TabularMethods.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.6"
    },
    "colab": {
      "name": "TabularMethods.ipynb",
      "provenance": [],
      "collapsed_sections": []
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "40a0QPEvRhUe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5eddf857-3bb4-4756-a72e-3b19a67b5e21"
      },
      "source": [
        "# @title If you need in google colab:\n",
        "!pip install colorama"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting colorama\n",
            "  Downloading https://files.pythonhosted.org/packages/44/98/5b86278fbbf250d239ae0ecb724f8572af1c91f4a11edf4d36a206189440/colorama-0.4.4-py2.py3-none-any.whl\n",
            "Installing collected packages: colorama\n",
            "Successfully installed colorama-0.4.4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PpNeLPdclEYF",
        "cellView": "form"
      },
      "source": [
        "#@title Environment\n",
        "import random\n",
        "import pprint\n",
        "import io\n",
        "import numpy as np\n",
        "import sys\n",
        "from gym.envs.toy_text import discrete\n",
        "from colorama import Fore, Back, Style\n",
        "import collections\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.special import softmax\n",
        "\n",
        "UP = 0\n",
        "RIGHT = 1\n",
        "DOWN = 2\n",
        "LEFT = 3\n",
        "\n",
        "class GridworldEnv(discrete.DiscreteEnv):\n",
        "  metadata = {'render.modes': ['human', 'ansi']}\n",
        "\n",
        "  def __init__(self, shape=[10,10]):\n",
        "    if not isinstance(shape, (list, tuple)) or not len(shape) == 2:\n",
        "        raise ValueError('shape argument must be a list/tuple of length 2')\n",
        "        \n",
        "    self.shape = shape\n",
        "\n",
        "    nS = np.prod(shape)\n",
        "    nA = 4\n",
        "\n",
        "    MAX_Y = shape[0]\n",
        "    MAX_X = shape[1]\n",
        "\n",
        "    P = {}\n",
        "    grid = np.arange(nS).reshape(shape)\n",
        "    it = np.nditer(grid, flags=['multi_index'])\n",
        "\n",
        "    while not it.finished:\n",
        "      s = it.iterindex\n",
        "      y, x = it.multi_index\n",
        "\n",
        "      # P[s][a] = (prob, next_state, reward, is_done)\n",
        "      P[s] = {a : [] for a in range(nA)}\n",
        "\n",
        "      #Reaching target\n",
        "      is_done = lambda s: s == 0\n",
        "\n",
        "      #Due to existance of walls, these moves are not available\n",
        "      no_up = lambda s: s in [44,45,63,64]\n",
        "      no_down = lambda s: s in [23,24,25,44]\n",
        "      no_left = lambda s: s in [44,36,55]\n",
        "      no_right = lambda s: s in [32,42,52]\n",
        "\n",
        "      #Barries in the path\n",
        "      pit = lambda s: s in [13,62,41]\n",
        "      wall = lambda s: s in [43,33,53,34,35,54]\n",
        "\n",
        "      #Rewards of each state\n",
        "      reward = 10.0 if is_done(s) else -1.0\n",
        "      reward = -10.0 if pit(s) else reward\n",
        "      \n",
        "      ns_up = s if y == 0 else s - MAX_X\n",
        "      ns_right = s if x == (MAX_X - 1) else s + 1\n",
        "      ns_down = s if y == (MAX_Y - 1) else s + MAX_X\n",
        "      ns_left = s if x == 0 else s - 1\n",
        "      \n",
        "      P[s][UP] = [(1, ns_up, reward, is_done(ns_up))]\n",
        "      P[s][RIGHT] = [(1.0, ns_right, reward, is_done(ns_right))]\n",
        "      P[s][DOWN] = [(1, ns_down, reward, is_done(ns_down))]\n",
