not in W.terminal_states:\n",
    "        if s in visited:\n",
    "            cycle = True\n",
    "            break\n",
    "        visited.add(s)\n",
    "        a = best_move(A, Q, s)\n",
    "        s = goto_state(s, a)\n",
    "        cumulative_reward += W.R(s)\n",
    " \n",
    "        \n",
    "    # show all the data structures if you want\n",
    "    \n",
    "    if display:    \n",
    "        W.display_heat_map()\n",
    "        print()\n",
    "        W.print_rewards()\n",
    "        print()\n",
    "        print_Q_table(W,A,Q)   \n",
    "        print()\n",
    "        print_strategy(W,A,Q)\n",
    "        print()\n",
    "    \n",
    "    if cycle:\n",
    "        return 0\n",
    "    else:\n",
    "        return cumulative_reward\n",
    "# test\n",
    "print(\"Reward:\",run_experiment(4, num_trials=300, display=True, epsilon=1.0, lam=1.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running experiments\n",
    "\n",
    "What parameters will solve the problem in the fewest number of trials?\n",
    "      \n",
    "\"Solving\" the problem means learning a \"steady-state\" strategy, meaning that if we increase\n",
    "the number of trials, the strategy does not change.  The agent may accidentally hit on \n",
    "an optimal strategy, but continuing to search may \"unlearn\" the solution. The system\n",
    "can only be said to have learned the optimal strategy only if it does not change as the number\n",
    "of trials is increased. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# World 0\n",
    "I wrote a function, optimize(), to perform grid search on the parameters and find the ones that yield the best results.\n",
    "\n",
    "For World 0, all sets of parameters manage to find max reward in at most 3 trials. Half manage to find it on the very first trial. I'm surprised that we don't find the optimal policy on the first trial at any epsilon=0; in a 2x2 world, any agent should be finding the win state immediately after any step, and with no random exploration, it should, theoretically, immediately pick the winning state.\n",
    "\n",
    "The optimal parameters in this case are fairly meaningless, as about half of the parameter pairs achieve the same result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1050,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Epsilon    Lambda    Steady State Trials    Reward\n",
      "---------  --------  ---------------------  --------\n",
      "     0.00      0.00                      2        99\n",
      "     0.00      0.20                      2        99\n",
      "     0.00      0.40                      2        99\n",
      "     0.00      0.60                      2        99\n",
      "     0.00      0.80                      2        99\n",
      "     0.00      1.00                      2        99\n",
      "     0.20      0.00                      2        99\n",
      "     0.20      0.20                      2        99\n",
      "     0.20      0.40                      2        99\n",
      "     0.20      0.60                      2        99\n",
      "     0.20      0.80                      2        99\n",
      "     0.20      1.00                      2        99\n",
      "     0.40      0.00                      2        99\n",
      "     0.40      0.20                      2        99\n",
      "     0.40      0.40                      2        99\n",
      "     0.40      0.60                      2        99\n",
      "     0.40      0.80                      2        99\n",
      "     0.40      1.00                      2        99\n",
      "     0.60      0.00                      0        99\n",
      "     0.60      0.20                      0        99\n",
      "     0.60      0.40                      0        99\n",
      "     0.60      0.60                      0        99\n",
      "     0.60      0.80                      2        99\n",
      "     0.60      1.00                      2        99\n",
      "     0.80      0.00                      0        99\n",
      "     0.80      0.20                      0        99\n",
      "     0.80      0.40                      0        99\n",
      "     0.80      0.60                      0        99\n",
      "     0.80      0.80                      2        99\n",
      "     0.80      1.00                      2        99\n",
      "     1.00      0.00                      0        99\n",
      "     1.00      0.20                      0        99\n",
      "     1.00      0.40                      0        99\n",
      "     1.00      0.60                      0        99\n",
      "     1.00      0.80                      2        99\n",
      "     1.00      1.00                      2        99\n",
      "\n",
      "Optimal epsilon: 0.6000000000000001\n",
      "Optimal lambda: 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reward: 99\n",
      "Optimal epsilon: 0.6000000000000001\n",
      "Optimal lambda: 0.0\n"
     ]
    }
   ],
   "source": [
    "# Plotting the rewards to find smallest number of trials which produce a steady-state maximum reward\n",
    "\n",
    "from tabulate import tabulate\n",
    "\n",
    "def plot_rewards(N,lower_bound,upper_bound,epsilon=0.25,lam=1.0, display=True):\n",
    "    \n",
    "    X = range(lower_bound,upper_bound+1)\n",
    "\n",
    "    Y = [run_experiment(N,epsilon=epsilon,lam=lam,num_trials=k,display=False) for k in X]\n",
    "#     Y = []\n",
    "#     for k in X:\n",
    "#         result = run_experiment(N, epsilon=epsilon, lam=lam, num_trials=k, display=False)\n",
    "#         print(result)\n",
    "#         Y.append(result)\n",
    "    if display:\n",
    "        plt.figure(figsize=(8,4))\n",
    "        plt.title('Rewards Exploring Grid World '+str(N))\n",
    "        plt.plot(X,Y)\n",
    "        plt.scatter(X,Y,marker='.')\n",
    "        plt.show()\n",
    "\n",
    "        print(\"Reward:\",Y[-1])\n",
    "    \n",
    "    # under assumption that steady state was reached by the upper_bound, \n",
    "    # find the first time that value was found in this range\n",
    "    steady_state_trials = lower_bound\n",
    "    for k in range(len(Y)-1,-1, -1):\n",
    "        if Y[k] < Y[-1]:\n",
    "            steady_state_trials = X[k + 1]\n",
    "            if display:\n",
    "                print(\"Steady state found at\",steady_state_trials,\"trials.\")\n",
    "            break\n",
    "            \n",
    "    return steady_state_trials, Y[-1]\n",
    "# example\n",
    "\n",
    "def optimize(N, lower_bound, upper_bound, print_each=True):\n",
    "    # Define the range of epsilon and lambda values to search over\n",
    "    epsilon_values = np.arange(0, 1.2, 0.2)\n",
    "    lambda_values = np.arange(0, 1.2, 0.2)\n",
    "\n",
    "    # Initialize variables to keep track of the best parameter combination and the fastest steady state\n",
    "    best_epsilon = None\n",
    "    best_lambda = None\n",
    "    fastest_steady = float('inf')\n",
    "    highest_reward = float('-inf')\n",
    "\n",
    "    # Create a list to store the results for each combination of epsilon and lambda values\n",
    "    results = []\n",
    "\n",
    "    # Iterate over all combinations of epsilon and lambda values\n",
    "    for epsilon in epsilon_values:\n",
    "        for lam in lambda_values:\n",
    "            # Run the plot_rewards function and get the steady state\n",
    "            steady, reward = plot_rewards(N, lower_bound, upper_bound, epsilon=epsilon, lam=lam, display=print_each)\n",
    "\n",
    "            # Store the results for this combination\n",
    "            results.append((epsilon, lam, steady, reward))\n",
    "\n",
    "            # If the current reward is higher than the highest one found so far, update the best parameters and the highest reward\n",
    "            if reward > highest_reward:\n",
    "                highest_reward = reward\n",
    "                fastest_steady = steady\n",
    "                best_epsilon = epsilon\n",
    "                best_lambda = lam\n",
    "            # If the current reward is equal to the highest one found so far, check if the steady state is faster and update the best parameters if needed\n",
    "            elif reward == highest_reward and steady < fastest_steady:\n",
    "                fastest_steady = steady\n",
    "                best_epsilon = epsilon\n",
    "                best_lambda = lam\n",
    "\n",
    "    # Print the table of results\n",
    "    headers = ['Epsilon', 'Lambda', 'Steady State Trials', 'Reward']\n",
    "    print(tabulate(results, headers=headers, floatfmt=\".2f\"))\n",
    "\n",
    "    # Return the best parameter combination\n",
    "    print()\n",
    "    print(\"Optimal epsilon:\", best_epsilon)\n",
    "    print(\"Optimal lambda:\", best_lambda)\n",
    "    plot_rewards(N, lower_bound, upper_bound, best_epsilon, best_lambda)\n",
    "    return best_epsilon, best_lambda\n",
    "\n",
    "best_epsilon, best_lambda = optimize(0, 0, 200, print_each=False)\n",
    "print(\"Optimal epsilon:\", best_epsilon)\n",
    "print(\"Optimal lambda:\", best_lambda)\n",
    "\n",
    "# plot_rewards(0,0,100)\n",
    "# plot_rewards(0,0,100, epsilon=0)\n",
    "# plot_rewards(0,0,100, epsilon=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discussion on world 0 is above the code cell"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# World 1\n",
    "Optimal epsilon: 0.2\n",
    "Optimal lambda: 0.8\n",
    "\n",
    "We find that a moderately low, slowly decreasing exploration rate works best in this case, but not significantly better. It's hard to make any meaningful judgements on why these parameters work better; the world is really small and it could just be due to randomness. Interestingly, lambda=1.0 seems to perform the worst here by far. This is probably because the world is very small and has one optimal path, so it we quickly get the optimal policy and exploring further only increases the chance that one of the random explorations will lead to a losing state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1051,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Epsilon    Lambda    Steady State Trials    Reward\n",