        "      P[s][LEFT] = [(1, ns_left, reward, is_done(ns_left))]\n",
        "\n",
        "      #Terminal state\n",
        "      if is_done(s):\n",
        "        P[s][UP] = [(1.0, s, reward, True)]\n",
        "        P[s][RIGHT] = [(1.0, s, reward, True)]\n",
        "        P[s][DOWN] = [(1.0, s, reward, True)]\n",
        "        P[s][LEFT] = [(1.0, s, reward, True)]\n",
        "\n",
        "      #Encountering walls\n",
        "      if no_up(s):\n",
        "        P[s][UP] = [(1.0, s, -3.0 , False)]                \n",
        "      if no_down(s):\n",
        "        P[s][DOWN] = [(1.0, s, -3.0 , False)]                \n",
        "      if no_right(s):\n",
        "        P[s][RIGHT] = [(1.0, s, -3.0 , False)]  \n",
        "      if no_left(s):\n",
        "        P[s][LEFT] = [(1.0, s, -3.0 , False)] \n",
        "\n",
        "      it.iternext() \n",
        "\n",
        "    # Initial state distribution is uniform\n",
        "    isd = np.zeros(100)\n",
        "    isd[44]=1\n",
        "    self.P = P\n",
        "\n",
        "    super(GridworldEnv, self).__init__(nS, nA, P, isd)\n",
        "\n",
        "  def _render(self, mode='human', close=False):\n",
        "    if close:\n",
        "      return\n",
        "\n",
        "    outfile = io.StringIO() if mode == 'ansi' else sys.stdout\n",
        "\n",
        "    grid = np.arange(self.nS).reshape(self.shape)\n",
        "    it = np.nditer(grid, flags=['multi_index'])\n",
        "\n",
        "    while not it.finished:\n",
        "      s = it.iterindex\n",
        "      y, x = it.multi_index\n",
        "\n",
        "      if self.s == s and not s==0:\n",
        "        output =  Back.CYAN + Style.BRIGHT + Fore.WHITE +  \"  웃 \" + Style.RESET_ALL if s not in [13,62,41] else Back.BLUE + Style.BRIGHT + Fore.WHITE + \"  웃 \" + Style.RESET_ALL\n",
        "      elif s == 0:\n",
        "          output = Back.GREEN + Style.BRIGHT + Fore.WHITE + \"     \" + Style.RESET_ALL if not self.s==0 else Back.GREEN + Style.BRIGHT + Fore.WHITE +  \"  웃 \" + Style.RESET_ALL\n",
        "      elif s in [13,62,41]:\n",
        "          output = Back.BLUE + \"     \" + Style.RESET_ALL\n",
        "      elif s in [43,33,53,34,35,54]:\n",
        "          output = Back.CYAN + Style.BRIGHT + Fore.BLACK +   \"  █  \"  + Style.RESET_ALL\n",
        "      else:\n",
        "          output = Back.CYAN + Style.BRIGHT + Fore.BLACK +  \"  .  \" + Style.RESET_ALL\n",
        "\n",
        "      if x == 0:\n",
        "          output = output.lstrip()\n",
        "      if x == self.shape[1] - 1:\n",
        "          output = output.rstrip()\n",
        "\n",
        "      outfile.write(output)\n",
        "\n",
        "      if x == self.shape[1] - 1:\n",
        "          outfile.write(\"\\n\")\n",
        "\n",
        "      it.iternext()"
      ],
      "execution_count": 134,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 245
        },
        "id": "SoKSR1jD1mtv",
        "outputId": "966f141f-ca59-4846-cb5e-edbef0acbbb9"
      },
      "source": [
        "# @title Instantiate Environment\n",
        "from IPython.display import Image\n",
        "display(Image(filename='env.jpeg') )\n",
        "env =  GridworldEnv()\n",
        "env.reset()"
      ],
      "execution_count": 158,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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/wj+tf9Ai/wD/AAGf/Cnzx7hyS7GdRWj/AMI/rX/QIv8A/wABn/wo/wCEf1r/AKBF/wD+Az/4Uc8e4ckuxnUVem8NaxPBJC2k6iFdSpK27g4P4VFY+FNWsLKK1i0rUmjiXaC9u5P8qXOr7hyO2xWrI8T/APIu3X/AP/Q1rqP+Ef1r/oEX/wD4DP8A4Vl+IvDWvT6FcxxaJqUjnbhUtXJPzDtiurB1IrE0239pfmOMZcy0PJ6K3P8AhCvFf/Qs6z/4AS//ABNH/CFeK/8AoWdZ/wDACX/4mvvfrNH+dfejrszDorc/4QrxX/0LOs/+AEv/AMTR/wAIV4r/AOhZ1n/wAl/+Jo+s0f5196CzMOvUNK/5A9l/17x/+giuL/4QrxX/ANCzrP8A4AS//E16Npvh3XI9Ks0fRtQVlgQFTauCDtHHSvBz+tTlThyyT17mVWLstCCitH/hH9a/6BF//wCAz/4VW1DwjqupWUlpNpWprHJ1McDg/wAq+Xc1bRmCg76or0Vfj8OaxHGqLpGoYUADNu5P8qd/wj+tf9Ai/wD/AAGf/Cjnj3Dkl2M6itH/AIR/Wv8AoEX/AP4DP/hR/wAI/rX/AECL/wD8Bn/wo549w5JdjOorR/4R/Wv+gRf/APgM/wDhVSz8HapZT3UsWlaoWuZPMcPA5APtxS513DkfYhorR/4R/Wv+gRf/APgM/wDhR/wj+tf9Ai//APAZ/wDCnzx7hyS7GdRWj/wj+tf9Ai//APAZ/wDCj/hH9a/6BF//AOAz/wCFHPHuHJLsZ1FTXvg7VL+S2eXStUU28nmJsgcZPvxVv/hH9a/6BF//AOAz/wCFLnXcOR9jOorR/wCEf1r/AKBF/wD+Az/4Uf8ACP61/wBAi/8A/AZ/8KfPHuHJLsZ1FaP/AAj+tf8AQIv/APwGf/Cg+HtZII/sjUOf+nZ/8KOePcOSXYzqKm07wfqmmWv2eDStTZNxbMkDsck59Kt/8I/rX/QIv/8AwGf/AApKatqwcHfRGdRWj/wj+tf9Ai//APAZ/wDCj/hH9a/6BF//AOAz/wCFPnj3Dkl2M6itH/hH9a/6BF//AOAz/wCFVH8HapJqkWoHStU86OMxhRA+3B9Rik5rowUH1RDRWj/wj+tf9Ai//wDAZ/8ACj/hH9a/6BF//wCAz/4U+ePcOSXYzqK0f+Ef1r/oEX//AIDP/hR/wj+tf9Ai/wD/AAGf/Cjnj3Dkl2M6irV54V1a+s5bWXSdSCSrtYpbuDj24p9v4Z1e2t44E0nUSsahQWt3JwPU4pc6vuHI7bFKuz+Gf/IyXH/Xo3/oaVzv/CP61/0CL/8A8Bn/AMK634eaXqFlr88l3Y3UEZtWUNLCyAnenGSOvBrOvKLpvU1oRkqi0PS6KKK8c9cK87+Kf/MJ/wC23/sleiV538U/+YT/ANtv/ZK6ML/FX9dDnxX8J/11POqKKK9c8kKKqWEl9IJvt0EUREhEXltncnYn3q3STurjas7BRRRTEFFFVLqS+S8tVtoInt2Y+e7NgoO2BSbsCVy3RRRTAKKKKACimTGRYJDCqtKFOxWOAT2qKxe6ksomvYkiuSv7xEOQDSvrYdtLliiiimIKKKKACiqgkvv7VMZgi+w+XkS7vm356Y9Kt0k7g1YKKKKYBRRVbUHvI7KRrCKOW5H3EkOAaG7K4JXdizRTYy5jUyAB8DcAcgGnUAFFFFABRRVSzkvnnuhdwRxxLJiBkbJZfU0rhYt0UUUwCiiigAoqpeyXySWws4IpEaTExdsbU9RVulcLBRRRTAKKKQ5wcde1AC0VU06S9ktd2oQxwz7j8sbZGM8VbpJ3Vwas7BRRRTAKKKqPJfDVIo0gjNkYyXkLfMG7ACk3YaVy3RRRTEFFFFABRUF41ylnK1pGklwF/do5wCfen27TNbxtcIqTFQXVTkA98Ur62C2lySuz+Gf/ACMlx/16N/6GlcZXZ/DP/kZLj/r0b/0NKyxH8KRrQ/iI9Wooorxj2Qrg/iRcxW/9mebY291u83HnNINv3Omxl/XPSu8rzv4p/wDMJ/7bf+yVvhleqv66GGJdqTOL/tK0/wCgJYf99z//AByj+0rT/oCWH/fc/wD8crOor1uVHlczNH+0rT/oCWH/AH3P/wDHKP7StP8AoCWH/fc//wAcrGtL61vhIbaZZBE5jfHZh2qxQop6r8wba3/I0f7StP8AoCWH/fc//wAco/tK0/6Alh/33P8A/HKzqKOVBzM0f7StP+gJYf8Afc//AMco/tK0/wCgJYf99z//ABys6q899a21xBbzTKks5IjU/wARFDilv+YKTe35Gz/aVp/0BLD/AL7n/wDjlH9pWn/QEsP++5//AI5WdRRyoOZmj/aVp/0BLD/vuf8A+OUf2laf9ASw/wC+5/8A45WdRRyoOZmj/aVp/wBASw/77n/+OUf2laf9ASw/77n/APjlZcsqQxPLIwVEBZmPYCmWt1De2yXFvIJInGVYd6OVXt+oXdr/AKGv/aVp/wBASw/77n/+OUf2laf9ASw/77n/APjlZ1FHKg5maP8AaVp/0BLD/vuf/wCOVFc6nbLazMmjWCsEJDB5+DjrzJVOorr/AI9Jv+ubfyocVYFJ3PK/+Ey1/wD5/wD/AMgx/wDxNezw6nbGGMtotgSVGSXn54/66V8917nD/qI/90fyriwkpTvzN/edmLjGFuVL7jU/tK0/6Alh/wB9z/8Axyj+0rT/AKAlh/33P/8AHKzqK7eVHHzM0f7StP8AoCWH/fc//wAcrz7x14mv7LWIY9OENlEYQTHEu4E5POXLH9a7CvNviD/yG4f+uA/ma58TeNO8X+JvhrSqWkjrPAXiC4vrG8bUra2vnWQBGlDIVGOg8tlH51139pWn/QEsP++5/wD45XnXw6/5B97/ANdR/Ku0q6C5qabZNd8tRpI0f7StP+gJYf8Afc//AMco/tK0/wCgJYf99z//ABys6iteVGXMyDxRrItvDl5NZ6bZ21wqjZNGZWK8joGcj8xXAeH/ABbrE+v2MVzcJPA0oDxPGoDj0JUA/kRXV+Lf+RYvf90fzFeceG/+RjsP+uwrixEpRqxSbt6nbQjGVKTaX3Huf9pWn/QEsP8Avuf/AOOUf2laf9ASw/77n/8AjlZ1FdvKji5maP8AaVp/0BLD/vuf/wCOUf2laf8AQEsP++5//jlZ1FHKg5maP9pWn/QEsP8Avuf/AOOUf2laf9ASw/77n/8AjlY1zfWtm8KXEyxtM+yMH+JvSrFHKv6Ycz/pGj/aVp/0BLD/AL7n/wDjlH9pWn/QEsP++5//AI5WdRRyoOZmj/aVp/0BLD/vuf8A+OUf2laf9ASw/wC+5/8A45WdQSACScAUcqDmZo/2laf9ASw/77n/APjlH9pWn/QEsP8Avuf/AOOVjWd7bahB59rKJY8ldw9RVihRT1X5g5NaP8jR/tK0/wCgJYf99z//AByj+0rT/oCWH/fc/wD8crOoo5UHMzR/tK0/6Alh/wB9z/8Axyj+0rT/AKAlh/33P/8AHKzqrtfWyXyWTTKLl1LrH3IFDilv+YJt7fkbP9pWn/QEsP8Avuf/AOOUf2laf9ASw/77n/8AjlZ1FHKg5maP9pWn/QEsP++5/wD45R/aVp/0BLD/AL7n/wDjlZ1FHKg5maP9pWn/AEBLD/vuf/45R/aVp/0BLD/vuf8A+OVk3NzDaW8lxO4SKMZZj2FOhmjuIUmiYPG6hlYdwaOVXt+oXdr/AKGp/aVp/wBASw/77n/+OV1vw8u4LjX50j061tmFqx3xNISfnTj5nIx+HauBrs/hn/yMlx/16N/6GlZV4r2bNaEn7RHq1FFFeOeuFcH8SLaK4/szzb63tdvm485ZDu+502K364613