      "---------  --------  ---------------------  --------\n",
      "     0.00      0.00                      4        97\n",
      "     0.00      0.20                      4        97\n",
      "     0.00      0.40                      4        97\n",
      "     0.00      0.60                      4        97\n",
      "     0.00      0.80                      4        97\n",
      "     0.00      1.00                      4        97\n",
      "     0.20      0.00                      4        97\n",
      "     0.20      0.20                      4        97\n",
      "     0.20      0.40                      4        97\n",
      "     0.20      0.60                      4        97\n",
      "     0.20      0.80                      3        97\n",
      "     0.20      1.00                      5        97\n",
      "     0.40      0.00                      4        97\n",
      "     0.40      0.20                      4        97\n",
      "     0.40      0.40                      4        97\n",
      "     0.40      0.60                      4        97\n",
      "     0.40      0.80                      4        97\n",
      "     0.40      1.00                      7        97\n",
      "     0.60      0.00                      4        97\n",
      "     0.60      0.20                      4        97\n",
      "     0.60      0.40                      4        97\n",
      "     0.60      0.60                      4        97\n",
      "     0.60      0.80                      4        97\n",
      "     0.60      1.00                      6        97\n",
      "     0.80      0.00                      4        97\n",
      "     0.80      0.20                      4        97\n",
      "     0.80      0.40                      4        97\n",
      "     0.80      0.60                      4        97\n",
      "     0.80      0.80                      4        97\n",
      "     0.80      1.00                     21        97\n",
      "     1.00      0.00                      4        97\n",
      "     1.00      0.20                      4        97\n",
      "     1.00      0.40                      4        97\n",
      "     1.00      0.60                      4        97\n",
      "     1.00      0.80                      3        97\n",
      "     1.00      1.00                     22        97\n",
      "\n",
      "Optimal epsilon: 0.2\n",
      "Optimal lambda: 0.8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reward: 97\n",
      "Steady state found at 3 trials.\n",
      "Optimal epsilon: 0.2\n",
      "Optimal lambda: 0.8\n"
     ]
    }
   ],
   "source": [
    "best_epsilon, best_lambda = optimize(1, 0, 200, print_each=False)\n",
    "print(\"Optimal epsilon:\", best_epsilon)\n",
    "print(\"Optimal lambda:\", best_lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# World 2\n",
    "Optimal epsilon: 0.4\n",
    "Optimal lambda: 1.0\n",
    "\n",
    "This world is interesting because 2 pairs of parameters yield a slightly higher reward than all the others, even though other parameters reach a steady state sooner at a slightly lower reward. Specifically, these two sets of parameters manage to find the only optimal path, while all the others make a mistake that they later have to correct for, with a total loss of 2 points. Both of the winning sets of parameters them have lambda=1.0. At the same time, in all cases, a constant exploration rate finds a steady state significantly later, for reasons I outlined in the previous comment. I'd guess that having a higher exploration rate later on helps correct these errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1052,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Epsilon    Lambda    Steady State Trials    Reward\n",
      "---------  --------  ---------------------  --------\n",
      "     0.00      0.00                     33        86\n",
      "     0.00      0.20                     33        86\n",
      "     0.00      0.40                     33        86\n",
      "     0.00      0.60                     33        86\n",
      "     0.00      0.80                     33        86\n",
      "     0.00      1.00                     33        86\n",
      "     0.20      0.00                     33        86\n",
      "     0.20      0.20                     33        86\n",
      "     0.20      0.40                     33        86\n",
      "     0.20      0.60                     33        86\n",
      "     0.20      0.80                     33        86\n",
      "     0.20      1.00                     42        86\n",
      "     0.40      0.00                     33        86\n",
      "     0.40      0.20                     33        86\n",
      "     0.40      0.40                     33        86\n",
      "     0.40      0.60                     33        86\n",
      "     0.40      0.80                     30        86\n",
      "     0.40      1.00                     48        88\n",
      "     0.60      0.00                     33        86\n",
      "     0.60      0.20                     33        86\n",
      "     0.60      0.40                     33        86\n",
      "     0.60      0.60                     34        86\n",
      "     0.60      0.80                     30        86\n",
      "     0.60      1.00                     90        88\n",
      "     0.80      0.00                     33        86\n",
      "     0.80      0.20                     33        86\n",
      "     0.80      0.40                     33        86\n",
      "     0.80      0.60                     34        84\n",
      "     0.80      0.80                     32        84\n",
      "     0.80      1.00                    149        86\n",
      "     1.00      0.00                     33        86\n",
      "     1.00      0.20                     33        86\n",
      "     1.00      0.40                     33        86\n",
      "     1.00      0.60                     34        84\n",
      "     1.00      0.80                     32        84\n",
      "     1.00      1.00                     11         0\n",
      "\n",
      "Optimal epsilon: 0.4\n",
      "Optimal lambda: 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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0qGZgs9nUq1cvffzxx1q3bp1HiSx3CsBrr73msb/c3Fxt27ZN/fr1O4dP5J3P9PLLL2vcuHG65ZZbrMoQQLii5xUIEYmJiZo2bZoeeughLVmyRLfccotefPFFDR48WNdee60yMzN1wQUX6N///re2bdumb7/91iNg6devn5xOp1atWqXFixdby/v376+ZM2fKZrN55Pe1b99ebdq00dSpU2WMUaNGjfThhx9aObK1cckll+iWW27RX/7yF0VHR6t///7avHmznnnmGTVo0MBj26uuukpDhgzRpZdeqsTERG3btk2vvvpqrQO+HTt2WCkNlblrpjqdTo0ZM0Y2m01LlixRZGSkXn75Zas6w+rVq1WvXj3rfUlJSerbt69mzJihuLg4zZ8/Xz/++ONpy2VFREToqaee0s0336whQ4borrvuUmlpqZ5++mkdPHhQTzzxRK3P3bmaPn26PvzwQ/Xr10/Tp09XbGysFi5cqCNHjlhtPJ0xY8Zoy5Ytmjt3rr7//ntlZmaqbdu2crlcys/Pt+qoVv7H6Gzcdttt+vOf/6zbbrtNc+fOVdu2bfXRRx/pk08+qfU+bDabevfurbffflvGGI+eV+lEAP/AAw/IGOMRvF588cW688479fzzzysiIkKDBw/Wrl27NGPGDLVo0UIPPvhgQD7TW2+9pTvuuEOXX3657rrrriq9uJ07d67yTyQQ0gI5WgzA2XNXG8jNza2y7tixY6Zly5ambdu2pry83BhjzPfff29GjhxpmjZtaqKjo01ycrLp27evNfrazeVymaSkJCPJ/Prrr9byr776ykgyXbp0qXK8rVu3mgEDBpj4+HiTmJhoRowYYXbv3m0kmZkzZ1rbuUfHVx7h7lZaWmomT55smjZtamJiYkz37t3N2rVrTVpamke1galTp5pu3bqZxMREY7fbzYUXXmgefPBBU1RUdNrzdaZqA9OnTzfGnBi9HRERUWX0+Jo1a0xUVJS5//77rWWSzIQJE8z8+fNNmzZtTHR0tGnfvr15/fXXqz22u9qA2/vvv2+uuuoqExMTY+Li4ky/fv3MV1995bHN6c5ZTdUGrrvuuirbnjry3RhjvvzyS3PVVVcZu91ukpOTzX/+53+aJ5980kgyBw8erPY8nuqLL74wo0aNMs2bNzfR0dGmfv36pkOHDuYPf/iDWb9+fZU2dOzYsdr9VNe+X375xQwfPtz85je/MfHx8Wb48OFmzZo1ZzUyf/78+UaSadKkSZV13333nfXz37Fjh8c6p9NpnnzySdOuXTsTHR1tkpKSzC233OJRlcLfn2ns2LGnvYZPVyECCEU2Y3zwvQ8AhDB3If4XXngh0E3xmoEDB2rXrl366aefAt0UADgt0gYAIMxMmjRJnTt3VosWLfTvf/9br7/+ulasWOExixgA1FUErwAQZpxOpx599FEVFhbKZrOpQ4cOevXVV3XLLbcEumkAcEakDQAAACBoUCoLAAAAQYPgFQAAAEGD4BUAAABBIywGbLlcLu3Zs0fx8fHMSgIAAFAHGWN06NAhpaamnnbClLAIXvfs2aMWLVoEuhkAAAA4g/z8/Bqn2ZbCJHh1T1OYn59fZcpJAAAABF5JSYlatGhxxumlwyJ4dacKNGjQgOAVAACgDjtTiicDtgAAABA0CF4BAAAQNAheAQAAEDQIXgEAABA0CF4BAAAQNAheAQAAEDQIXgEAABA0CF4BAAAQNMJikgKgrigoPqa8oiNqnRQnSef0PK5epI6UOf32Po7NsTk2x+bYHDslIVZ1BcEr4CdLc3dr2rub5DKSe+4Qo7N/7uav93Fsjs2xOTbHDu9jR9ikecM6adQVLVUXELwCflBQfMwKXCXPPxxn+9zf7+PYHJtjc2yOHd7Hdhnpj+9uVq92TepEDyzBK0LC2XwdX/mrEn/9EuYVHbECVwAAgo3TGO0qOkrwCnjD2X4d7+bPr0FaJ8XJpur/6wUAoK6LtNnUKql+oJshiWoDCHLVfR3vDhBreu7m/hqkoPiYz9vZND5GTeLt1mubJJvt3J6f6z44Nsfm2BybY3Psc9lHpM2mx4el14leV4meVwS58/063mmMlv9QoOsuTbH254tRmiu37dW+Q6WKs0fqr6M7q0NqA0nSrqKj1n+ytX1ev16Ejpa5/PY+js2xOTbH5tgcu64ErpJkM8aE/DeZJSUlSkhIUHFxsRo0aBDo5sCLCoqP6eonPguafFKbpCeG150RmwAA1BW1jddIG0BQS0mI1bxhnTyW1farkkAw8l+qAgAAoYi0AQS9UVe01Iz3t6jM6dJ79/RUckLMGb8qyd11QI8t3xaQ9talEZsAAAQbgleEBIfLJUm6IDFWTeNjPALD6p43bRCjxz/aFpB0g7o0YhMAgGBD2gCCntNl5M7crhdZu0vanW4QeTKXwF8jPevaiE0AAIINPa8Ieg6ny3oeXcvgVTqRbtCrXRO/jhCtayM2AQAINgSvCHpl5xi8Sid6YM+UYnC65+f7PgAAcHZIG0DQc5RXDl7rQEkBAADgMwSvCHoO54mE1+hIm2x1oR4WAADwGYJXBD13zuvZpgwAAIDgE/C7fatWrWSz2ao8JkyYIEnKzMyssq579+4BbjXqEnfOa1QEva4AAIS6gA/Yys3NldPptF5v3rxZAwYM0IgRI6xlgwYNUlZWlvW6Xr16fm0j6jZ3z2u9qID/LwYAAHws4MFrkyZNPF4/8cQTatOmjTIyMqxldrtdycnJ/m4agoSj3J3zSvAKAECoq1N3+7KyMr322mu6/fbbPQbe5OTkqGnTpmrXrp3Gjx+vffv2BbCVqGvKyHkFACBsBLzntbL3339fBw8eVGZmprVs8ODBGjFihNLS0pSXl6cZM2aob9++2rBhg+x2e7X7KS0tVWlpqfW6pKTE101HAFUM2CLnFQCAUFengtdFixZp8ODBSk1NtZaNGjXKep6enq5u3bopLS1Ny5cv17Bhw6rdz7x58zR79myftxd1Q7mTtAEAAMJFnbnb//zzz1q5cqXGjRt32u1SUlKUlpamHTt21LjNtGnTVFxcbD3y8/O93VzUIQzYAgAgfNSZntesrCw1bdpU11133Wm3279/v/Lz85WSklLjNna7vcaUAoQecl4BAAgfdeJu73K5lJWVpbFjxyoqqiKePnz4sKZMmaK1a9dq165dysnJ0fXXX6+kpCT97ne/C2CLUZeQ8woAQPioEz2vK1eu1O7du3X77bd7LI+MjNSmTZv0yiuv6ODBg0pJSVGfPn20dOlSxcfHB6i1qGuYYQsAgPBRJ4LXgQMHyhhTZXlsbKw++eSTALQIwYQ6rwAAhA/u9gh6ZaQNAAAQNgheEfRIGwAAIHxwt0fQs0plEbwCABDyuNsj6DmYpAAAgLDB3R5Br6z8ZNpAFDmvAACEOoJXBL1yFzmvAACEC+72CHrutAFyXgEACH3c7RH0rLQBglcAAEIed3sEPUplAQAQPrjbI+i5g9coJikAACDkEbwi6JHzCgBA+OBuj6DH9LAAAIQPglcEPYdV55XLGQCAUMfdHkGPAVsAAIQP7vYIeuS8AgAQPrjbI+jR8woAQPjgbo+g52DAFgAAYYPgFUHPnTbAgC0AAEIfd3sEPavnNYLLGQCAUMfdHkGPOq8AAIQPglcEPavnlbQBAABCHnd7BD1HOaWyAAAIF9ztEfQolQUAQPjgbo+gR84rAADhg+AVQY+eVwAAwkfA7/azZs2SzWbzeCQnJ1vrjTGaNWuWUlNTFRsbq969e2vLli0BbDHqGmt6WAZsAQAQ8urE3b5jx44qKCiwHps2bbLWPfXUU3ruuef0wgsvKDc3V8nJyRowYIAOHToUwBajrnC5jJyuk5MU0PMKAEDIqxN3+6ioKCUnJ1uPJk2aSDrR6/qXv/xF06dP17Bhw5Senq7Fixfr6NGjWrJkSYBbjbrA4XJZz8l5BQAg9NWJ4HXHjh1KTU1V69atNXr0aP3rX/+SJOXl5amwsFADBw60trXb7crIyNCaNWtq3F9paalKSko8HghN7pQBiZ5XAADCQcDv9ldddZVeeeUVffLJJ/rv//5vFRYWqmfPntq/f78KCwslSc2aNfN4T7Nmzax11Zk3b54SEhKsR4sWLXz6GRA4jvLKPa8Bv5wBAICPBfxuP3jwYA0fPlydOnVS//79tXz5cknS4sWLrW1sNs+vg40xVZZVNm3aNBUXF1uP/Px83zQeAeeuNBBhkyIjSBsAACDUBTx4PVVcXJw6deqkHTt2WFUHTu1l3bdvX5Xe2MrsdrsaNGjg8UBoKqNMFgAAYaXO3fFLS0u1bds2paSkqHXr1kpOTtaKFSus9WVlZfr888/Vs2fPALYSdYVVJovgFQCAsBAV6AZMmTJF119/vVq2bKl9+/bpscceU0lJicaOHSubzaYHHnhAjz/+uNq2bau2bdvq8ccfV/369XXTTTcFuumoA6wJCqjxCgBAWAh48PrLL79ozJgxKioqUpMmTdS9e3etW7dOaWlpkqSHHnpIx44d0z333KMDBw7oqquu0qeffqr4+PgAtxx1QVk5U8MCABBObMYYc+bNgltJSYkSEhJUXFxM/muI2bj7gH43f42aJ8Zq9cN9A90cAABwjmobr/FdK4IaOa8AAIQX7vgIauVUGwAAIKxwx0dQc5fKiiLnFQCAsEDwiqDmThug5xUAgPDAHR9BzV0qi5xXAADCA3d8BLWKOq+kDQAAEA4IXhHUKuq8cikDABAOuOMjqJHzCgBAeOGOj6BGzisAAOGFOz6CmpXzSqksAADCAsErgloZkxQAABBWuOMjqJW7c16juJQBAAgH3PER1Ky0gQjSBgAACAcErwhqpA0AABBeuOMjqDnKSRsAACCccMdHUHPQ8woAQFjhjo+gVlHnlZxXAADCAcErgho5rwAAhBfu+AhqTA8LAEB44Y6PoOYoP9nzyoAtAADCAnd8BDVyXgEACC8Erwhq5LwCABBeuOMjqLmnh40ieAUAICxwx0dQI20AAIDwEvDgdd68ebriiisUHx+vpk2b6sYbb9T27ds9tsnMzJTNZvN4dO/ePUAtRl3CJAUAAISXgN/xP//8c02YMEHr1q3TihUrVF5eroEDB+rIkSMe2w0aNEgFBQXW46OPPgpQi1GXlFEqCwCAsBIV6AZ8/PHHHq+zsrLUtGlTbdiwQb169bKW2+12JScn+7t5qOPoeQUAILzUuTt+cXGxJKlRo0Yey3NyctS0aVO1a9dO48eP1759+wLRPNQxVs5rFDmvAACEg4D3vFZmjNGkSZN0zTXXKD093Vo+ePBgjRgxQmlpacrLy9OMGTPUt29fbdiwQXa7vcp+SktLVVpaar0uKSnxS/vhf9YkBfS8AgAQFupU8Dpx4kT98MMPWr16tcfyUaNGWc/T09PVrVs3paWlafny5Ro2bFiV/cybN0+zZ8/2eXsReOS8AgAQXurMHf/ee+/VsmXLlJ2drebNm59225SUFKWlpWnHjh3Vrp82bZqKi4utR35+vi+ajDqAnFcAAMJLwHtejTG699579d577yknJ0etW7c+43v279+v/Px8paSkVLvebrdXm06A0FNR55XgFQCAcBDwO/6ECRP02muvacmSJYqPj1dhYaEKCwt17NgxSdLhw4c1ZcoUrV27Vrt27VJOTo6uv/56JSUl6Xe/+12AW49AcwevUUxSAABAWAh4z+uCBQskSb179/ZYnpWVpczMTEVGRmrTpk165ZVXdPDgQaWkpKhPnz5aunSp4uPjA9Bi1BXGGDnIeQUAIKwEPHg1xpx2fWxsrD755BM/tQbBpNxVce2QNgAAQHjgjo+g5U4ZkKRo6rwCABAWCF4RtBzlFT2vpA0AABAeuOMjaJVV6nmNiqDnFQCAcEDwiqBVuUyWzUbwCgBAOCB4RdCqmKCAwBUAgHBB8IqgZQWvUVzGAACEC+76CFplJwdsRUVwGQMAEC646yNoVeS8kjYAAEC4IHhF0CJtAACA8MNdH0GLqWEBAAg/3PURtCqqDXAZAwAQLrjrI2iR8woAQPgheEXQoucVAIDww10fQauMnFcAAMIOd30ELUc51QYAAAg33PURtMh5BQAg/BC8Imi5g1dm2AIAIHxw10fQsnJeSRsAACBscNdH0KqoNkDaAAAA4YLgFUGr3Mp55TIGACBccNdH0KJUFgAA4Ye7PoIWkxQAABB+uOsjaFXUeSXnFQCAcEHwiqDlIOcVAICww10fQYucVwAAwk/Q3PXnz5+v1q1bKyYmRl27dtWXX34Z6CYhwMh5BQAg/EQFugG1sXTpUj3wwAOaP3++rr76ar344osaPHiwtm7dqpYtWwa6eeekoPiY8oqOKK5epI6UOdU6KU6SlFd05KyfV95HSkJslWPU5n3eOLY/3lf5+b6S45KkY47yc/45AACA4GIzxphAN+JMrrrqKnXp0kULFiywll1yySW68cYbNW/evDO+v6SkRAkJCSouLlaDBg182dRaWZq7W9Pe3SRXpTPvHnJkzuG5W4RNmjesk0Zd0dLjGGd6nzeO7a/31bSPJ4af+NwAACA41TZeq/Pft5aVlWnDhg0aOHCgx/KBAwdqzZo11b6ntLRUJSUlHo+6oqD4mKa+4xm4SieCMXOOz91cRvrju5v1ff4Bj+D4TO/zxrH99b6a9vHHdzeroPiYAABAaKvzwWtRUZGcTqeaNWvmsbxZs2YqLCys9j3z5s1TQkKC9WjRooU/mloreUVHqgRf3uQ0Rrm7DlQJjkOd0xjtKjoa6GYAAAAfq/PBq5vN5lnL0xhTZZnbtGnTVFxcbD3y8/P90cRaaZ0UJ19WJY202XRFq0SfHqMuirTZ1CqpfqCbAQAAfKzOB69JSUmKjIys0su6b9++Kr2xbna7XQ0aNPB41BUpCbEa2LFqu22S3LH42T6vvI/Hh6XrshaJenjwxWfct7eP7Y/3VbePSJtNjw9L9xisBgAAQlOdrzZQr149de3aVStWrNDvfvc7a/mKFSt0ww03BLBl5+6SlAb6ZMte9WvfVPf1u0hHy1xWr+GuoqNn/Xx+zk59uaNI9/a7yBq0NDg9RU/873bZoyKU85+9q31f/XoR533sc92Ht49N4AoAQHio88GrJE2aNEm33nqrunXrph49euhvf/ubdu/erbvvvjvQTTsnzpMJqc0TY3VZi0SPdZWDsNo+f2v9ibSI+vUqfpyOkwX87VER1vY17eN8jn2++/DmsQEAQOgLiuB11KhR2r9/v+bMmaOCggKlp6fro48+UlpaWqCbdk7cgWVkhHeyNqIiT3yPXn6yaL8klbso4A8AAEJPUASvknTPPffonnvuCXQzvKLcmhnKO8Oqok4GqO6g+MQxzMl14TZ0CwAAhDK65QKg3OXdwDI64mTPq6ui59U9dWqUl3p3AQAA6gIimwBwB5neSxs4sZ/yyj2vJwNkb/XuAgAA1AUErwHgDjLdPabny92DWzltwOp5JecVAACEECKbAKhIG/DO6Y8+2YPrrJQ2YOW8eilABgAAqAsIXgOg3MpH9XLPq6ty2gDVBgAAQOghsgkAh7cHbFk5r5UHbFFtAAAAhB6C1wBwOr2bNuDuwS2vplRWNNUGAABACCGyCQD3V/reSxs4Wee1mrQBel4BAEAoIXgNAGvAlpeC1+jqZtjycu8uAABAXUBkEwDWV/peSxuoZoYt94Atqg0AAIAQQvAaAO4arJFerjbgOcMWA7YAAEDoIXgNAKeXZ7+qSBuoPGCLSQoAAEDoIbIJAKtUlremh7XSBirlvLq8O4sXAABAXUDwGgDuXtFIb/e8uipPD8uALQAAEHqIbALAShvwcs+rZ7UB9wxb9LwCAIDQQfAaAL4asFW52oC3UxMAAADqAiKbACj3+oCtkz2vrqo9r1QbAAAAoYTgNQC8PYFAtdPDurxbSxYAAKAuILIJAN9ND1u5zqt3jwEAAFAXELwGQLmXJxCovs4r1QYAAEDoIbIJgHKf1XllelgAABDaCF4DoNzLX+lHn3Z6WH7EAAAgdBDZBIBVxspLaQPuALW66WGp8woAAEIJwWsAOL1cCcDdg1t5etiKOq8ErwAAIHQELHjdtWuX7rjjDrVu3VqxsbFq06aNZs6cqbKyMo/tbDZblcfChQsD1OrzZ4yxgldvTVJQUee1as8raQMAACCURAXqwD/++KNcLpdefPFFXXTRRdq8ebPGjx+vI0eO6JlnnvHYNisrS4MGDbJeJyQk+Lu5XlN5UJXXpoc9mRrgdBkZY2Sz2awUAtIGAABAKAlY8Dpo0CCPgPTCCy/U9u3btWDBgirBa8OGDZWcnOzvJvqEs1LvqNdKZVUKgh1Oo3pRNqaHBQAAIalORTbFxcVq1KhRleUTJ05UUlKSrrjiCi1cuFCuSqPqg03liQS8lTZQOQh2VxxgelgAABCKAtbzeqp//vOfev755/Xss896LP/Tn/6kfv36KTY2VqtWrdLkyZNVVFSkRx55pMZ9lZaWqrS01HpdUlLis3afrcoVAbw2YKtSgOpOS6hIG6hT/58AAACcF69HNrNmzap2kFXlx/r16z3es2fPHg0aNEgjRozQuHHjPNY98sgj6tGjhy6//HJNnjxZc+bM0dNPP33aNsybN08JCQnWo0WLFt7+mOfM3TNqs3lxwFal1AB3j6vDy1PQAgAA1AVe73mdOHGiRo8efdptWrVqZT3fs2eP+vTpox49euhvf/vbGfffvXt3lZSUaO/evWrWrFm120ybNk2TJk2yXpeUlNSZANaattWLQWVEhE0RNsllKioO0PMKAABCkdeD16SkJCUlJdVq219//VV9+vRR165dlZWVpYhaDC7auHGjYmJi1LBhwxq3sdvtstvttW2yX1UEr94NKqMiI1RW7rJqvTrIeQUAACEoYDmve/bsUe/evdWyZUs988wz+r//+z9rnbuywIcffqjCwkL16NFDsbGxys7O1vTp03XnnXfW2eD0TNxpA94OKqMjbCpTRXBcTrUBAAAQggIWvH766afauXOndu7cqebNm3usM+bkV97R0Zo/f74mTZokl8ulCy+8UHPmzNGECRMC0WSvKPfRzFcnJiNwVqk2QJ1XAAAQSgIWvGZmZiozM/O025xaCzYUOHw085U7SHUHx+6qA94aFAYAAFAX8J2yn7knKYj2ds/ryfSAirQBd88rP2IAABA6iGz8zOoR9fLX+e4cWnfPrjUwjLQBAAAQQghe/czKRfXyQCp3D2tF2oC7zis/YgAAEDqIbPzMnTbg7R5R9wAwq+fVnZ5AzysAAAghBK9+5nC5B1J5v86rVCnn1Uob4EcMAABCB5GNn/mqhFVFtQHP6WG9PTAMAAAgkAhe/cxndV6ttAEjp8voZKlcel4BAEBIIbLxM19OD+vevzvv9cRyel4BAEDoIHj1M59ND1spbcDduyt5v6oBAABAIBHZ+JmvBlK5e3IdTmPl1Z44Dj2vAAAgdBC8+pnV8+rlnFer59XpsiZC8MVxAAAAAong1c8cTl8N2DrZ8+oyHgGyzUbwCgAAQgfBq585rckDvD1gq6LnlalhAQBAqCJ49TN3JYBIH5XKqlxtgMFaAAAg1BDd+JnPpoeNdKcNVFQboOcVAACEGoJXP3MHlt7uFa0YsFXR88oEBQAAINQQ3fiZlTbg7Z7XCPckBRU5r0wNCwAAQg3Bq59ZA7a8nfN6Mhj2qDZAzysAAAgxRDd+5vDRJAXRkRU9rw6qDQAAgBBF8Opn7tmvvF/n9WTPq9NU6t3lxwsAAEIL0Y2f+aoSgLsnt9zlqjRgi55XAAAQWghe/axi9isvpw1UqvNa7qPUBAAAgEAjuvGzcl9ND+uu8+qsGLBFtQEAABBqCF79rCJtwEd1Xl0M2AIAAKGL4NXPfD1gq7xyzytpAwAAIMQENLpp1aqVbDabx2Pq1Kke2+zevVvXX3+94uLilJSUpPvuu09lZWUBavH5c/h6etjKpbJIGwAAACEmKtANmDNnjsaPH2+9/s1vfmM9dzqduu6669SkSROtXr1a+/fv19ixY2WM0fPPPx+I5p43p8/qvLrTBhiwBQAAQlfAg9f4+HglJydXu+7TTz/V1q1blZ+fr9TUVEnSs88+q8zMTM2dO1cNGjTwZ1O9oqLagG+mh3U4XZXSBuh5BQAAoSXgXXNPPvmkGjdurMsvv1xz5871SAlYu3at0tPTrcBVkq699lqVlpZqw4YNNe6ztLRUJSUlHo+6wldf6bvTEMqdptIxAv7jBQAA8KqA9rzef//96tKlixITE/XNN99o2rRpysvL00svvSRJKiwsVLNmzTzek5iYqHr16qmwsLDG/c6bN0+zZ8/2advPlTX7lY+mh3W6TMWgMHpeAQBAiPF619ysWbOqDMI69bF+/XpJ0oMPPqiMjAxdeumlGjdunBYuXKhFixZp//791v5stqoBmDGm2uVu06ZNU3FxsfXIz8/39sc8Z+7ZryJ9NT2sy2WV42J6WAAAEGq83vM6ceJEjR49+rTbtGrVqtrl3bt3lyTt3LlTjRs3VnJysr7++muPbQ4cOCCHw1GlR7Yyu90uu91+dg33Eyuw9HKvqLvn9UTaAD2vAAAgNHk9eE1KSlJSUtI5vXfjxo2SpJSUFElSjx49NHfuXBUUFFjLPv30U9ntdnXt2tU7DfYza5ICL/eKugNVh9NlVRugzisAAAg1Act5Xbt2rdatW6c+ffooISFBubm5evDBBzV06FC1bNlSkjRw4EB16NBBt956q55++mn9+9//1pQpUzR+/PigrDQgVUxSEOntOq8ng+Fyl5HDRxUNAAAAAi1gwavdbtfSpUs1e/ZslZaWKi0tTePHj9dDDz1kbRMZGanly5frnnvu0dVXX63Y2FjddNNNeuaZZwLV7PNm9Yp6uefVqvNaqeeVOq8AACDUBCx47dKli9atW3fG7Vq2bKn/+Z//8UOL/MOq8+qzGbYqqg1Q5xUAAIQauub8rCLn1TfVBspdroopaKk2AAAAQgzRjZ/56iv9ytUGqPMKAABCFcGrn/lsethqqg0wYAsAAIQaglc/q+h59XKdV49qAwzYAgAAoYnoxs+sCQR8VOe1nAFbAAAghBG8+pnTRzNsWWkDLpccTgZsAQCA0ER042fur/QjvZyP6k4bMEYqY8AWAAAIUQSvflbxlb5v0gYk6XiZ8+QxCF4BAEBoIXj1I5fL6GTHq9crAVQOho85nCePwY8XAACEFqIbP3JPUCD5YMBWpWDYHbzS8woAAEINwasfuWu8St7PR62cQ3usjJ5XAAAQmohu/Mij59XLwavNZrN6Wo+70wboeQUAACGG4NWP3BMUSL7pFXXvsyJtgB8vAAAILUQ3fuSuNGCzeb9UllTR01oxYIueVwAAEFoIXv3InTYQ7aNcVHdPq3FXNKDnFQAAhBiiGz9ypw34otdVqtrTSrUBAAAQaghe/cjh8u3MV6fmuFJtAAAAhBqiGz9yutMGfPR1/qlBMT2vAAAg1BC8+pHj5IAtf6UNkPMKAABCDdGNH7lzXqN9FLxWTRug5xUAAIQWglc/clcb8FWPaNW0AX68AAAgtBDd+JG7zquvekRPHaDFDFsAACDUELz6kdPqefVV2sApPa9UGwAAACGG6MaPHO7g1UdBJT2vAAAg1BG8+pGVNuCjoPLU/RK8AgCAUBOw4DUnJ0c2m63aR25urrVddesXLlwYqGafF2vAlp+qDZA2AAAAQk1UoA7cs2dPFRQUeCybMWOGVq5cqW7dunksz8rK0qBBg6zXCQkJfmmjt7lLZfms2kCloDjCJkVQKgsAAISYgAWv9erVU3JysvXa4XBo2bJlmjhxomw2z6CrYcOGHtsGq3KXb6sNVO55ZYICAAAQiupMhLNs2TIVFRUpMzOzyrqJEycqKSlJV1xxhRYuXCjXySCwJqWlpSopKfF41AU+73mtlOPqq4kQAAAAAilgPa+nWrRoka699lq1aNHCY/mf/vQn9evXT7GxsVq1apUmT56soqIiPfLIIzXua968eZo9e7avm3zWfN3zWnnaWXpeAQBAKPJ6hDNr1qwaB2K5H+vXr/d4zy+//KJPPvlEd9xxR5X9PfLII+rRo4cuv/xyTZ48WXPmzNHTTz992jZMmzZNxcXF1iM/P9+rn/FcOZw+HrBVaYDWqTVfAQAAQoHXe14nTpyo0aNHn3abVq1aebzOyspS48aNNXTo0DPuv3v37iopKdHevXvVrFmzarex2+2y2+21brO/uCcp8NW0rZXTBnxVSxYAACCQvB68JiUlKSkpqdbbG2OUlZWl2267TdHR0WfcfuPGjYqJiVHDhg3Po5WB4ThZ5zXSLwO26HkFAAChJ+A5r5999pny8vKqTRn48MMPVVhYqB49eig2NlbZ2dmaPn267rzzzjrZs3om5T6eHrZyOoKvencBAAACKeDB66JFi9SzZ09dcsklVdZFR0dr/vz5mjRpklwuly688ELNmTNHEyZMCEBLz5+VNuCr6WEr97xSbQAAAISggAevS5YsqXHdoEGDPCYnCHZW2oCPel4rD9Ki2gAAAAhFRDh+5K7z6qsarFFUGwAAACGO4NWPKnJe/VFtgOAVAACEHoJXPyp3+np6WNIGAABAaCPC8SPfVxsgbQAAAIQ2glc/qpge1jenvXLAGskkBQAAIAQR4fhRuY+nh62cKuCrQWEAAACBRPDqRw6njwdsRVTOeSV4BQAAoYfg1Y+cJ9MGfJWP6jk9LD9aAAAQeohw/MhxcsBWpM/SBipND0vaAAAACEEEr35klcryWdoAPa8AACC0EeH4kdPl2xm2KqcjUCoLAACEIoJXP3IP2PJd2kClnldKZQEAgBBEhONH5daALR/VeaXaAAAACHEEr35k1Xn11Qxbleu8kvMKAABCEBGOH1nTw/qh2oCvjgEAABBIBK9+ZFUb8NX0sFQbAAAAIY4Ix4+snlefpQ1Q5xUAAIQ2glc/snJefdXzWjltgJ5XAAAQgohw/Mjhck9S4KOe14jKA7boeQUAAKGH4NWPrEkK/JA2wIAtAAAQighe/ajcmqTAV2kDDNgCAAChjQjHjxxWtQFfpQ0wPSwAAAhtBK9+VJE24JvTzvSwAAAg1BHh+JG75zXSRz2vntUG6HkFAAChx6fB69y5c9WzZ0/Vr19fDRs2rHab3bt36/rrr1dcXJySkpJ03333qayszGObTZs2KSMjQ7Gxsbrgggs0Z84cGWN82XSfKPf1gK0IpocFAAChLcqXOy8rK9OIESPUo0cPLVq0qMp6p9Op6667Tk2aNNHq1au1f/9+jR07VsYYPf/885KkkpISDRgwQH369FFubq5++uknZWZmKi4uTpMnT/Zl889ZQfEx5RUdUeukOKUkxFrLKyYp8EOdV6oNAACAEOTT4HX27NmSpJdffrna9Z9++qm2bt2q/Px8paamSpKeffZZZWZmau7cuWrQoIFef/11HT9+XC+//LLsdrvS09P1008/6bnnntOkSZNks9WtIG1p7m5Ne3eTXEaKsEnzhnXSqCtaSqo8Paxv2myz2RQZYZPTZeh5BQAAISmgEc7atWuVnp5uBa6SdO2116q0tFQbNmywtsnIyJDdbvfYZs+ePdq1a1e1+y0tLVVJSYnHwx8Kio9p6jsnAldJchnpj+9uVkHxMblcxlruy15R977JeQUAAKEooMFrYWGhmjVr5rEsMTFR9erVU2FhYY3buF+7tznVvHnzlJCQYD1atGjhg9ZXlVd0RKdm4jqN0a6io1bKgOTbGqzuwWAlxxw+OwYAAECgnHUUNWvWLNlsttM+1q9fX+v9Vfe1vzHGY/mp27gHa9WUMjBt2jQVFxdbj/z8/Fq353y0TorTqZ2qkTabWiXVV/nJqWEl3/W8Ls3draNlTknSxCUbtTR3t0+OAwAAEChnnfM6ceJEjR49+rTbtGrVqlb7Sk5O1tdff+2x7MCBA3I4HFbvanJycpUe1n379klSlR5ZN7vd7pFm4C8pCbGaN6yTpr6zSUaSTdLjw9KVkhCrkuMVPaG++Eq/oPiYpr27yXptdCJloVe7Jh6DxgAAAILZWQevSUlJSkpK8srBe/Tooblz56qgoEApKSmSTgzistvt6tq1q7XNH//4R5WVlalevXrWNqmpqbUOkv1p1BUt9Rt7lCYs2aimDeyVBmtVpA1E+2ACgbyiI3KdkrPgTlkgeAUAAKHCpzmvu3fv1nfffafdu3fL6XTqu+++03fffafDhw9LkgYOHKgOHTro1ltv1caNG7Vq1SpNmTJF48ePV4MGDSRJN910k+x2uzIzM7V582a99957evzxx+tkpQG33hc3VYRN2ltSqsLi45IqKg3YbFKED9IGTpeyAAAAECp8Grw++uij6ty5s2bOnKnDhw+rc+fO6ty5s5UTGxkZqeXLlysmJkZXX321Ro4cqRtvvFHPPPOMtY+EhAStWLFCv/zyi7p166Z77rlHkyZN0qRJk3zZ9PMSZ49S++QTwffG3QckVZqgwEfTtrpTFiJPBvSRNpuVsgAAABAqbCYYp6o6SyUlJUpISFBxcbHVo+tr09/bpNe/3q07e12oP/72Eu3ef1S9ns5W/XqR2jpnkM+OW1B8TLuKjqpVUn0CVwAAEDRqG69Ryd5HOrdMlCR9+/OJnlfHyWoDkT6e+SolIVY92jQmcAUAACGJ4NVHurRsKEna9GuxyspdcrrTBpj5CgAA4JwRSflI66Q4JcRGq7TcpR8LS+Rw+qfnFQAAIJQRvPqIzWZT55O9r+9s+MWqOuByGRUUHwtgywAAAIIXwasPRZ+cjGDx2p91x+ITFRb2HynT1U98xuxXAAAA54Dg1UcKio9p5dZ91a5zmROzX9EDCwAAcHYIXn0kr+iITleDzD37FQAAAGqP4NVHqpvxqjJmvwIAADh7BK8+cuqMVzadmBpWYvYrAACAcxUV6AaEslFXtFSvdk2sGa8kMfsVAADAeSB49bGUhFiPQJWgFQAA4NyRNgAAAICgQfAKAACAoEHwCgAAgKBB8AoAAICgQfAKAACAoEHwCgAAgKBB8AoAAICgQfAKAACAoBEWkxQYYyRJJSUlAW4JAAAAquOO09xxW03CIng9dOiQJKlFixYBbgkAAABO59ChQ0pISKhxvc2cKbwNAS6XS3v27FF8fLxsNpvPj1dSUqIWLVooPz9fDRo08Pnxggnnpnqcl5pxbqrHeake56VmnJvqcV5q5u9zY4zRoUOHlJqaqoiImjNbw6LnNSIiQs2bN/f7cRs0aMAvQg04N9XjvNSMc1M9zkv1OC8149xUj/NSM3+em9P1uLoxYAsAAABBg+AVAAAAQYPg1Qfsdrtmzpwpu90e6KbUOZyb6nFeasa5qR7npXqcl5pxbqrHealZXT03YTFgCwAAAKGBnlcAAAAEDYJXAAAABA2CVwAAAAQNglcAAAAEDYJXH5g/f75at26tmJgYde3aVV9++WWgm+RX8+bN0xVXXKH4+Hg1bdpUN954o7Zv3+6xTWZmpmw2m8eje/fuAWqxf8yaNavKZ05OTrbWG2M0a9YspaamKjY2Vr1799aWLVsC2GL/adWqVZVzY7PZNGHCBEnhc7188cUXuv7665Wamiqbzab333/fY31trpHS0lLde++9SkpKUlxcnIYOHapffvnFj5/CN053bhwOhx5++GF16tRJcXFxSk1N1W233aY9e/Z47KN3795VrqPRo0f7+ZN415mumdr87oTjNSOp2r85NptNTz/9tLVNqF0ztbk/B8PfGYJXL1u6dKkeeOABTZ8+XRs3btT/+3//T4MHD9bu3bsD3TS/+fzzzzVhwgStW7dOK1asUHl5uQYOHKgjR454bDdo0CAVFBRYj48++ihALfafjh07enzmTZs2WeueeuopPffcc3rhhReUm5ur5ORkDRgwQIcOHQpgi/0jNzfX47ysWLFCkjRixAhrm3C4Xo4cOaLLLrtML7zwQrXra3ONPPDAA3rvvff05ptvavXq1Tp8+LCGDBkip9Ppr4/hE6c7N0ePHtW3336rGTNm6Ntvv9W7776rn376SUOHDq2y7fjx4z2uoxdffNEfzfeZM10z0pl/d8LxmpHkcU4KCgr097//XTabTcOHD/fYLpSumdrcn4Pi74yBV1155ZXm7rvv9ljWvn17M3Xq1AC1KPD27dtnJJnPP//cWjZ27Fhzww03BK5RATBz5kxz2WWXVbvO5XKZ5ORk88QTT1jLjh8/bhISEszChQv91MK64/777zdt2rQxLpfLGBOe14sk895771mva3ONHDx40ERHR5s333zT2ubXX381ERER5uOPP/Zb233t1HNTnW+++cZIMj///LO1LCMjw9x///2+bVwAVXdezvS7wzVT4YYbbjB9+/b1WBbq18yp9+dg+TtDz6sXlZWVacOGDRo4cKDH8oEDB2rNmjUBalXgFRcXS5IaNWrksTwnJ0dNmzZVu3btNH78eO3bty8QzfOrHTt2KDU1Va1bt9bo0aP1r3/9S5KUl5enwsJCj2vHbrcrIyMj7K6dsrIyvfbaa7r99ttls9ms5eF4vVRWm2tkw4YNcjgcHtukpqYqPT097K6j4uJi2Ww2NWzY0GP566+/rqSkJHXs2FFTpkwJi282Tve7wzVzwt69e7V8+XLdcccdVdaF8jVz6v05WP7ORPnlKGGiqKhITqdTzZo181jerFkzFRYWBqhVgWWM0aRJk3TNNdcoPT3dWj548GCNGDFCaWlpysvL04wZM9S3b19t2LChzs3k4S1XXXWVXnnlFbVr10579+7VY489pp49e2rLli3W9VHdtfPzzz8HorkB8/777+vgwYPKzMy0loXj9XKq2lwjhYWFqlevnhITE6tsE05/g44fP66pU6fqpptuUoMGDazlN998s1q3bq3k5GRt3rxZ06ZN0/fff2+lqYSiM/3ucM2csHjxYsXHx2vYsGEey0P5mqnu/hwsf2cIXn2gcm+RdOICOXVZuJg4caJ++OEHrV692mP5qFGjrOfp6enq1q2b0tLStHz58ip/PELF4MGDreedOnVSjx491KZNGy1evNgaQMG1Iy1atEiDBw9WamqqtSwcr5eanMs1Ek7XkcPh0OjRo+VyuTR//nyPdePHj7eep6enq23bturWrZu+/fZbdenSxd9N9Ytz/d0Jp2tGkv7+97/r5ptvVkxMjMfyUL5maro/S3X/7wxpA16UlJSkyMjIKv957Nu3r8p/MeHg3nvv1bJly5Sdna3mzZufdtuUlBSlpaVpx44dfmpd4MXFxalTp07asWOHVXUg3K+dn3/+WStXrtS4ceNOu104Xi+1uUaSk5NVVlamAwcO1LhNKHM4HBo5cqTy8vK0YsUKj17X6nTp0kXR0dFhdR2d+rsT7teMJH355Zfavn37Gf/uSKFzzdR0fw6WvzMEr15Ur149de3atcrXCStWrFDPnj0D1Cr/M8Zo4sSJevfdd/XZZ5+pdevWZ3zP/v37lZ+fr5SUFD+0sG4oLS3Vtm3blJKSYn0tVfnaKSsr0+effx5W105WVpaaNm2q66677rTbheP1UptrpGvXroqOjvbYpqCgQJs3bw7568gduO7YsUMrV65U48aNz/ieLVu2yOFwhNV1dOrvTjhfM26LFi1S165dddlll51x22C/Zs50fw6avzN+GRYWRt58800THR1tFi1aZLZu3WoeeOABExcXZ3bt2hXopvnNH/7wB5OQkGBycnJMQUGB9Th69KgxxphDhw6ZyZMnmzVr1pi8vDyTnZ1tevToYS644AJTUlIS4Nb7zuTJk01OTo7517/+ZdatW2eGDBli4uPjrWvjiSeeMAkJCebdd981mzZtMmPGjDEpKSkhfU4qczqdpmXLlubhhx/2WB5O18uhQ4fMxo0bzcaNG40k89xzz5mNGzdaI+Zrc43cfffdpnnz5mblypXm22+/NX379jWXXXaZKS8vD9TH8orTnRuHw2GGDh1qmjdvbr777juPvzulpaXGGGN27txpZs+ebXJzc01eXp5Zvny5ad++vencuXNQn5vTnZfa/u6E4zXjVlxcbOrXr28WLFhQ5f2heM2c6f5sTHD8nSF49YH/+q//MmlpaaZevXqmS5cuHiWiwoGkah9ZWVnGGGOOHj1qBg4caJo0aWKio6NNy5YtzdixY83u3bsD23AfGzVqlElJSTHR0dEmNTXVDBs2zGzZssVa73K5zMyZM01ycrKx2+2mV69eZtOmTQFssX998sknRpLZvn27x/Jwul6ys7Or/d0ZO3asMaZ218ixY8fMxIkTTaNGjUxsbKwZMmRISJyr052bvLy8Gv/uZGdnG2OM2b17t+nVq5dp1KiRqVevnmnTpo257777zP79+wP7wc7T6c5LbX93wvGacXvxxRdNbGysOXjwYJX3h+I1c6b7szHB8XfGdvLDAAAAAHUeOa8AAAAIGgSvAAAACBoErwAAAAgaBK8AAAAIGgSvAAAACBoErwAAAAgaBK8AAAAIGgSvAAAACBoErwAAAAgaBK8AAAAIGgSvAAAACBoErwAAAAga/x8z3Lic0HNvFwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reward: 88\n",
      "Steady state found at 48 trials.\n",
      "Optimal epsilon: 0.4\n",
      "Optimal lambda: 1.0\n"
     ]
    }
   ],
   "source": [
    "best_epsilon, best_lambda = optimize(2, 0, 200, print_each=False)\n",
    "print(\"Optimal epsilon:\", best_epsilon)\n",
    "print(\"Optimal lambda:\", best_lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# World 3\n",
    "Best pairs, all steady at 57 trials:\n",
    "\n",
    "Epsilon, Lambda:\n",
    "[0.2, 0.8] \n",
    "[1.0, 0.4] \n",
    "[1.0, 0.6]\n",
    "[1.0, 0.8]\n",
    "\n",
    "A high starting exploration rate seems to generally do better, but only slightly. This world is a maze with one path, which means the biggest threat is cycles. High exploration rates at the start probably help the policy get out of cycles more often. At the same time, there are losing states at almost every move, so we're also risking these more often in the initial trials, but it seems like the tradeoff is overall worth it. We also see that 0.2, 0.8 performs well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1053,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Epsilon    Lambda    Steady State Trials    Reward\n",
      "---------  --------  ---------------------  --------\n",
      "     0.00      0.00                     58        73\n",
      "     0.00      0.20                     58        73\n",
      "     0.00      0.40                     58        73\n",
      "     0.00      0.60                     58        73\n",
      "     0.00      0.80                     58        73\n",
      "     0.00      1.00                     58        73\n",
      "     0.20      0.00                     58        73\n",
      "     0.20      0.20                     58        73\n",
      "     0.20      0.40                     58        73\n",
      "     0.20      0.60                     58        73\n",
      "     0.20      0.80                     57        73\n",
      "     0.20      1.00                    162         0\n",
      "     0.40      0.00                     58        73\n",
      "     0.40      0.20                     58        73\n",
      "     0.40      0.40                     58        73\n",
      "     0.40      0.60                     58        73\n",
      "     0.40      0.80                     59        73\n",
      "     0.40      1.00                    137         0\n",
      "     0.60      0.00                     58        73\n",
      "     0.60      0.20                     58        73\n",
      "     0.60      0.40                     58        73\n",
      "     0.60      0.60                     59        73\n",
      "     0.60      0.80                     59        73\n",
      "     0.60      1.00                    180         0\n",
      "     0.80      0.00                     58        73\n",
      "     0.80      0.20                     58        73\n",
      "     0.80      0.40                     59        73\n",
      "     0.80      0.60                     59        73\n",
      "     0.80      0.80                     59        73\n",
      "     0.80      1.00                    144         0\n",
      "     1.00      0.00                     58        73\n",
      "     1.00      0.20                     58        73\n",
      "     1.00      0.40                     57        73\n",
      "     1.00      0.60                     57        73\n",
      "     1.00      0.80                     57        73\n",
      "     1.00      1.00                      0      -107\n",
      "\n",
      "Optimal epsilon: 0.2\n",
      "Optimal lambda: 0.8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reward: 73\n",
      "Steady state found at 57 trials.\n",
      "Optimal epsilon: 0.2\n",
      "Optimal lambda: 0.8\n"
     ]
    }
   ],
   "source": [
    "best_epsilon, best_lambda = optimize(3, 0, 200, print_each=False)\n",
    "print(\"Optimal epsilon:\", best_epsilon)\n",
    "print(\"Optimal lambda:\", best_lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# World 4\n",
    "This is a big world with no losing states, and we see that constant 100% exploration (1.0, 1,0) somehow gets the highest reward and also arrives at a steady rate the fastest by far at 25 trials. I'm guessing that this world is bad for greedy exploitation because the variable rewards deceptively distract from the optimal long-term behavior. By simply never looking at the rewards at all, the policy rather quickly arrives at the optimal path. I honestly have no idea how this happens in only 25 trials. All the other parameter pairs with lambda=1.0 also perform better, even if they always reach a steady state much later. Constant exploration helps iron out the suboptimal paths.\n",
    "\n",
    "Overall, the immediate rewards appear to be deceptive enough that they always prevent arriving at the true optimal policy, unless we keep exploring in later trials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1054,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Epsilon    Lambda    Steady State Trials    Reward\n",
      "---------  --------  ---------------------  --------\n",
      "     0.00      0.00                     76     63.46\n",
      "     0.00      0.20                     76     63.46\n",
      "     0.00      0.40                     76     63.46\n",
      "     0.00      0.60                     76     63.46\n",
      "     0.00      0.80                     76     63.46\n",