led/FP/AJhP/bb/ANkrfDfxV/XQwxP8JnF/2baf9Buw/wC+J/8A43R/Ztp/0G7D/vif/wCN1nUV63K+55V12L0ej2EO7ytX01Nx3NtinGT6n911p/8AZtp/0G7D/vif/wCN1nUUcr7hzLsXpbKxgheWTXbBURSzHy7g4A5P/LKsv+1fDn/Qz2H/AID3X/xmotV/5A97/wBe8n/oJry+vayvLKeLhKVSTVn0t/kaU4xktUeq/wBq+HP+hnsP/Ae6/wDjNMe/8MSOjv4j01nQ5RjbXJK/T9zxXltFer/q9hv55fh/8iaezj2PVf7V8Of9DPYf+A91/wDGaP7V8Of9DPYf+A91/wDGa8qoo/1ew/8APL8P/kQ9nHseyWSaXqEJltfEFhIgbaT5VwOeveL3FWP7NtP+g3Yf98T/APxuuM8Gf8geb/r4P/oK10VfM4ygqNeVOLdk/L/IwlZO1jQbS7NlKtrWnkEYIMc/P/kKkj0mxhjWOLWNORFGFVY5wAPYeVVCiublfcXMuxo/2baf9Buw/wC+J/8A43R/Ztp/0G7D/vif/wCN1nUUcr7hddjR/s20/wCg3Yf98T//ABuobvTrUWU5GtWBIjbgJPzx/wBc6qVFdf8AHpN/1zb+VDi7bgmr7Hh1fQcGnWpt4j/bVgPkHBSf0/6518+V7nD/AKiP/dH8q4MEr8x3Y125TU/s20/6Ddh/3xP/APG6P7NtP+g3Yf8AfE//AMbrOorv5X3OG67Gj/Ztp/0G7D/vif8A+N1yXibwFLr2pxTWmv6SAECbXW5yTnsBCfWtytfw7K9nqSXipbuseVZZJ0jYZHVdxHNZVqfNBpv8jSjU5ZppfmYnhn4eX/huxuvt+oWgV3Db1gutoGMckwitX+zbT/oN2H/fE/8A8bro7S3Gj3M2pK0sv2hW8pZp4ER8nu3mHd+ArkLiJoZmR/L3df3bq6/gQSKmhtyp6IqtvzNasuf2baf9Buw/74n/APjdH9m2n/QbsP8Avif/AON1nUVvyvuY3XYXXPD0Op6PcWcOu6askgABdbgDr7RVyWk/Da4sNWtrqXxFopjicMwUXOce37musorKeHjOSk27o1hXlCLiktTR/s20/wCg3Yf98T//ABuj+zbT/oN2H/fE/wD8brOorXlfcyuuxo/2baf9Buw/74n/APjdH9m2n/QbsP8Avif/AON1nUUcr7hddi9Jo9hKUMmr6a5Q7lLRTnafUfuuKf8A2baf9Buw/wC+J/8A43WdRRyvuHMuxo/2baf9Buw/74n/APjdH9m2n/QbsP8Avif/AON1nUUcr7hddjR/s20/6Ddh/wB8T/8Axuj+zbT/AKDdh/3xP/8AG6zqKOV9w5l2L0Wj2ECbItX02NM52pFOBn/v1T/7NtP+g3Yf98T/APxus6ijlfcOZdjR/s20/wCg3Yf98T//ABuj+zbT/oN2H/fE/wD8brOoo5X3C67Gj/Ztp/0G7D/vif8A+N0w6PYGYTHV9NMqjaHMU+4D0z5VUaKOV9w5l2NH+zbT/oN2H/fE/wD8bo/s20/6Ddh/3xP/APG6zqKOV9wuuxo/2baf9Buw/wC+J/8A43R/Ztp/0G7D/vif/wCN1nUUcr7hddi/JpNjLG0cmsac6MMFWjnII+nlUq6XZooVda09VAwAI5wAP+/VZ9FHK+4cy7Gj/Ztp/wBBuw/74n/+N12Pw70xYdWu7uG/tbmNIPLYRCQFSzAj7yLx8prz2vRfhZ/zFv8Atj/7PWGJuqTdzbD2dVKx6JRRRXknrBXnfxT/AOYT/wBtv/ZK9Erg/iRqF7Y/2Z9jvLi33+bu8mQpuxsxnB56mt8N/FVv60MMT/CdzzKitH/hINa/6C9//wCBL/40f8JBrX/QXv8A/wACX/xr1ry7HlWj3MOwtJrQTCa8lufMkLqZB9wH+Ee1W60f+Eg1r/oL3/8A4Ev/AI0f8JBrX/QXv/8AwJf/ABpLmStb8Qdm7t/gYeq/8ge9/wCveT/0E15fXtn/AAkGtf8AQXv/APwJf/Gj/hINa/6C9/8A+BL/AONetl+aSwcZR5L387foy4TjE8Tor2z/AISDWv8AoL3/AP4Ev/jR/wAJBrX/AEF7/wD8CX/xr0f9Ypf8+v8Ayb/7Uv20TxOivbP+Eg1r/oL3/wD4Ev8A40f8JBrX/QXv/wDwJf8Axo/1il/z6/8AJv8A7UPbROM8Gf8AIHm/6+D/AOgrXRVo/wDCQa1/0F7/AP8AAl/8aP8AhINa/wCgvf8A/gS/+NeBia8q9aVW1r+f/AMpOLdzLmRpYJI1kaNmUgOvVT61FY28lrZRQS3D3EiLgyv1b3rZ/wCEg1r/AKC9/wD+BL/40f8ACQa1/wBBe/8A/Al/8a59b3t+ItLWv+BnUVo/8JBrX/QXv/8AwJf/ABo/4SDWv+gvf/8AgS/+NO8uwWj3M6orr/j0m/65t/Ktb/hINa/6C9//AOBL/wCNQ3evaw1lOratfkGNgQbl+ePrQ3K2wJRvufP1e5w/6iP/AHR/KvDK+g4Nf1kW8QGrX4AQYAuX9PrXBgr+9Y7sbb3blKitH/hINa/6C9//AOBL/wCNH/CQa1/0F7//AMCX/wAa77y7HDaPczqsWcEE8u24vI7ZBjLMjMT9AoP64qz/AMJBrX/QXv8A/wACX/xryv4lXl1e6/BJdXM07iAANK5YgZPGTWVapKnHmt/X3GlGmqkrX/r7z2S7m0W9s4rSG8u4HtwdstwGeOT/AICCdn4CsCRQkjKrq4BwGXOD+YBrk/hjqV9Y6bfraXtzbq0ylhFKyAnHfBru/wDhINa/6C9//wCBL/40UW3HmXXz/wCAOskpcr6eX/BM6itH/hINa/6C9/8A+BL/AONH/CQa1/0F7/8A8CX/AMa1vLsZWj3M1wWRlDFSRgEdqrafay2dkkE11JdSLnMsnU81t/8ACQa1/wBBe/8A/Al/8aP+Eg1r/oL3/wD4Ev8A40tb3t+IaWtf8DOorR/4SDWv+gvf/wDgS/8AjR/wkGtf9Be//wDAl/8AGneXYLR7mdRWj/wkGtf9Be//APAl/wDGj/hINa/6C9//AOBL/wCNF5dgtHuYbWkx1VLsXkohWMobf+En+9VutH/hINa/6C9//wCBL/40f8JBrX/QXv8A/wACX/xpLmXT8Qdn1/AzqK0f+Eg1r/oL3/8A4Ev/AI0f8JBrX/QXv/8AwJf/ABp3l2C0e5nVWv7aS7spYIbl7aRxgSp1Wtr/AISDWv8AoL3/AP4Ev/jR/wAJBrX/AEF7/wD8CX/xofM1awLlTvcy4kMcSIzl2VQCx6t70+tH/hINa/6C9/8A+BL/AONH/CQa1/0F7/8A8CX/AMaPe7B7vczqK0f+Eg1r/oL3/wD4Ev8A40f8JBrX/QXv/wDwJf8AxovLsFo9zOqpa2k0F5dTSXksyTMCkTdIsdhW5/wkGtf9Be//APAl/wDGj/hINa/6C9//AOBL/wCNJ8z6fiCsuv4GdRWj/wAJBrX/AEF7/wD8CX/xo/4SDWv+gvf/APgS/wDjTvLsFo9zOorR/wCEg1r/AKC9/wD+BL/40f8ACQa1/wBBe/8A/Al/8aLy7BaPcw9QtJryOJYbyS2KSBy0f8QH8J9qt1o/8JBrX/QXv/8AwJf/ABo/4SDWv+gvf/8AgS/+NL3r3t+IaWtf8DOr0X4Wf8xb/tj/AOz1xf8AwkGtf9Be/wD/AAJf/Gut+Hmqahe6/PHd311PGLVmCyzM4B3pzgnryayxHM6TNsPyqqj0uiiivIPWCvO/in/zCf8Att/7JXolcH8SHsk/sz7Zb3EufN2+TOI8fcznKNnt6Vvhv4q/roYYn+EzzKitHztF/wCfC/8A/A1P/jVHnaL/AM+F/wD+Bqf/ABqvW5n2PKsu5h2F3NdiYzWctt5chRRIfvgfxD2q3Wj52i/8+F//AOBqf/GqPO0X/nwv/wDwNT/41STaW35A0m9H+ZnUVo+dov8Az4X/AP4Gp/8AGqPO0X/nwv8A/wADU/8AjVPmfYLLuZ1VLq7mgvLWGOzlmSZiHlXpFjua3PO0X/nwv/8AwNT/AONUedov/Phf/wDgan/xqk2+35Aku/5mdRWj52i/8+F//wCBqf8AxqjztF/58L//AMDU/wDjVPmfYLLuZ1FVNZ8U6LpF4lv/AGLfy7ow+7+0UXuRj/Un0rO/4T3Rf+hfv/8AwaJ/8YrvpZbi6sFOFO6fnH/MpUm9UzZmdooJJFjaRlUkIvVj6VFY3El1ZRTy2728jrkxP1X2rL/4T3Rf+hfv/wDwaJ/8Yo/4T3Rf+hfv/wDwaJ/8Yq/7Ix1/4f4x/wAyvZOxuUVh/wDCe6L/ANC/f/8Ag0T/AOMVb0zxhoupajFaf2Hfx+Zn5v7SQ4wCenke1KeWYyEXOVPRa7x/zE6TRo1Fdf8AHpN/1zb+Va3naL/z4X//AIGp/wDGqbI+iSRshsNQwwIOL5P/AI1XnNvsQku589V7nD/qI/8AdH8qx/8AhA/B/wDzw1z/AMGMP/xiurWTRUQKLDUMAY/4/k/+NVyYWnOnfmR1YmpCpblZn0Vo+dov/Phf/wDgan/xqjztF/58L/8A8DU/+NV18z7HLZdzOrzb4g/8huH/AK4D+Zr1rztF/wCfC/8A/A1P/jVYmseHPDGt3S3Fza6ujquwCO/iAx+MBrHERlOHLFG2HlGE+aTOV+HX/IPvf+uo/lXaU3RdJ8OaFDLFa2equsjBj5t/GT+kIrT87Rf+fC//APA1P/jVVRUoQUWiazjObkmZ1FaPnaL/AM+F/wD+Bqf/ABqjztF/58L/AP8AA1P/AI1WnM+xnZdzOqpZ3c1zPdRy2ckCwybUd+kg9RW552i/8+F//wCBqf8AxqjztF/58L//AMDU/wDjVK77fkFl3/MzqK0fO0X/AJ8L/wD8DU/+NUedov8Az4X/AP4Gp/8AGqfM+wWXczqK0fO0X/nwv/8AwNT/AONUedov/Phf/wDgan/xqjmfYLLuYd7dzWslssVnLcCWTY7J/wAsx/eNW60fO0X/AJ8L/wD8DU/+NUedov8Az4X/AP4Gp/8AGqV32/ILLv8AmZ1FaPnaL/z4X/8A4Gp/8ao87Rf+fC//APA1P/jVPmfYLLuZ1ITgE4z7Vpedov8Az4X/AP4Gp/8AGqPO0X/nwv8A/wADU/8AjVHM+wWXcw9Ou5r2186e0ktX3EeXJ1wD1q3Wj52i/wDPhf8A/gan/wAao87Rf+fC/wD/AANT/wCNUk3bb8gaV9/zM6itHztF/wCfC/8A/A1P/jVHnaL/AM+F/wD+Bqf/ABqnzPsFl3M6qj3cyapFaCzkaF4yxuB91SOxrc87Rf8Anwv/APwNT/41R52i/wDPhf8A/gan/wAapNvt+QJLv+ZnUVo+dov/AD4X/wD4Gp/8ao87Rf8Anwv/APwNT/41T5n2Cy7mdRWj52i/8+F//wCBqf8AxqjztF/58L//AMDU/wDjVHM+wWXcx7yeS2s5ZooHndFysSdWPoKfbyNNbxyvE0TOoJjbqp9DWr52i/8APhf/APgan/xqjztF/wCfC/8A/A1P/jVK7vt+QWVt/wAzOrs/hn/yMlx/16N/6Glc752i/wDPhf8A/gan/wAarrfh5Jp76/OLS1uopPsrZaW4WQY3pxgIvPTvWddv2b0NaCXtFqel0UUV4564V538U/8AmE/9tv8A2SvRK4P4kWUt5/ZnlPbrs83PnXEcXXZ03kZ6dq3wztVV/wCtDDEq9J2PMqK0f7Eu/wDnrYf+DCD/AOLo/sS7/wCeth/4MIP/AIuvW549zyuSXYy45opt3lSI+07W2sDg+h96fVm08LGxEgthp0YlcyPjUIOWPf79WP7Eu/8AnrYf+DCD/wCLpKatqwcHfRGdRWj/AGJd/wDPWw/8GEH/AMXR/Yl3/wA9bD/wYQf/ABdPnj3Dkl2M6mPNFG6I8iK7nCKWALfT1rU/sS7/AOeth/4MIP8A4uq8/hY3NxBcTf2c8sBJjY6hB8pP/A6TmujBQfVFaitH+xLv/nrYf+DCD/4uj+xLv/nrYf8Agwg/+Lp88e4ckux5r4z/AOQxD/17j/0Jq52vQfE3gzWtQ1KOW1WwkQQhSf7TthzknvJ7isb/AIV74j/542H/AINLX/45X2uX43DQwsIyqRTt3R0wT5UcvRXUf8K98R/88bD/AMGlr/8AHKP+Fe+I/wDnjYf+DS1/+OV2/wBoYT/n7H/wJf5lHL1r+GP+Ritf+B/+gNWj/wAK98R/88bD/wAGlr/8crR0LwPrtnrNvcXCWCRJu3N/adscZUjtJ71zYvHYWWHqJVIttPqu3qKS0Z0VFaP9iXf/AD1sP/BhB/8AF0f2Jd/89bD/AMGEH/xdfDc8e5y8kuxl+dF53k+Ynm43bNw3Y9celPqz/wAIsRfm+xp32kp5fmf2hBnb6ffqx/Yl3/z1sP8AwYQf/F0lNdWDg+iM6itH+xLv/nrYf+DCD/4uj+xLv/nrYf8Agwg/+Lp88e4ckuxnUyWWOGMySyLGi9Wc4A/GtT+xLv8A562H/gwg/wDi6gu/DL31s9vcnT5In+8p1CDn/wAfoc1bRgoO+qKoIIBByD3orQTQbmNFRJNPCqMADUIOB/33S/2Jd/8APWw/8GEH/wAXRzx7hyS7GdRWj/Yl3/z1sP8AwYQf/F0f2Jd/89bD/wAGEH/xdHPHuHJLsZ1MSaKVnWORHZDtcKwJU+h9K1P7Eu/+eth/4MIP/i6r2/hY2ks8kH9nI87b5CNQg+Y/990uddw5H2K1FaP9iXf/AD1sP/BhB/8AF0f2Jd/89bD/AMGEH/xdPnj3Dkl2M6itH+xLv/nrYf8Agwg/+Lo/sS7/AOeth/4MIP8A4ujnj3Dkl2MuSaKIoJJEQudqhmA3H0HrT6s3PhY3jwvcf2dI0L74ydQg+VvX79WP7Eu/+eth/wCDCD/4ulzruHI+xnUVo/2Jd/8APWw/8GEH/wAXR/Yl3/z1sP8AwYQf/F0+ePcOSXYzqK0f7Eu/+eth/wCDCD/4ug6HdEEGWwIP/UQg/wDi6OePcOSXYy4pop03xSJImcbkYEZp9WbPwu2nweRa/wBnRR5LbRqEHU/8Dqx/Yl3/AM9bD/wYQf8AxdJTVtWDg76IzqK0f7Eu/wDnrYf+DCD/AOLo/sS7/wCeth/4MIP/AIunzx7hyS7GdTDNEJhCZEErDcELDcR64rU/sS7/AOeth/4MIP8A4uq7eFi98l639nG5RSiyf2hBkA/8DpOa6MFB9UVqK0f7Eu/+eth/4MIP/i6P7Eu/+eth/wCDCD/4unzx7hyS7GdRWj/Yl3/z1sP/AAYQf/F0f2Jd/wDPWw/8GEH/AMXRzx7hyS7GZJIkUbSSOqIoyWY4AH1pVZXUMrBlIyCDkEVdufDkt3byW87ae8UgwynUIOR/33TofD09vCkMT6ekaKFVRqEHAH/A6XOr7hyO2xRrs/hn/wAjJcf9ejf+hpXO/wBiXf8Az1sP/BhB/wDF11vw806e01+eSR7VlNqy4iuo5D99OysTj3rOvKLpvU1oRkqi0PS6KKK8c9cK87+Kf/MJ/wC23/sleiV538U/+YT/ANtv/ZK6ML/FX9dDnxX8J/11POqKKK9c8kKKqWEd9GJvt08UpMhMXlrjanYH3q3STuhtWYUUUUxBRRVS6jvnvLVraeJLdWPnoy5Ljtg0m7Alct0UUUwCiiigAopkwkaCQQsqylTsZhkA9qisUuo7KJb2VJbkL+8dBgE0r62HbS5YooopiCiiigAoqoI77+1TIZ4vsPl4EW35t+eufSrdJO4NWCiiimAUUVW1BLySykWwljiuT9x5BkChuyBK7LNFNjDiNRIQXwNxAwCadQAUUUUAFFFVLOO+Se6N3PHJE0mYFRcFV9DSuFi3RRRTAKKKKACiql7HfPJbGznijRZMzB1zuT0FW6VwsFFFFMAoopDnBx17UALRVTTo72O126hNHNPuPzRrgYzxVukndXBqzCiiimAUUVUeO+OqRSJPGLIRkPGV+Yt2INJuw0rluiiimIKKKKACioLxbl7OVbSRI7gr+7dxkA+9Pt1mW3jW4dXmCgOyjAJ74pX1sFtLkldn8M/+RkuP+vRv/Q0rjK7P4Z/8jJcf9ejf+hpWWI/hSNaH8RHq1FFFeMeyFcH8SL2Wz/szykt23+bnzreOXps6bwcde1d5XnfxT/5hP/bb/wBkrfDK9VX/AK0MMS7UnY4v+27v/nlYf+C+D/4ij+27v/nlYf8Agvg/+IrOor1uSPY8rnl3NH+27v8A55WH/gvg/wDiKP7bu/8AnlYf+C+D/wCIrDsNRh1ETGFZV8mQxN5ibckentVukowaukDlJOzZo/23d/8APKw/8F8H/wARR/bd3/zysP8AwXwf/EVnUU+SPYOeXc0f7bu/+eVh/wCC+D/4ij+27v8A55WH/gvg/wDiKzqqXWow2l5a20iyl7liqFVyBj1Pak4wW6BSk9mbn9t3f/PKw/8ABfB/8RR/bd3/AM8rD/wXwf8AxFZ1FPkj2Dnl3NH+27v/AJ5WH/gvg/8AiKP7bu/+eVh/4L4P/iKzqKOSPYOeXc0f7bu/+eVh/wCC+D/4ij+27v8A55WH/gvg/wDiKy5pVggkmYMVRSxCjJwKisbyO/sorqJXWOVdwDjBpcsL2sHNK17mz/bd3/zysP8AwXwf/EUf23d/88rD/wAF8H/xFZ1FPkj2Dnl3NH+27v8A55WH/gvg/wDiKP7bu/8AnlYf+C+D/wCIrOoo5I9g55dzR/tu7/55WH/gvg/+Io/tu7/55WH/AIL4P/iKwxqMJ1U6dtl84R+bu2fLjOOvrVukoweyBykt2aP9t3f/ADysP/BfB/8AEUf23d/88rD/AMF8H/xFZ1FPkj2Dnl3NH+27v/nlYf8Agvg/+Io/tu7/AOeVh/4L4P8A4is6q2oX0Wm2Ul3MsjRx9RGuTQ4xSu0ClJuyZtf23d/88rD/AMF8H/xFH9t3f/PKw/8ABfB/8RWZG4kjV1zhgCMjBp1HJHsHNLuaP9t3f/PKw/8ABfB/8RR/bd3/AM8rD/wXwf8AxFZ1FHJHsHPLuaP9t3f/ADysP/BfB/8AEUf23d/88rD/AMF8H/xFZ1VLPUYb2e6iiWQNbSeW5dcAn2pcsFpYOaW9zc/tu7/55WH/AIL4P/iKP7bu/wDnlYf+C+D/AOIrOop8kewc8u5o/wBt3f8AzysP/BfB/wDEUf23d/8APKw/8F8H/wARWdRRyR7Bzy7mj/bd3/zysP8AwXwf/EUf23d/88rD/wAF8H/xFYd7qMNhJbJKsrG4k8tNi5wferdLlhtYOaW9zR/tu7/55WH/AIL4P/iKP7bu/wDnlYf+C+D/AOIrOop8kewc8u5o/wBt3f8AzysP/BfB/wDEUf23d/8APKw/8F8H/wARWdSE4BPpRyR7Bzy7ml/bd3/zysP/AAXwf/EUf23d/wDPKw/8F8H/AMRWHp2oQ6na/aIFkVNxXEi7TkHFW6SjFq6QOUk7Nmj/AG3d/wDPKw/8F8H/AMRR/bd3/wA8rD/wXwf/ABFZ1FPkj2Dnl3NH+27v/nlYf+C+D/4ij+27v/nlYf8Agvg/+IrOqo+owx6pFp5WTzpIzIGC/LgeppOMFugUpPZm5/bd3/zysP8AwXwf/EUf23d/88rD/wAF8H/xFZ1FPkj2Dnl3NH+27v8A55WH/gvg/wDiKP7bu/8AnlYf+C+D/wCIrOoo5I9g55dzR/tu7/55WH/gvg/+Io/tu7/55WH/AIL4P/iKx7y6jsbOW6lDlIl3MEGTj2p9vOtzbxzoGCyKGAYYOD6ilywvawc0rXuav9t3f/PKw/8ABfB/8RXW/DzUZ7vX545EtVUWrNmK1jjP307qoOPauBrs/hn/AMjJcf8AXo3/AKGlZ14xVN6GtCUnUWp6tRRRXjnrhXB/EhLJ/wCzPtlxcRY83b5MAkz9zOcuuO3rXeV538U/+YT/ANtv/ZK3w38Vf10MMT/CZxfk6L/z/wB//wCASf8Ax2jydF/5/wC//wDAJP8A47WdRXrcr7nlXXY0fJ0X/n/v/wDwCT/47R5Oi/8AP/f/APgEn/x2s6ijlfcLrsaPk6L/AM/9/wD+ASf/AB2jydF/5/7/AP8AAJP/AI7WdRRyvuF12NHydF/5/wC//wDAJP8A47R5Oi/8/wDf/wDgEn/x2s6ijlfcLrsaPk6L/wA/9/8A+ASf/HaPJ0X/AJ/7/wD8Ak/+O1nUUcr7hddjR8nRf+f+/wD/AACT/wCO0eTov/P/AH//AIBJ/wDHazqKOV9wuuxo+Tov/P8A3/8A4BJ/8do8nRf+f+//APAJP/jtZ1FHK+4XXY0fJ0X/AJ/7/wD8Ak/+O0eTov8Az/3/AP4BJ/8AHazqKOV9wuuxo+Tov/P/AH//AIBJ/wDHaPJ0X/n/AL//AMAk/wDjtZ1FHK+4XXY0fJ0X/n/v/wDwCT/47R5Oi/8AP/f/APgEn/x2s6ijlfcLrsaPk6L/AM/9/wD+ASf/AB2jydF/5/7/AP8AAJP/AI7WdRRyvuF12NHydF/5/wC//wDAJP8A47R5Oi/8/wDf/wDgEn/x2s6ijlfcLrsaPk6L/wA/9/8A+ASf/HaPJ0X/AJ/7/wD8Ak/+O1nUUcr7hddjR8nRf+f+/wD/AACT/wCO0eTov/P/AH//AIBJ/wDHazqKOV9wuuxo+Tov/P8A3/8A4BJ/8do8nRf+f+//APAJP/jtZ1FHK+4XXY0fJ0X/AJ/7/wD8Ak/+O0eTov8Az/3/AP4BJ/8AHazqKOV9wuuxo+Tov/P/AH//AIBJ/wDHaPJ0X/n/AL//AMAk/wDjtZ1FHK+4XXY0fJ0X/n/v/wDwCT/47R5Oi/8AP/f/APgEn/x2s6ijlfcLrsaPk6L/AM/9/wD+ASf/AB2jydF/5/7/AP8AAJP/AI7WdRRyvuF12NHydF/5/wC//wDAJP8A47R5Oi