      "     0.00      1.00                     76     63.46\n",
      "     0.20      0.00                     76     63.46\n",
      "     0.20      0.20                     76     63.46\n",
      "     0.20      0.40                     76     63.46\n",
      "     0.20      0.60                     76     63.46\n",
      "     0.20      0.80                     76     63.46\n",
      "     0.20      1.00                    142     67.44\n",
      "     0.40      0.00                     76     63.46\n",
      "     0.40      0.20                     76     63.46\n",
      "     0.40      0.40                     76     63.46\n",
      "     0.40      0.60                     76     63.46\n",
      "     0.40      0.80                     76     63.46\n",
      "     0.40      1.00                    197     69.41\n",
      "     0.60      0.00                     76     63.46\n",
      "     0.60      0.20                     76     63.46\n",
      "     0.60      0.40                     76     63.46\n",
      "     0.60      0.60                     76     63.46\n",
      "     0.60      0.80                     86     63.78\n",
      "     0.60      1.00                     94     69.41\n",
      "     0.80      0.00                     76     63.46\n",
      "     0.80      0.20                     76     63.46\n",
      "     0.80      0.40                     76     63.46\n",
      "     0.80      0.60                     77     68.92\n",
      "     0.80      0.80                     85     67.84\n",
      "     0.80      1.00                     65     69.41\n",
      "     1.00      0.00                     76     63.46\n",
      "     1.00      0.20                     76     63.46\n",
      "     1.00      0.40                     77     68.92\n",
      "     1.00      0.60                     77     68.92\n",
      "     1.00      0.80                     80     67.58\n",
      "     1.00      1.00                     25     69.41\n",
      "\n",
      "Optimal epsilon: 1.0\n",
      "Optimal lambda: 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reward: 69.41\n",
      "Steady state found at 25 trials.\n",
      "Optimal epsilon: 1.0\n",
      "Optimal lambda: 1.0\n"
     ]
    }
   ],
   "source": [
    "best_epsilon, best_lambda = optimize(4, 0, 200, print_each=False)\n",
    "print(\"Optimal epsilon:\", best_epsilon)\n",
    "print(\"Optimal lambda:\", best_lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# World 5\n",
    "This is also a maze without lose states like the previous world, but it's harder. Again, we can see that constant exploration rates are the only ones that manage to get the maximum reward. I'm realizing now - and this also applies to the previous world - that going down one long path of a maze is rewarding enough that it is likely to be exploited repeatedly, and the \"walls\" are \"thin\" enough that they don't affect the Q values near the start of the path enough to prevent the agent from exploiting a suboptimal path. The difference between two completely paths is often just one move, and that is the move the policy needs to \"explore\" in to have a chance at finding the optimal path. If exploration rates quickly become lower as we go on, the chance of exploring at the exact right time drops dramatically.\n",
    "\n",
    "Again- we only achieve optimal policy if exploration is constant throughout all trials, regardless of the epsilon. Even at epsilon=0.2, there is a reasonable chance of exploration of every move, and with 140 trials, this manages to stack up to an optimal path.\n",
    "\n",
    "Disregarding rewards altogether gets us the optimal path in 10 trials. This makes sense: just because there is a path in a maze wouldn't at all suggest to you that it's the right path. Near the start of the maze especially, it's entirely random which path is the best, regardless of which ones capture your intuition. So we need to ensure that we're exploring all possible paths, and this only happens if we keep exploring indefinitely."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1055,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Epsilon    Lambda    Steady State Trials    Reward\n",
      "---------  --------  ---------------------  --------\n",
      "     0.00      0.00                     51     28.80\n",
      "     0.00      0.20                     51     28.80\n",
      "     0.00      0.40                     51     28.80\n",
      "     0.00      0.60                     51     28.80\n",
      "     0.00      0.80                     51     28.80\n",
      "     0.00      1.00                     51     28.80\n",
      "     0.20      0.00                     51     28.80\n",
      "     0.20      0.20                     51     28.80\n",
      "     0.20      0.40                     51     28.80\n",
      "     0.20      0.60                     51     28.80\n",
      "     0.20      0.80                     51     28.80\n",
      "     0.20      1.00                    140     36.30\n",
      "     0.40      0.00                     51     28.80\n",
      "     0.40      0.20                     51     28.80\n",
      "     0.40      0.40                     50     38.00\n",
      "     0.40      0.60                     50     38.00\n",
      "     0.40      0.80                     50     38.00\n",
      "     0.40      1.00                     82     44.30\n",
      "     0.60      0.00                     51     28.80\n",
      "     0.60      0.20                     51     28.80\n",
      "     0.60      0.40                     50     38.00\n",
      "     0.60      0.60                     50     38.00\n",
      "     0.60      0.80                     50     38.00\n",
      "     0.60      1.00                     74     40.30\n",
      "     0.80      0.00                     51     28.80\n",
      "     0.80      0.20                     50     38.00\n",
      "     0.80      0.40                     50     38.00\n",
      "     0.80      0.60                     50     38.00\n",
      "     0.80      0.80                     50     38.00\n",
      "     0.80      1.00                     78     44.30\n",
      "     1.00      0.00                     51     28.80\n",
      "     1.00      0.20                     50     38.00\n",
      "     1.00      0.40                     50     38.00\n",
      "     1.00      0.60                     50     38.00\n",
      "     1.00      0.80                     50     38.00\n",
      "     1.00      1.00                     10     44.30\n",
      "\n",
      "Optimal epsilon: 1.0\n",
      "Optimal lambda: 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reward: 44.3\n",
      "Steady state found at 10 trials.\n",
      "Optimal epsilon: 1.0\n",
      "Optimal lambda: 1.0\n"
     ]
    }
   ],
   "source": [
    "best_epsilon, best_lambda = optimize(5, 0, 200, print_each=False)\n",
    "print(\"Optimal epsilon:\", best_epsilon)\n",
    "print(\"Optimal lambda:\", best_lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# World 6\n",
    "Maze again, but this time with losing states instead of just slightly less rewarding states as walls. Here, the walls are bad enough that we never exploit them. There are only two places where the paths split up into the wrong and right paths, and one place where the path splits into the winning path and a slightly worse winning path.\n",
    "\n",
    "0.6, 0.8 lands at the steady state the soonest. This appears to be enough exploration for the small world that we rule out the worse paths the soonest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1056,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Epsilon    Lambda    Steady State Trials    Reward\n",
      "---------  --------  ---------------------  --------\n",
      "     0.00      0.00                     32        92\n",
      "     0.00      0.20                     32        92\n",
      "     0.00      0.40                     32        92\n",
      "     0.00      0.60                     32        92\n",
      "     0.00      0.80                     32        92\n",
      "     0.00      1.00                     32        92\n",
      "     0.20      0.00                     32        92\n",
      "     0.20      0.20                     32        92\n",
      "     0.20      0.40                     32        92\n",
      "     0.20      0.60                     32        92\n",
      "     0.20      0.80                     33        92\n",
      "     0.20      1.00                     60        92\n",
      "     0.40      0.00                     32        92\n",
      "     0.40      0.20                     32        92\n",
      "     0.40      0.40                     32        92\n",
      "     0.40      0.60                     32        92\n",
      "     0.40      0.80                     32        92\n",
      "     0.40      1.00                    159        92\n",
      "     0.60      0.00                     32        92\n",
      "     0.60      0.20                     32        92\n",
      "     0.60      0.40                     32        92\n",
      "     0.60      0.60                     32        92\n",
      "     0.60      0.80                     31        92\n",
      "     0.60      1.00                     94         0\n",
      "     0.80      0.00                     32        92\n",
      "     0.80      0.20                     32        92\n",
      "     0.80      0.40                     32        92\n",
      "     0.80      0.60                     32        92\n",
      "     0.80      0.80                     34        92\n",
      "     0.80      1.00                    186         0\n",
      "     1.00      0.00                     32        92\n",
      "     1.00      0.20                     32        92\n",
      "     1.00      0.40                     32        92\n",
      "     1.00      0.60                     32        92\n",
      "     1.00      0.80                     34        92\n",
      "     1.00      1.00                      0      -106\n",
      "\n",
      "Optimal epsilon: 0.6000000000000001\n",