/8/wDf/wDgEn/x2s6ijlfcLrsaPk6L/wA/9/8A+ASf/HaPJ0X/AJ/7/wD8Ak/+O1nUUcr7hddjR8nRf+f+/wD/AACT/wCO0eTov/P/AH//AIBJ/wDHazqKOV9wuuxo+Tov/P8A3/8A4BJ/8do8nRf+f+//APAJP/jtZ1FHK+4XXY0fJ0X/AJ/7/wD8Ak/+O0eTov8Az/3/AP4BJ/8AHazqKOV9wuuxo+Tov/P/AH//AIBJ/wDHaPJ0X/n/AL//AMAk/wDjtZ1FHK+4XXY0fJ0X/n/v/wDwCT/47R5Oi/8AP/f/APgEn/x2s6ijlfcLrsaPk6L/AM/9/wD+ASf/AB2ut+Hkenpr85tLq6lk+ytlZbdYxjenOQ7c9O1cDXZ/DP8A5GS4/wCvRv8A0NKyrp+zeprQa9otD1aiiivHPXCuD+JGn3t9/Zn2OzuLjZ5u7yYy+3OzGcDjoa7yirpz9nJSRFSHPFxZ4P8A8I/rX/QIv/8AwGf/AAo/4R/Wv+gRf/8AgM/+Fe8UV1/Xpdjl+pR7nz5YeDtU04TCHStUbzpDK3mQu2CfTjpVv/hH9a/6BF//AOAz/wCFe8UUljWlZRG8Gm7tng//AAj+tf8AQIv/APwGf/Cj/hH9a/6BF/8A+Az/AOFe8UU/r0uwvqUe54P/AMI/rX/QIv8A/wABn/wqpdeDtUu7y1uZNK1QPbMWQLA4Bz6jHNfQdFJ41vdAsGlszwf/AIR/Wv8AoEX/AP4DP/hR/wAI/rX/AECL/wD8Bn/wr3iin9el2D6lHueD/wDCP61/0CL/AP8AAZ/8KP8AhH9a/wCgRf8A/gM/+Fe8UUfXpdg+pR7ngk3hrWJ4JIW0nUQrqVJW3cHB/CorHwpq1hZRWsWlak0cS7QXt3J/lX0BRS+uu97D+pq1rng//CP61/0CL/8A8Bn/AMKP+Ef1r/oEX/8A4DP/AIV7xRT+vS7C+pR7ng//AAj+tf8AQIv/APwGf/Cj/hH9a/6BF/8A+Az/AOFe8UUfXpdg+pR7nz4PB2qDVTqP9lap5xj8rb5L7cZz0x1q3/wj+tf9Ai//APAZ/wDCveKKSxrW0QeDT3Z4P/wj+tf9Ai//APAZ/wDCj/hH9a/6BF//AOAz/wCFe8UU/r0uwfUo9zwf/hH9a/6BF/8A+Az/AOFVtQ8I6rqVlJaTaVqaxydTHA4P8q+gaKTxras0CwaTumeCx+HNYjjVF0jUMKABm3cn+VO/4R/Wv+gRf/8AgM/+Fe8UUfXZdg+pR7ng/wDwj+tf9Ai//wDAZ/8ACj/hH9a/6BF//wCAz/4V7xRT+vS7B9Sj3PB/+Ef1r/oEX/8A4DP/AIVUs/B2qWU91LFpWqFrmTzHDwOQD7cV9B0Uvrretg+pra54P/wj+tf9Ai//APAZ/wDCj/hH9a/6BF//AOAz/wCFe8UU/r0uwfUo9zwf/hH9a/6BF/8A+Az/AOFH/CP61/0CL/8A8Bn/AMK94oo+vS7B9Sj3Pny98HapfyWzy6Vqim3k8xNkDjJ9+Kt/8I/rX/QIv/8AwGf/AAr3iil9de9g+pra54P/AMI/rX/QIv8A/wABn/wo/wCEf1r/AKBF/wD+Az/4V7xRT+vS7B9Sj3PB/wDhH9a/6BF//wCAz/4UHw9rJBH9kahz/wBOz/4V7xRR9el2D6lHufPmneD9U0y1+zwaVqbJuLZkgdjknPpVv/hH9a/6BF//AOAz/wCFe8UUljWlZIHg03ds8H/4R/Wv+gRf/wDgM/8AhR/wj+tf9Ai//wDAZ/8ACveKKf16XYPqUe54P/wj+tf9Ai//APAZ/wDCqj+DtUk1SLUDpWqedHGYwogfbg+oxX0HRSeNb3Q1g0tmeD/8I/rX/QIv/wDwGf8Awo/4R/Wv+gRf/wDgM/8AhXvFFP69LsL6lHueD/8ACP61/wBAi/8A/AZ/8KP+Ef1r/oEX/wD4DP8A4V7xRR9el2D6lHueAXnhXVr6zltZdJ1IJKu1ilu4OPbin2/hnV7a3jgTSdRKxqFBa3cnA9TivfKKX113vYPqata54P8A8I/rX/QIv/8AwGf/AArrfh5peoWWvzyXdjdQRm1ZQ0sLICd6cZI68GvS6KmeLlOLjYqGEjCSlcKKKK5DrCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooA/9k=\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "44"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 158
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EsG-dw7RJ7iR"
      },
      "source": [
        "# @title Hyperparams\n",
        "total_episodes = 10000 #@param {type:\"integer\"}\n",
        "max_step = 150 #@param {type:\"integer\"}\n",
        "gamma = 0.95 #@param {type:\"number\"}\n",
        "max_alpha = 0.99 #@param {type:\"number\"}\n",
        "min_alpha = 0.0001 #@param {type:\"number\"}\n",
        "max_epsilon =  0.99#@param {type:\"number\"}\n",
        "min_epsilon = 0.0001 #@param {type:\"number\"}\n",
        "decay_rate =  0.0005#@param {type:\"number\"}"
      ],
      "execution_count": 136,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 541
        },
        "id": "FV5ookUJaOnF",
        "outputId": "2f5ff9f9-5ab8-40ec-8364-2115a0ab827d"
      },
      "source": [
        "# @title Check decay rates\n",
        "episodes = np.array(range(total_episodes))\n",
        "plt.plot(episodes,\n",
        "         min_epsilon + (max_epsilon - min_epsilon) * np.exp(-decay_rate * episodes), color='red')\n",
        "    \n",
        "plt.xlabel(\"iteration\")\n",
        "plt.ylabel(\"epsilon\")\n",
        "plt.show()\n",
        "\n",
        "episodes = np.array(range(total_episodes))\n",
        "plt.plot(episodes,\n",
        "         min_alpha + (max_alpha - min_alpha) * np.exp(-decay_rate * episodes), color='blue')\n",