      "Optimal lambda: 0.8\n"
     ]
    },
    {
     "data": {
      "image/png": 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cqalTp8atqX+wQYMGae/evfakOcvRfDR+yimnqHXr1nr77bf13nvvOboZuFwunXfeeXrjjTe0evVqR4ssqwTgT3/6k+N4a9as0WeffaYhQ4Ycwzv69u/phz/8oVwul/72t785tv/tb3+TMSbtW8ABR4vMK3CcaNGihWbOnKlbb71VTz/9tK688ko99thjGjlypIYPH66JEyfqhBNO0H//+1999tln+vDDDx0By5AhQ+T3+7Vs2TI9/vjj9vbzzz9fd911l1wul6O+r3v37urSpYtmzJghY4xatmypV1991a6RjcV3v/tdXXnllfrNb34jt9ut888/Xxs3btSDDz6oZs2aOfY955xzdOGFF+rUU09VixYt9Nlnn+nJJ5+MOeDbtGmTXdIQzOqZ6vf7NX78eLlcLj399NPKzs7W4sWL7e4MK1asUG5urv26oqIiDR48WHfccYfy8/M1f/58ff755w1myO6//35dccUVuvDCC3XdddeppqZGDzzwgPbs2aN777035mt3rGbNmqVXX31VQ4YM0axZs5SXl6cFCxZo//799hjrM378eH3yySeaO3euPv74Y02cOFFdu3ZVIBBQeXm53Uc1+H+MjsbVV1+tX//617r66qs1d+5cde3aVa+//rrefPPNmI/hcrk0cOBA/fWvf5UxxpF5lQ4H8DfffLOMMY7g9eSTT9ZPfvITPfLII8rKytLIkSO1detW3XHHHWrfvr1uueWWpLyn7t27a/LkyZo/f74KCgo0cuRIffnll7r99tt1xhlnfOt6ZSDtJHGyGIBjYHUbWLNmTdhzBw8eNB06dDBdu3Y1Pp/PGGPMxx9/bC677DLTpk0b43a7TXFxsRk8eLA9+9oSCARMUVGRkWT+/e9/29v//ve/G0nmzDPPDDvfp59+aoYOHWoKCgpMixYtzJgxY8y2bduMJHPXXXfZ+1mz44NnuFtqamrMtGnTTJs2bUyTJk1M3759zapVq0zHjh0d3QZmzJhh+vTpY1q0aGE8Ho858cQTzS233GJ27txZ7/VqqNvArFmzjDHGzJo1y2RlZYXNHl+5cqXJyckxP/vZz+xtkszkyZPN/PnzTZcuXYzb7Tbdu3c3Tz31VMRzW90GLC+99JI555xzTJMmTUx+fr4ZMmSI+fvf/+7Yp75rFq3bwAUXXBC2b+jMd2OMee+998w555xjPB6PKS4uNj//+c/NfffdZySZPXv2RLyOod59910zduxY065dO+N2u03Tpk1Njx49zA033GDWrl0bNoZTTjkl4nEije/rr782l156qfnOd75jCgoKzKWXXmpWrlwZ08x8y/z5840k07p167DnPvroI/vff9OmTY7n/H6/ue+++0y3bt2M2+02RUVF5sorr3R0pUjGe/L5fObee+81J510knG73aakpMTccMMNZvfu3Q2+FjjeuIxJwOc+AHAcsxrx/+53v0v2UOJm2LBh2rp1q7788stkDwUA6kXZAABkmKlTp+qMM85Q+/bt9d///ldPPfWUlixZ4lhFDABSFcErAGQYv9+vO++8U5WVlXK5XOrRo4eefPJJXXnllckeGgA0iLIBAAAApA1aZQEAACBtELwCAAAgbRC8AgAAIG0kdMLWu+++qwceeEDr1q1TRUWFXnzxRV1yySX288YYzZkzR7///e+1e/dunXPOOfqf//kfnXLKKfY+NTU1mj59uv785z/r4MGDGjJkiObPnx91BZtIAoGAtm/froKCgrgvtQgAAIBvzxijvXv3qrS0tP4FUxLZRPb11183s2bNMs8//7yRZF588UXH8/fee68pKCgwzz//vNmwYYMZO3asKSkpMdXV1fY+119/vTnhhBPMkiVLzIcffmgGDRpkTjvtNLsBeyzKy8vrbVLOgwcPHjx48ODBIzUeoYuChGq0bgMul8uReTXGqLS0VDfffLNuu+02SYezrG3bttV9992n6667TlVVVWrdurWefPJJjR07VpK0fft2tW/fXq+//rqGDx8e07mrqqrUvHlzlZeXhy05CQAAgOSrrq5W+/bttWfPHhUWFkbdL2l9Xrds2aLKykoNGzbM3ubxeDRgwACtXLlS1113ndatWyev1+vYp7S0VD179tTKlSujBq81NTWqqamxv9+7d68kqVmzZgSvAAAAKayhEs+kTdiqrKyUJLVt29axvW3btvZzlZWVys3NVYsWLaLuE8m8efNUWFhoP9q3bx/n0QMAACAZkt5tIDS6NsY0GHE3tM/MmTNVVVVlP8rLy+MyVgAAACRX0oLX4uJiSQrLoO7YscPOxhYXF6u2tla7d++Ouk8kHo/HLhGgVAAAAOD4kbTgtXPnziouLtaSJUvsbbW1tXrnnXfUv39/SVLv3r3ldrsd+1RUVGjjxo32PgAAAMgcCZ2wtW/fPm3evNn+fsuWLfroo4/UsmVLdejQQTfffLPuuecede3aVV27dtU999yjpk2b6vLLL5ckFRYW6pprrtG0adPUqlUrtWzZUtOnT1evXr10/vnnJ3LoAAAASEEJDV7Xrl2rQYMG2d9PnTpVkjRhwgQtXrxYt956qw4ePKgbb7zRXqTgrbfeUkFBgf2aX//618rJydFll11mL1KwePFiZWdnJ3LoAAAASEGN1uc1maqrq1VYWKiqqirqXwEAAFJQrPFa0rsNAAAAALFK2iIFwLGqqDqoLTv3Kz83W/tr/epclC9J2rJzf0xfH+vr4nEMzs25OTfn5tycOx3PXVKYp1RB8Iq08uyabZr5wgYFgopdrI6/Jsavj/V18TgG5+bcnJtzc27OnW7nznJJ80b30tizOigVELwibVRUHdSM5zc4fugk5w9hLF8f6+vicQzOzbk5N+fm3Jw73c4dMNIvXtio87q1TokMLDWvSBtbdu6P+IMHAAASy2+Mtu48kOxhSCJ4RRqx6m8AAEDjyna51KmoabKHIYngFWmkpDBP/bu0CtvukuRyxf71sb4uHsfg3Jybc3Nuzs250+3c2S6X7hndMyVKBiRqXpFmOrbK18p/7tKY3u10Zd8OOlAbsP9PcOvOAzF93TQ365heF49jcG7Ozbk5N+fm3Ol47lQJXCWxSAHSy8+f+1jPrftat43orhsGdkn2cAAAQJywSAGOS15/QJLkznY1sCcAADgeEbwirXj9hz8ocGdz6wIAkImIAJBW6jKv3LoAAGQiIgCkFSt4zaFsAACAjETwirTiO7IubC6ZVwAAMhIRANJKrY/MKwAAmYzgFWnFyrxS8woAQGYiAkBasWpeKRsAACAzEQEgrVA2AABAZiN4RVqhbAAAgMxGBIC0wgpbAABkNoJXpBUfK2wBAJDRiACQVmqtRQqyuHUBAMhERABIKz6r20AOZQMAAGQiglekFe+RsgEyrwAAZKakRwCdOnWSy+UKe0yePFmSNHHixLDn+vbtm+RRI1mssgF3TtJvXQAAkAQ5yR7AmjVr5Pf77e83btyooUOHasyYMfa2ESNGaNGiRfb3ubm5jTpGpA4f3QYAAMhoSQ9eW7du7fj+3nvvVZcuXTRgwAB7m8fjUXFxcWMPDSnGHzA60uZVbsoGAADISCkVAdTW1upPf/qTfvzjH8vlqsusLV++XG3atFG3bt00adIk7dixo97j1NTUqLq62vFA+rN6vEqUDQAAkKlSKgJ46aWXtGfPHk2cONHeNnLkSD311FN6++239dBDD2nNmjUaPHiwampqoh5n3rx5KiwstB/t27dvhNEj0YKD15wsygYAAMhELmOMSfYgLMOHD1dubq5effXVqPtUVFSoY8eOeuaZZzR69OiI+9TU1DiC2+rqarVv315VVVVq1qxZ3MeNxrF7f63O+OUSSdI/7/mBsglgAQA4blRXV6uwsLDBeC3pNa+Wr776SkuXLtULL7xQ734lJSXq2LGjNm3aFHUfj8cjj8cT7yEiyazMa5ZLBK4AAGSolCkbWLRokdq0aaMLLrig3v127dql8vJylZSUNNLIkCrsNlksDQsAQMZKiSggEAho0aJFmjBhgnJy6pLB+/bt0/Tp07Vq1Spt3bpVy5cv10UXXaSioiL98Ic/TOKIkQy+IwsU5BK8AgCQsVKibGDp0qXatm2bfvzjHzu2Z2dna8OGDXriiSe0Z88elZSUaNCgQXr22WdVUFCQpNEiWayygRx6vAIAkLFSIngdNmyYIs0by8vL05tvvpmEESEVWUvDUjYAAEDmIgpA2vBS8woAQMYjCkDa8AVYGhYAgExH8Iq0Ues7XDaQQ+YVAICMRRSAtEHZAAAAIApA2rDKBnIpGwAAIGMRvCJtUDYAAACIApA2mLAFAAAIXpE2qHkFAABEAUgbXh+LFAAAkOmIApA2vEfKBnKyKBsAACBTEbwibXh9R8oGcrhtAQDIVEQBSBu+wOGygVzKBgAAyFhEAUgbtX7KBgAAyHQEr0gbPv+RCVuUDQAAkLGIApA27FZZZF4BAMhYBK9IG7X0eQUAIOMRBSBtWGUDLA8LAEDmIgpA2rDKBnJZHhYAgIxF8Iq04fWzwhYAAJmOKABpw8q8UjYAAEDmIgpA2vDZE7YoGwAAIFMRvCJtUDYAAACIApA2aJUFAACIApA2fHbNK2UDAABkqqQHr7Nnz5bL5XI8iouL7eeNMZo9e7ZKS0uVl5engQMH6pNPPkniiJEsVtlALplXAAAyVkpEAaeccooqKirsx4YNG+zn7r//fj388MP63e9+pzVr1qi4uFhDhw7V3r17kzhiJIOXzCsAABkvJYLXnJwcFRcX24/WrVtLOpx1/c1vfqNZs2Zp9OjR6tmzpx5//HEdOHBATz/9dJJHjcbmpeYVAICMlxJRwKZNm1RaWqrOnTtr3Lhx+te//iVJ2rJliyorKzVs2DB7X4/HowEDBmjlypVRj1dTU6Pq6mrHA+nPF6BsAACATJf0KOCcc87RE088oTfffFP/+7//q8rKSvXv31+7du1SZWWlJKlt27aO17Rt29Z+LpJ58+apsLDQfrRv3z6h7wGNo9ZH2QAAAJku6cHryJEjdemll6pXr146//zz9dprr0mSHn/8cXsfl8sZrBhjwrYFmzlzpqqqquxHeXl5YgaPRkXZAAAASLkoID8/X7169dKmTZvsrgOhWdYdO3aEZWODeTweNWvWzPFA+rPKBlhhCwCAzJVywWtNTY0+++wzlZSUqHPnziouLtaSJUvs52tra/XOO++of//+SRwlksHrI/MKAECmy0n2AKZPn66LLrpIHTp00I4dO/SrX/1K1dXVmjBhglwul26++Wbdc8896tq1q7p27ap77rlHTZs21eWXX57soaOReY9kXnOyCF4BAMhUSQ9ev/76a40fP147d+5U69at1bdvX61evVodO3aUJN166606ePCgbrzxRu3evVvnnHOO3nrrLRUUFCR55GhsVs1rbg5lAwAAZCqXMcYkexCJVl1drcLCQlVVVVH/msZ63vWm9tX49M7PB6pjq/xkDwcAAMRRrPEan78ibdTaK2xx2wIAkKmIApA26lplUTYAAECmInhFWvAHjKwCFzcTtgAAyFhEAUgLVtZVktw53LYAAGQqogCkheDgNSeLsgEAADIVwSvSgtdf1xSDRQoAAMhcRAFIC74jmdfsLJeyybwCAJCxCF6RFuw2WQSuAABkNIJXpAWrbCCXkgEAADIakQDSgs9eoIDMKwAAmYzgFWmh1l6ggFsWAIBMRiSAtOA7UjZA8AoAQGYjEkBaYGlYAAAgEbwiTVA2AAAAJIJXpAmrbCCH4BUAgIxGJIC0YJUN5FI2AABARiN4RVrwknkFAAAieEWaYMIWAACQCF6RJnwBJmwBAACCV6QJr48+rwAAgOAVaaKWsgEAACCCV6QJ35HglQlbAABkNiIBpAWr20AuwSsAABmNSABpwXtkwlZOFmUDAABksqQHr/PmzdNZZ52lgoICtWnTRpdccom++OILxz4TJ06Uy+VyPPr27ZukESMZ7AlbOUm/ZQEAQBIlPRJ45513NHnyZK1evVpLliyRz+fTsGHDtH//fsd+I0aMUEVFhf14/fXXkzRiJIPdKovMKwAAGS0n2QN44403HN8vWrRIbdq00bp163TeeefZ2z0ej4qLixt7eEgRdd0Gkv7/WwAAIIlSLhKoqqqSJLVs2dKxffny5WrTpo26deumSZMmaceOHckYHpLEKhug2wAAAJkt6ZnXYMYYTZ06Veeee6569uxpbx85cqTGjBmjjh07asuWLbrjjjs0ePBgrVu3Th6PJ+w4NTU1qqmpsb+vrq5ulPEjcayygVz6vAIAkNFSKnidMmWK/vGPf2jFihWO7WPHjrW/7tmzp/r06aOOHTvqtdde0+jRo8OOM2/ePM2ZMyfh40Xj8VI2AAAAlEJlAz/96U/1yiuvqKysTO3atat335KSEnXs2FGbNm2K+PzMmTNVVVVlP8rLyxMxZDQiq88rZQMAAGS2pGdejTH66U9/qhdffFHLly9X586dG3zNrl27VF5erpKSkojPezyeiOUESF9elocFAABKgczr5MmT9ac//UlPP/20CgoKVFlZqcrKSh08eFCStG/fPk2fPl2rVq3S1q1btXz5cl100UUqKirSD3/4wySPHo3FdyTzStkAAACZLemZ10cffVSSNHDgQMf2RYsWaeLEicrOztaGDRv0xBNPaM+ePSopKdGgQYP07LPPqqCgIAkjRjLQKgsAAEgpELwaY+p9Pi8vT2+++WYjjQapyiobyKFsAACAjEYaC2nBKhvIJfMKAEBGIxJAWqBsAAAASASvSBM+ygYAAIAIXpEmvJQNAAAAEbwiTTBhCwAASASvSBMsDwsAACSCV6QJr71IAZlXAAAyGcEr0oKPzCsAABDBK9JELcvDAgAAEbwiTfgCVuaVsgEAADIZwSvSgtdH2QAAACB4RZrwBg6XDeQQvAIAkNGIBJDyjDFBrbIoGwAAIJMRvCLl+QNG5nDiVe4sblkAADIZkQBSnu9IyYAkuXO4ZQEAyGREAkh5tUdKBiTKBgAAyHQEr0h5Pn9Q5pWyAQAAMhqRAFKeNVkrO8ulrCwyrwAAZDKCV6S82iM9XnMIXAEAyHgEr0h51oStXHq8AgCQ8YgGkPKssoEcJmsBAJDxCF6R8uoWKOB2BQAg0xENIOV5j3QbIHgFAABEA0h5PpaGBQAAR6RN8Dp//nx17txZTZo0Ue/evfXee+8le0hoJLWUDQAAgCPSIhp49tlndfPNN2vWrFlav369vv/972vkyJHatm1bsoeGRmCVDeQQvAIAkPFykj2AWDz88MO65pprdO2110qSfvOb3+jNN9/Uo48+qnnz5iV5dOEqqg5qy8796lyUL0n1fp2fm639tX51LspXSWFexGNE2x7pGA2d72jPHfy64H2+7TU4mjHvqD4kSarx+VVRdfCoxgEAAI4vKR+81tbWat26dZoxY4Zj+7Bhw7Ry5cokjSq6Z9ds04znN8g0vKuDS9K9l/bS2LM6OI6R5ZLmjT68/ZkPvtLMFzYe9bGP9dzBgsfRkGO9Bg3513/263v3vh3zOAAAwPEn5T+H3blzp/x+v9q2bevY3rZtW1VWVkZ8TU1Njaqrqx2PxlBRdVAzXzi2oM1I+sULG/Vx+W7HMQImeHv8A9f6zh3MGkdF1cF6j1VRdTAhgevRjgMAAByfUj54tbhczpnmxpiwbZZ58+apsLDQfrRv374xhqgtO/cr8C2iNr8xWrN1d9gxrO2JCgjrO3foPlt3Hqj3OFt27k/oOGMdBwAAOD6lfPBaVFSk7OzssCzrjh07wrKxlpkzZ6qqqsp+lJeXN8ZQ1bkoX1nfoptTtsulszq1UOghom2Pp1jOke1yqVNR03qP07koP6HjjHUcAADg+JTywWtubq569+6tJUuWOLYvWbJE/fv3j/gaj8ejZs2aOR6NoaQwT/NG91L2kYywS5KVHI72tcUl6Z7RPXVa+xb65SWn2NuzgrZfckapY/9Ix2jofEdz7mDZLpfuGd2zwclSJYV5unXEyQ2O6VjHHOs4AADA8SnlJ2xJ0tSpU3XVVVepT58+6tevn37/+99r27Ztuv7665M9tDBjz+qg87q11tadB+zsYH1fP7tmm176aLvGn9PBnoR08ekn6PaXPpEkPX7N2fp+19aSpDM6tNCL67fr7M4t9f+NO90+RtPcLB2oDcR0vkjnvjzo3Jec0c4+9ws39NPoR1fJJWnFjEExB4wjepbovje+UJ47W29PHxDx3Mc65k5FTQlcAQDIYGkRvI4dO1a7du3S3XffrYqKCvXs2VOvv/66OnbsmOyhRVRSmOcIsOr7+r1N/5EkeXLqkuA+f13VaIumufbXVr/Tts2a2MeJFMjFeu537XNnB507YH/dodXhdlVGUpuCJpHfbATWMTzurIjj/DZjBgAAmS0tgldJuvHGG3XjjTcmexhxZzXeDw5YvYG6ANIbFEzay6R+m8LaINZxfI7z1Y0jOKD2+gPKzqoLcutjLyqQlfJVKQAAIM0QXSRZpAAyOJD1BcK/zsmOT/BqB85B5/Af+dqd7XIsx+o7ijYK1ntxx2mcAAAAFoLXJLMCyOCMpyML6w/PwsZrmdRsK3COcI7sLJdygjK8wfs0pG45V4JXAAAQXwSvSZYTKYCMloU98nXcygayrXOHZ3fdWVl2cCs5g+uG+IOOAQAAEE9EF0lmZSe9gciZV0c9aiC+mVerJtV5buscLrlcrroANxB75tUXlL0FAACIJ4LXJKubsBV5klakcoJ4fRxfl3kNP581LivA9R1F5tUbcB4DAAAgXoguksyesBVtkpY/wmSqOH0cX++ErSPjssoavEdR82p3RaDmFQAAxBnBa5LZE7YifHQvhbaxiu/H8REnbB05X/aRwNPK8vqPottAXassglcAABBfBK9JVt9H94e3R5iwFe+ygQiZXiu7G6kbQkN8ca7NBQAAsBBdJFmkmlJHz9fGmLAVYSEEK+MaqQ9tQ4J7xQIAAMQTwWuS1XUbiNweK+KErQS2yrInW32LzKu1bzatsgAAQJwRXSRZxAAyQiZUCl65Kl6LFESasOWcbJUToayhIfFexhYAAMBC8JpkET+6j7Ak7OF94r08bHhJQF3W1CobCA9wG+KN8zK2AAAAFoLXJMuJMGkqep9XK6MZn382d6R629A+r9nH3iqLCVsAACDeiC6SzB1hkQJfhIBVqgtw45159UYsTXD2eT2aRQrivYwtAACAheA1yeoWAYi2JGx4VjRefV4jtcqq69HqnLB1VMvDssIWAABIEKKLJHNHCA69/vAJVMH7xH3CVoTzhWVej6Lm1S4bIPMKAADijOA1yXIidBuIVkIQ75WrciL0cA2bsJUdHuA2hAlbAAAgUQhekywnwmz+SB/jH94e38xrpMA0dLLVt5qwRZ9XAAAQZ0QXSRZpeVhnIBuehU3shC3nZKtIwXVDfKywBQAAEoTgNcnsFawCkcsGvBEWL4hXRjNSD1dvSKusSMF1Q7y0ygIAAAlCdJFk7qzw4DBSb1cp/hnN7AjdBqwJW1Y97LEsD+sPyd4CAADEC8FrklnBYcBIgSNBn6NUIEKrrHhlNOsLnK2SAneESV0NqZv0xe0FAADii+giyYLrV71HAkRfhFIBqS6AjFu3gXoCZ6s0ITtCH9qG1E36IvMKAADii+A1yYKXerWCVmef10iZ1/hO2JLCA2e7z+sxtMpiwhYAAEiUpAWvW7du1TXXXKPOnTsrLy9PXbp00V133aXa2lrHfi6XK+yxYMGCJI06/oIDSCtAjLZgQbwnbAVncEMD59AJW/6jKhugVRYAAEiMnGSd+PPPP1cgENBjjz2mk046SRs3btSkSZO0f/9+Pfjgg459Fy1apBEjRtjfFxYWNvZwEyY4gLSyn9GWio13RjM4uLSOHTZhKyu8G0JDQrO3AAAA8ZK04HXEiBGOgPTEE0/UF198oUcffTQseG3evLmKi4sbe4iNwuVyKSfLJV/A1GVeo6ywFfcJW46s75HA2VodK+vYW2X5AvEdJwAAgCWloouqqiq1bNkybPuUKVNUVFSks846SwsWLFDgKD7CTgehiwU4+64GlRBYK2zFacKWy+WyJ2RZ5wydbFU3tqOpeY3vxDIAAABL0jKvof75z3/qkUce0UMPPeTY/stf/lJDhgxRXl6eli1bpmnTpmnnzp26/fbbox6rpqZGNTU19vfV1dUJG3c8uLOydEgBO4CMtOKVP2BkjsSP8cxo5mS55A+YusA5dMKWvZDB0SwPG9+JZQAAAJa4Z15nz54dcZJV8GPt2rWO12zfvl0jRozQmDFjdO211zqeu/3229WvXz+dfvrpmjZtmu6++2498MAD9Y5h3rx5KiwstB/t27eP99uMq5yQj+Z9ERYpCA4e4xkUWtlRv90qK1rZQOyZVyZsAQCARIl75nXKlCkaN25cvft06tTJ/nr79u0aNGiQ+vXrp9///vcNHr9v376qrq7WN998o7Zt20bcZ+bMmZo6dar9fXV1dUoHsKGrWEXqNhAcPLrjGBQePrc/7NxWgGwtNHB0ZQNM2AIAAIkR9+C1qKhIRUVFMe3773//W4MGDVLv3r21aNEiZcUQlK1fv15NmjRR8+bNo+7j8Xjk8XhiHXLSha5iFanbQHDwGs/Mq51ZDTl3WOb1qMoGyLwCAIDESFrN6/bt2zVw4EB16NBBDz74oP7zn//Yz1mdBV599VVVVlaqX79+ysvLU1lZmWbNmqWf/OQnaRWcNqS+zKtdBxtcNhDHiVB2Tas/yoStrKMvG6jrNkDmFQAAxFfSgte33npLmzdv1ubNm9WuXTvHc+bIzCS326358+dr6tSpCgQCOvHEE3X33Xdr8uTJyRhywoTWvHojtMey/puddbhuON7nDu10ELbC1jFM2HLTKgsAAMRZ0oLXiRMnauLEifXuE9oL9njltmf0R+rzagW0iWk/FTZhK1rZwNFM2DoS6GbTKgsAAMQZqbEUUG+f15AuAPHOZkYrWWCFLQAAkIoIXlOA/dG83+rzGqFVVkgtatzOHWWymDWm0JKGWDBhCwAAJArRRQoI7TYQaXnY0P6rcTt3SOAc2ior9PlYeJmwBQAAEoTgNQWELsHqLBuIvPJV/M8dcp4jQbJVt+o9iglb/gSVOAAAABBdpAB3yIx+b4TMqzeQ2LKBsBW27Mzrt1lhi8wrAACIL4LXFGAFeZFW0/IFjIwxYRnR+J3bOSHL548yYeuoal4TU+IAAABAdJECQidshfZU9QeMHVTGu/1UtB6zYRO2jqbbQIKyxAAAAASvKSDaEq0WX8AETYJqpAlbWc4JW/4Yg1djTFAATPAKAADii+A1BWRnhfRaDfmI3usP2NviPWErdEJW6OpYdSUNsZUNBAe58S5xAAAAILpIAXarLOuj+5Asp88flM2Mc9mAFQxHn7B1dK2ygssLyLwCAIB4I3hNAaF1pWGZ10DADi7jXTaQEyXra0/YCilpaEhw8EqrLAAAEG9EFymgbonWgAIBo9DyUp/f2MFjovq8hmZ97QlbIcFtQ4IDb1plAQCAeCN4TQF1ZQMm4mIAzrKBOE/YyrJ6zDozr267VdbRLQ8bHOTGuzMCAAAAwWsKsDOvgYCjttTKsh7enqAJW0ErbAVnfUNbZYXW4UYT3K3A5SJ4BQAA8UXwmgJyglaxCg5em7izJR2eTGV/nB/3zGvdhK1Ik63qJmzFWPNKmywAAJBABK8pwP7o3h9wlA1YwWtwq6zsuNe81tW0Bk/KygkpGwgYKRBD9tUKgGmTBQAAEoEIIwUEfzRvZS6zs1zKDWpTVbc8bOImbAXXq1oZ3uDuBrGssmV3KyDzCgAAEoDgNQUEfzTvDWpVFdymymsvuZq4CVvBpQFuu2ygLgiNpV1W6PKyAAAA8USEkQJygroN2B+7Z2cFrW5l5LdXvkrQClv+gH3u7KDJVsE1trG0ywpdXhYAACCeCF5TQF23AeP42D14dauETdjKDp+wFRx4Bn8dy6QtLxO2AABAAhG8pgB3hLrTnKysoFrYQMJqSR0TtvzhWdOsLJesb4+m5pUJWwAAIBGIMFJA8CpWwStpZWcFTdgKKieI77mD6mqj1KsGrwDWkLplbMm8AgCA+CN4TQGOiVlBH7u7s4IzsompJXXW20ZeCCF4BbCGJKq8AQAAQCJ4TQluxyIFdR+71wW1Jqj5f5wzr0FZVV+UJWitfWLpNpColcAAAAAkgteUUFc2UDfj3zFhKxBI2Cz+iBO2QjOvQUF0Q7xBfWoBAADiLanBa6dOneRyuRyPGTNmOPbZtm2bLrroIuXn56uoqEg33XSTamtrkzTixAgODuvKA5ytshI1i98OnAORJ2wF7xNL2YAvQf1oAQAAJCkn2QO4++67NWnSJPv773znO/bXfr9fF1xwgVq3bq0VK1Zo165dmjBhgowxeuSRR5Ix3ITICVoe1hfUzzUnqFWWP0HLrkZaYSt8wlZdL9iG+BLUjxYAAEBKgeC1oKBAxcXFEZ9766239Omnn6q8vFylpaWSpIceekgTJ07U3Llz1axZs8YcasLUBYfGkbl0OyZyJahVlqOjQeTMa135QixlA3WZYwAAgHhLeoRx3333qVWrVjr99NM1d+5cR0nAqlWr1LNnTztwlaThw4erpqZG69ati3rMmpoaVVdXOx6pLLi2ta7Pq8vZQithE7bqAuRo7biCV+FqiJ0hJvMKAAASIKmZ15/97Gc688wz1aJFC33wwQeaOXOmtmzZoj/84Q+SpMrKSrVt29bxmhYtWig3N1eVlZVRjztv3jzNmTMnoWOPp8jtqrKCttdN2HInaMJWcEeD0MlWObTKAgAAKSLuEcbs2bPDJmGFPtauXStJuuWWWzRgwACdeuqpuvbaa7VgwQItXLhQu3btso/ncoUHa8aYiNstM2fOVFVVlf0oLy+P99uMq7rlYZ19XnMcE7kSlHl1ZHej9Hk9hlZZ2WReAQBAAsQ98zplyhSNGzeu3n06deoUcXvfvn0lSZs3b1arVq1UXFys999/37HP7t275fV6wzKywTwejzwez9ENPImcfV6Dl4cNbqGVmP6pjglbUbKmwTW5DbEnbNEqCwAAJEDcg9eioiIVFRUd02vXr18vSSopKZEk9evXT3PnzlVFRYW97a233pLH41Hv3r3jM+AUYE+aChj5g4JUKwD0B2de491tIOjcviiTwtxH0SrLS6ssAACQQEmreV21apVWr16tQYMGqbCwUGvWrNEtt9yiUaNGqUOHDpKkYcOGqUePHrrqqqv0wAMP6L///a+mT5+uSZMmHTedBqTgzKuzXVVd5rUusIx38/9YJmwF79MQWmUBAIBESlrw6vF49Oyzz2rOnDmqqalRx44dNWnSJN166632PtnZ2Xrttdd044036nvf+57y8vJ0+eWX68EHH0zWsBMiuJ9r8MSs4I/0EzWLPzirGnXCVnbsmVcfE7YAAEACJS14PfPMM7V69eoG9+vQoYP+7//+rxFGlDz2SlohE7bcQR/pJ2zCVoQes2ETtrKOJvOamH60AAAAUgr0eUXQbP6Qfq7BK1slvlVWIGpd7VFN2IpSegAAABAPRBgpILgllqNsICtCF4I4B4XZjrKByFnT4OVrG+JNUG0uAACARPCaEtxBmc5DXr+kkAlbgUDQLP54Lw8bYcJWlMxrLMvD0ioLAAAkEsFrCggOSA/awWvkzGtoYPltRSpZCF1gIHghg4b4aJUFAAASiAgjBTiC11qrbCDLsbJV8ESuRJw7tGQhWHArr4b4EjROAAAAieA1JUQuGwhulVW3eEFOvPu8Bh0vuGTBsY81YSuWsoEopQcAAADxQISRArKyXLJiSKtswJ2d5WiVlagJW8HHCy5ZcOxzZBz+GFpleWmVBQAAEojgNUVYQeTB2iMBZNAiBV5/0ISthGZe60oWgrmDMsANsYNsJmwBAIAEIHhNEVad6cEI3QYcE7binHkNPp5VNhBthS0mbAEAgGQjwkgRVrB3yC4bcDlWtrKXXY3zx/HZWS65jhwy+NyOsR3FClteMq8AACCBCF5ThBUw2pnXrCw7A2p9nC8lZiJUToSsr/P52DOvflbYAgAACUSEkSKsANGuec122QGgFVRa2xN+7rCygdhbZTFhCwAAJBLBa4rICcm8uoNaZVlBZfB+iTi3PWErO8qEraNolZVDqywAAJAARBgpIscuEagrG7ACwBpfXfCaiLIBK1g95IsyYcsuG4hlkYLEdEUAAACQCF5TRuiMfne2y854WhlRl+twT9i4n9sKnGsjT9g6mlZZiVoJDAAAQCJ4TRlhdaZZda2yDtT6JCVu1aqwCVsh57FbdsVUNhC59AAAACAeiDBSRGiwl5PtsoNKK2ZMVDYzJ2RiWPgKW7G3yqqreSXzCgAA4o/gNUWEBozu7KzwgDZBAWFDE7ZyjmWFLTKvAAAgAYgwUkRoSUBOlits4lSiPooPPXc8JmyF1s0CAADEA8Frigj7qD47K3ylq4SVDUSeoBX6fSw1r94j+4QGwAAAAPFA8JoiQj9mP9znNfJKV3E/d5RMa+j3sSxSUJd55dYCAADxR4SRItwRAsjQbYn6KD4sSI6S8Y1leVi75pXMKwAASACC1xQR6aP78KCycTKv4StsWa2yYu82QOYVAAAkAhFGiogUqEZrWRVvoYFm+ISto+g2cCTAZZECAACQCEkLXpcvXy6XyxXxsWbNGnu/SM8vWLAgWcNOmPCyAVd4B4IEBYRhXQ2OcZECY0zdClsJqs8FAACZLSdZJ+7fv78qKioc2+644w4tXbpUffr0cWxftGiRRowYYX9fWFjYKGNsTOETtiJlXhPUKquBrgZ1y8PWXzbgDwpuaZUFAAASIWnBa25uroqLi+3vvV6vXnnlFU2ZMkUulzPwad68uWPf41GkADK8FjVBE7aywjsdBLMys94GMq/BmVlaZQEAgERImc92X3nlFe3cuVMTJ04Me27KlCkqKirSWWedpQULFijQwMShmpoaVVdXOx6pLiyAzMqSy+VcqCBhrbIayPDaE7YayLwGL2LAhC0AAJAIScu8hlq4cKGGDx+u9u3bO7b/8pe/1JAhQ5SXl6dly5Zp2rRp2rlzp26//faox5o3b57mzJmT6CHHVbT2VDlZLvvj+ETVvMZrwlZw2QCtsgAAQCLEPT02e/bsqBOxrMfatWsdr/n666/15ptv6pprrgk73u23365+/frp9NNP17Rp03T33XfrgQceqHcMM2fOVFVVlf0oLy+P63tMhNAA0gpUg7cnKpvZ0DK01vfeBjLewX1gKRsAAACJEPfM65QpUzRu3Lh69+nUqZPj+0WLFqlVq1YaNWpUg8fv27evqqur9c0336ht27YR9/F4PPJ4PDGPORWE1bce+eg+ONuauFZZ9U/YysmOLfNqtclyZ7vC6pYBAADiIe7Ba1FRkYqKimLe3xijRYsW6eqrr5bb7W5w//Xr16tJkyZq3rz5txhl6gnuNpDlkrKyrLKBxGdeI9XbRnreFzAyxkQNTH20yQIAAAmW9JrXt99+W1u2bIlYMvDqq6+qsrJS/fr1U15ensrKyjRr1iz95Cc/SbvMakOC+7zmOEoF6rYn6qP40ExrdpRWWdLhADZa1wNrwhb1rgAAIFGSHrwuXLhQ/fv313e/+92w59xut+bPn6+pU6cqEAjoxBNP1N13363JkycnYaSJ5QhYHYFs5K/jKazeNnTCVtDz/oCROzvycXwJnlgGAACQ9OD16aefjvrciBEjHIsTHM/c2ZEzr46ygQR9HN/QhK3gYNbrD6hJlOjVLhugTRYAAEgQoowUERwguqNM0kpY5jXoHC5X9FZZUv2TtuwJW5QNAACABCF4TRHRsq05jdAqy1myEH6O4GC2vnZZXjKvAAAgwYgyUoQ7Sm1rtCxsPOU0MCnM5XLZ46g382pN2KLmFQAAJAjBa4qI1hIrJ0oXgvieu+HSBLtdVr1lA1arLIJXAACQGASvKSLaYgTR2mbF9dwx9JK1xld/2YDVKovbCgAAJAZRRopwZFujBKyJCgpjKU2wxldf5tV/JPOaqCAbAACA4DVFRO82EBzUJqrmNYbM65Hx+ZiwBQAAkogoI0VEq3NtlAlbWfVP2AreJ5ZWWdS8AgCARCF4TRE5URYpyG6MCVsxrOJlnbu+zKsV2CaqpRcAAABRRopwlAckc8JWlLpae8JWPZlXa8JWtOwtAADAt0XwmiKiLQ8bvFpVo0zYihIgu4+iVRYTtgAAQKIQvKaIqAFrdiNM2IqyopdjnxhaZdX1eeW2AgAAiUGUkSKiLRTgjvJ1XM8dw6SwnBhaZbHCFgAASDSC1xQRrc+rsxY2UStsRa63Dea2uw0wYQsAACQPUUaKcGRbY8jCJuzcDZYN1DNhi1ZZAAAgwQheU4Q7St2p29E2K4kTto6Mwx9DqywWKQAAAIlClJEiomVYs6NkYeN67hhKE6xx1Ncqy655JfMKAAAShOA1ReREWRI2uIQgWg/W+J472gpbsbfKYsIWAABIFILXFOEsG0hmq6xoZQNHJmzF0CqLCVsAACBRiDJSRHaUSVOpM2Hr8PZYVtiibAAAACQKwWuKcEdpV+VuhFZZ0c7t3Cf2VllM2AIAAIlClJEiYikVSFjZQJRzR9rHV0+rLKukwE3mFQAAJAjBa4pwZlsjB5OJqiV1rO7VwApb3noyr1ZJQTYTtgAAQIIQvKYIl8tlB46OgDUomMxOUEYzlklhdWUD0TOvfmvCVoLKGwAAABIaZcydO1f9+/dX06ZN1bx584j7bNu2TRdddJHy8/NVVFSkm266SbW1tY59NmzYoAEDBigvL08nnHCC7r77bhkTPYhKV1bgGK3Pa2O0yoqW3bUWSKivbMCesEXmFQAAJEhOIg9eW1urMWPGqF+/flq4cGHY836/XxdccIFat26tFStWaNeuXZowYYKMMXrkkUckSdXV1Ro6dKgGDRqkNWvW6Msvv9TEiROVn5+vadOmJXL4jc6dlaVDCjhLCBqhVVZME7aymbAFAACSL6HB65w5cyRJixcvjvj8W2+9pU8//VTl5eUqLS2VJD300EOaOHGi5s6dq2bNmumpp57SoUOHtHjxYnk8HvXs2VNffvmlHn74YU2dOlUu1/GT5bOCUyZsAQAARJbUFNmqVavUs2dPO3CVpOHDh6umpkbr1q2z9xkwYIA8Ho9jn+3bt2vr1q0Rj1tTU6Pq6mrHIx1YgaM76mpbSZywlRX7hC0yrwAAIFGSGmVUVlaqbdu2jm0tWrRQbm6uKisro+5jfW/tE2revHkqLCy0H+3bt0/A6OPPylg6AtZGyLy6XC67trbBFbbqXR6WRQoAAEBiHXXwOnv2bLlcrnofa9eujfl4kT72N8Y4tofuY03WilYyMHPmTFVVVdmP8vLymMeTTFbGMtrH+IlcdtUKOKNld+1WWfUtD2tnXgleAQBAYhx1zeuUKVM0bty4evfp1KlTTMcqLi7W+++/79i2e/dueb1eO7taXFwclmHdsWOHJIVlZC0ej8dRZpBu9tX47K/dMXykHw/u7CzV+AJRA8+cGFplWfWwiVoJDAAA4KiD16KiIhUVFcXl5P369dPcuXNVUVGhkpISSYcncXk8HvXu3dve5xe/+IVqa2uVm5tr71NaWhpzkJwOnl2zTdv+e0CSdPuLG5WT5dLYszo4Mq+J6vMqRZ4sFszK+vrqzbwembBF5hUAACRIQlNk27Zt00cffaRt27bJ7/fro48+0kcffaR9+/ZJkoYNG6YePXroqquu0vr167Vs2TJNnz5dkyZNUrNmzSRJl19+uTwejyZOnKiNGzfqxRdf1D333HNcdRqoqDqomS9ssL83kn7xwkZVVB20A9Zsl0uV1YcSNgZ7gYQoAbI1jm+qa1RRdVAVVQe18p87VVF10N6HCVsAACDREtoq684779Tjjz9uf3/GGWdIksrKyjRw4EBlZ2frtdde04033qjvfe97ysvL0+WXX64HH3zQfk1hYaGWLFmiyZMnq0+fPmrRooWmTp2qqVOnJnLojWrLzv0K7UDlN0Zbdx7Qyn/+x/7+e/e+rXmje2nsWR3iPgbro/5owev6bbslSeu+2q3+896WdDjIznLJHhOtsgAAQKIlNHhdvHhx1B6vlg4dOuj//u//6t2nV69eevfdd+M4stTSuShfWS45Athsl0tNc7P0u7f/aW8LmMMZ2fO6tVZJYV5cx1C3uld41rSi6qBe+PDf9vfBcXbwmA55DwevVYe8cR0bAACAhc93U0BJYZ7mje6lbFddicA9o3tqf61fodOjrIxsvFm50r014YHnlp37w8YROqZHlm22a3Zv/NOHenbNtriPEQAAIKGZV8Ru7FkddF631tq684A6FTVVSWGeKqoORszIdipqGtdzP7tmm8p3H65dvfOlT5SbneUoTehclC+XVG8A+/QHdcGqVbObiAwxAADIbGReU0hJYZ76dWllB3zRMrLxDAjrmywWPK57L60bRywVrYnKEAMAgMxG5jXFRcrIxlN9k8WCzxU6jnVf7daUp9dHPW4iMsQAAAAEr2mgpDAvYR+/R5ssFinwDB5H744Ke13w6+OdIQYAAJAoG8h4x1qaEOl1M0d2158n9dWKGYMS0s4LAADAZYypbx7OcaG6ulqFhYWqqqqyFz+AU0XVwWMqTTjW1wEAAASLNV6jbACSjr00IZElDQAAAKEoGwAAAEDaIHgFAABA2iB4BQAAQNogeAUAAEDaIHgFAABA2iB4BQAAQNogeAUAAEDaIHgFAABA2siIRQqsRcSqq6uTPBIAAABEYsVpDS3+mhHB6969eyVJ7du3T/JIAAAAUJ+9e/eqsLAw6vMu01B4exwIBALavn27CgoK5HK5En6+6upqtW/fXuXl5fWuzZuJuDaRcV2i49pExnWJjOsSHdcmMq5LdI19bYwx2rt3r0pLS5WVFb2yNSMyr1lZWWrXrl2jn7dZs2b8IETBtYmM6xId1yYyrktkXJfouDaRcV2ia8xrU1/G1cKELQAAAKQNglcAAACkDYLXBPB4PLrrrrvk8XiSPZSUw7WJjOsSHdcmMq5LZFyX6Lg2kXFdokvVa5MRE7YAAABwfCDzCgAAgLRB8AoAAIC0QfAKAACAtEHwCgAAgLRB8JoA8+fPV+fOndWkSRP17t1b7733XrKH1KjmzZuns846SwUFBWrTpo0uueQSffHFF459Jk6cKJfL5Xj07ds3SSNuHLNnzw57z8XFxfbzxhjNnj1bpaWlysvL08CBA/XJJ58kccSNp1OnTmHXxuVyafLkyZIy53559913ddFFF6m0tFQul0svvfSS4/lY7pGamhr99Kc/VVFRkfLz8zVq1Ch9/fXXjfguEqO+a+P1enXbbbepV69eys/PV2lpqa6++mpt377dcYyBAweG3Ufjxo1r5HcSXw3dM7H87GTiPSMp4u8cl8ulBx54wN7neLtnYvn7nA6/Zwhe4+zZZ5/VzTffrFmzZmn9+vX6/ve/r5EjR2rbtm3JHlqjeeeddzR58mStXr1aS5Yskc/n07Bhw7R//37HfiNGjFBFRYX9eP3115M04sZzyimnON7zhg0b7Ofuv/9+Pfzww/rd736nNWvWqLi4WEOHDtXevXuTOOLGsWbNGsd1WbJkiSRpzJgx9j6ZcL/s379fp512mn73u99FfD6We+Tmm2/Wiy++qGeeeUYrVqzQvn37dOGFF8rv9zfW20iI+q7NgQMH9OGHH+qOO+7Qhx9+qBdeeEFffvmlRo0aFbbvpEmTHPfRY4891hjDT5iG7hmp4Z+dTLxnJDmuSUVFhf74xz/K5XLp0ksvdex3PN0zsfx9TovfMwZxdfbZZ5vrr7/esa179+5mxowZSRpR8u3YscNIMu+88469bcKECebiiy9O3qCS4K677jKnnXZaxOcCgYApLi429957r73t0KFDprCw0CxYsKCRRpg6fvazn5kuXbqYQCBgjMnM+0WSefHFF+3vY7lH9uzZY9xut3nmmWfsff7973+brKws88YbbzTa2BMt9NpE8sEHHxhJ5quvvrK3DRgwwPzsZz9L7OCSKNJ1aehnh3umzsUXX2wGDx7s2Ha83zOhf5/T5fcMmdc4qq2t1bp16zRs2DDH9mHDhmnlypVJGlXyVVVVSZJatmzp2L58+XK1adNG3bp106RJk7Rjx45kDK9Rbdq0SaWlpercubPGjRunf/3rX5KkLVu2qLKy0nHveDweDRgwIOPundraWv3pT3/Sj3/8Y7lcLnt7Jt4vwWK5R9atWyev1+vYp7S0VD179sy4+6iqqkoul0vNmzd3bH/qqadUVFSkU045RdOnT8+ITzbq+9nhnjnsm2++0WuvvaZrrrkm7Lnj+Z4J/fucLr9nchrlLBli586d8vv9atu2rWN727ZtVVlZmaRRJZcxRlOnTtW5556rnj172ttHjhypMWPGqGPHjtqyZYvuuOMODR48WOvWrUu5lTzi5ZxzztETTzyhbt266ZtvvtGvfvUr9e/fX5988ol9f0S6d7766qtkDDdpXnrpJe3Zs0cTJ060t2Xi/RIqlnuksrJSubm5atGiRdg+mfQ76NChQ5oxY4Yuv/xyNWvWzN5+xRVXqHPnziouLtbGjRs1c+ZMffzxx3aZyvGooZ8d7pnDHn/8cRUUFGj06NGO7cfzPRPp73O6/J4heE2A4GyRdPgGCd2WKaZMmaJ//OMfWrFihWP72LFj7a979uypPn36qGPHjnrttdfCfnkcL0aOHGl/3atXL/Xr109dunTR448/bk+g4N6RFi5cqJEjR6q0tNTelon3SzTHco9k0n3k9Xo1btw4BQIBzZ8/3/HcpEmT7K979uyprl27qk+fPvrwww915plnNvZQG8Wx/uxk0j0jSX/84x91xRVXqEmTJo7tx/M9E+3vs5T6v2coG4ijoqIiZWdnh/2fx44dO8L+LyYT/PSnP9Urr7yisrIytWvXrt59S0pK1LFjR23atKmRRpd8+fn56tWrlzZt2mR3Hcj0e+err77S0qVLde2119a7XybeL7HcI8XFxaqtrdXu3buj7nM883q9uuyyy7RlyxYtWbLEkXWN5Mwzz5Tb7c6o+yj0ZyfT7xlJeu+99/TFF180+HtHOn7umWh/n9Pl9wzBaxzl5uaqd+/eYR8nLFmyRP3790/SqBqfMUZTpkzRCy+8oLfffludO3du8DW7du1SeXm5SkpKGmGEqaGmpkafffaZSkpK7I+lgu+d2tpavfPOOxl17yxatEht2rTRBRdcUO9+mXi/xHKP9O7dW26327FPRUWFNm7ceNzfR1bgumnTJi1dulStWrVq8DWffPKJvF5vRt1HoT87mXzPWBYuXKjevXvrtNNOa3DfdL9nGvr7nDa/ZxplWlgGeeaZZ4zb7TYLFy40n376qbn55ptNfn6+2bp1a7KH1mhuuOEGU1hYaJYvX24qKirsx4EDB4wxxuzdu9dMmzbNrFy50mzZssWUlZWZfv36mRNOOMFUV1cnefSJM23aNLN8+XLzr3/9y6xevdpceOGFpqCgwL437r33XlNYWGheeOEFs2HDBjN+/HhTUlJyXF+TYH6/33To0MHcdtttju2ZdL/s3bvXrF+/3qxfv95IMg8//LBZv369PWM+lnvk+uuvN+3atTNLly41H374oRk8eLA57bTTjM/nS9bbiov6ro3X6zWjRo0y7dq1Mx999JHj905NTY0xxpjNmzebOXPmmDVr1pgtW7aY1157zXTv3t2cccYZaX1t6rsusf7sZOI9Y6mqqjJNmzY1jz76aNjrj8d7pqG/z8akx+8ZgtcE+J//+R/TsWNHk5uba84880xHi6hMICniY9GiRcYYYw4cOGCGDRtmWrdubdxut+nQoYOZMGGC2bZtW3IHnmBjx441JSUlxu12m9LSUjN69GjzySef2M8HAgFz1113meLiYuPxeMx5551nNmzYkMQRN64333zTSDJffPGFY3sm3S9lZWURf3YmTJhgjIntHjl48KCZMmWKadmypcnLyzMXXnjhcXGt6rs2W7Zsifp7p6yszBhjzLZt28x5551nWrZsaXJzc02XLl3MTTfdZHbt2pXcN/Yt1XddYv3ZycR7xvLYY4+ZvLw8s2fPnrDXH4/3TEN/n41Jj98zriNvBgAAAEh51LwCAAAgbRC8AgAAIG0QvAIAACBtELwCAAAgbRC8AgAAIG0QvAIAACBtELwCAAAgbRC8AgAAIG0QvAIAACBtELwCAAAgbRC8AgAAIG0QvAIAACBt/P9HPcM04kDg3wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reward: 92\n",
      "Steady state found at 31 trials.\n",
      "Optimal epsilon: 0.6000000000000001\n",
      "Optimal lambda: 0.8\n"
     ]
    }
   ],
   "source": [
    "best_epsilon, best_lambda = optimize(6, 0, 200, print_each=False)\n",
    "print(\"Optimal epsilon:\", best_epsilon)\n",
    "print(\"Optimal lambda:\", best_lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# World 7\n",
    "Optimal epsilon: 0.8\n",
    "\n",
    "Optimal lambda: 0.8\n",
    "\n",
    "Similar maze to world 6, but going down the wrong paths is more costly because they further diverge more often. Also there are more wrong paths. High initial exploration lets the agent rule out dead-end paths. This sets up the Q values well for later trials, where the agent can venture down the high Q-value path and reach the winning state.\n",
    "\n",
    "If we have epsilon=1.0 and lambda=0.8, the initial exploration becomes too random and doesn't manage to set up the Q values soon enough to guarantee safe winning exploitation later on. In fact, the difference between these is only 1 trial, which is most likely the very first trial, where the agent is slightly more likely to run into a wall."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1085,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Epsilon    Lambda    Steady State Trials    Reward\n",
      "---------  --------  ---------------------  --------\n",
      "     0.00      0.00                     43        88\n",
      "     0.00      0.20                     43        88\n",
      "     0.00      0.40                     43        88\n",
      "     0.00      0.60                     43        88\n",
      "     0.00      0.80                     43        88\n",
      "     0.00      1.00                     43        88\n",
      "     0.20      0.00                     43        88\n",
      "     0.20      0.20                     43        88\n",
      "     0.20      0.40                     43        88\n",
      "     0.20      0.60                     43        88\n",
      "     0.20      0.80                     44        88\n",
      "     0.20      1.00                    100        88\n",
      "     0.40      0.00                     43        88\n",
      "     0.40      0.20                     43        88\n",
      "     0.40      0.40                     43        88\n",
      "     0.40      0.60                     43        88\n",
      "     0.40      0.80                     44        88\n",
      "     0.40      1.00                    121         0\n",
      "     0.60      0.00                     43        88\n",
      "     0.60      0.20                     43        88\n",
      "     0.60      0.40                     43        88\n",
      "     0.60      0.60                     43        88\n",
      "     0.60      0.80                     44        88\n",
      "     0.60      1.00                    183         0\n",
      "     0.80      0.00                     43        88\n",
      "     0.80      0.20                     43        88\n",
      "     0.80      0.40                     43        88\n",
      "     0.80      0.60                     43        88\n",
      "     0.80      0.80                     42        88\n",
      "     0.80      1.00                    116         0\n",
      "     1.00      0.00                     43        88\n",
      "     1.00      0.20                     43        88\n",
      "     1.00      0.40                     43        88\n",
      "     1.00      0.60                     42        88\n",
      "     1.00      0.80                     43        88\n",
      "     1.00      1.00                      0      -105\n",
      "\n",
      "Optimal epsilon: 0.8\n",
      "Optimal lambda: 0.8\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reward: 88\n",
      "Steady state found at 42 trials.\n",
      "Optimal epsilon: 0.8\n",
      "Optimal lambda: 0.8\n"
     ]
    }
   ],
   "source": [
    "best_epsilon, best_lambda = optimize(7, 0, 200, print_each=False)\n",
    "print(\"Optimal epsilon:\", best_epsilon)\n",
    "print(\"Optimal lambda:\", best_lambda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# World 8\n",
    "Similar maze to the previous two but much larger. With 0 exploration, the policy manages to achieve a steady state as soon as any other pair of parameters. Most of the pairs do equally well here.\n",
    "\n",
    "The agent doesn't need to explore much here. There is only 1 path that leads to the winning state, so the agent finds the path without any exploration by simply going into all the available dead ends first. Actually, I don't think I understand this one well enough, so that might be a stupid response.\n",
    "\n",
    "Lambda=1.0 fails every time because it probably results in cycles more often. Overall, exploring later on is not worthwhile, because almost all paths that aren't the winning path lead to dead ends and there is little space for slightly improving on an already winning path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1058,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Epsilon    Lambda    Steady State Trials    Reward\n",
      "---------  --------  ---------------------  --------\n",
      "     0.00      0.00                    172        52\n",
      "     0.00      0.20                    172        52\n",
      "     0.00      0.40                    172        52\n",
      "     0.00      0.60                    172        52\n",
      "     0.00      0.80                    172        52\n",
      "     0.00      1.00                    172        52\n",
      "     0.20      0.00                    172        52\n",
      "     0.20      0.20                    172        52\n",
      "     0.20      0.40                    172        52\n",
      "     0.20      0.60                    172        52\n",
      "     0.20      0.80                    172        52\n",
      "     0.20      1.00                    144         0\n",
      "     0.40      0.00                    172        52\n",
      "     0.40      0.20                    172        52\n",
      "     0.40      0.40                    172        52\n",
      "     0.40      0.60                    172        52\n",
      "     0.40      0.80                    172        52\n",
      "     0.40      1.00                    140         0\n",
      "     0.60      0.00                    172        52\n",
      "     0.60      0.20                    172        52\n",
      "     0.60      0.40                    172        52\n",
      "     0.60      0.60                    172        52\n",
      "     0.60      0.80                    172        52\n",
      "     0.60      1.00                    179         0\n",
      "     0.80      0.00                    172        52\n",
      "     0.80      0.20                    172        52\n",
      "     0.80      0.40                    172        52\n",
      "     0.80      0.60                    172        52\n",
      "     0.80      0.80                    174        52\n",
      "     0.80      1.00                    120         0\n",
      "     1.00      0.00                    172        52\n",
      "     1.00      0.20                    172        52\n",
      "     1.00      0.40                    172        52\n",
      "     1.00      0.60                    172        52\n",
      "     1.00      0.80                    174        52\n",
      "     1.00      1.00                      5         0\n",
      "\n",
      "Optimal epsilon: 0.0\n",
      "Optimal lambda: 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reward: 52\n",
      "Steady state found at 172 trials.\n",
      "Optimal epsilon: 0.0\n",
      "Optimal lambda: 0.0\n"
     ]
    }
   ],
   "source": [
    "best_epsilon, best_lambda = optimize(8, 0, 200, print_each=False)\n",
    "print(\"Optimal epsilon:\", best_epsilon)\n",
    "print(\"Optimal lambda:\", best_lambda)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}