        "    \n",
        "plt.xlabel(\"iteration\")\n",
        "plt.ylabel(\"alpha\")\n",
        "plt.show()"
      ],
      "execution_count": 137,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QNwN-KDkiVjI"
      },
      "source": [
        "# @title Epsilon Greedy Policy\n",
        "def epsilon_greedy(epsilon, best_action):\n",
        "  p = [epsilon / env.action_space.n] * env.action_space.n\n",
        "  p[best_action] += (1-epsilon)\n",
        "  return np.array(p)"
      ],
      "execution_count": 138,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AT9wHzC3aVaL"
      },
      "source": [
        "# @title Episode Generation\n",
        "def episode_generation(policy=None, Q=None, epsilon=None):\n",
        "  episode = []\n",
        "  state = env.reset()\n",
        "  step = 0\n",
        "\n",
        "  while step < max_step: # end of the episode\n",
        "    if policy is None: # behave greedy\n",
        "      p = epsilon_greedy(epsilon, np.argmax(Q))\n",
        "    else:\n",
        "      p = policy[state, :]\n",
        "    action = np.random.choice(env.action_space.n, p=p)\n",
        "    next_state, reward, done, info = env.step(action)\n",
        "    episode.append((state, action, reward))\n",
        "    \n",
        "    state = next_state\n",
        "    step += 1\n",
        "    if reward == 10.0:\n",
        "      break\n",
        "  \n",
        "  return episode, step"
      ],
      "execution_count": 139,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iHeszEtXqV5M"
      },
      "source": [
        "# @title Show Solution\n",
        "def show_solution(Q):\n",
        "  outfile = sys.stdout\n",
        "  solution = np.argmax(Q, axis=1).reshape(10, 10)\n",
        "  for i in range(solution.shape[0]):\n",
        "    for j in range(solution.shape[1]):\n",
        "      if solution[i, j] == 0:\n",
        "        output = Fore.GREEN + \" ↑ \"\n",
        "      elif solution[i, j] == 1:\n",
        "        output = Fore.RED + \" → \"\n",
        "      elif solution[i, j] == 2:\n",
        "        output = Fore.BLACK + \" ↓ \"\n",
        "      else:\n",
        "        output = Fore.BLUE + \" ← \"\n",
        "      outfile.write(output)\n",
        "    outfile.write(\"\\n\")\n",
        "    "
      ],
      "execution_count": 140,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cDWsRH1xHi3L"
      },
      "source": [
        "# @title Plot Function\r\n",
        "def plot(x, y, color, yscale, xlabel, ylabel, title, moving_avg=False, W=512):\r\n",
        "  if moving_avg:\r\n",
        "    y = np.convolve(y, np.ones(W), 'valid') / W\r\n",
        "    x = x[:len(y)]\r\n",
        "  plt.plot(x, y, color=color)\r\n",
        "  plt.yscale(yscale)\r\n",
        "  plt.xlabel(xlabel)\r\n",
        "  plt.ylabel(ylabel)\r\n",
        "  plt.title(title)\r\n",
        "  plt.show()"
      ],
      "execution_count": 141,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "skHNIqnNZXds"
      },
      "source": [
        "## On-policy first-visit Monte Carlo"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "LJPVTsKpZcxF",
        "outputId": "f4b5ad92-8f56-4da0-f862-aca695ff5769"
      },
      "source": [
        "policy = np.ones((env.observation_space.n, env.action_space.n)) / env.action_space.n\n",
        "Q = np.zeros((env.observation_space.n, env.action_space.n))\n",
        "returns = collections.defaultdict(float)\n",
        "state_actions_count = collections.defaultdict(int)\n",
        "on_policy_mc_episode_rewards = []\n",
        "on_policy_mc_episode_steps = []\n",
        "\n",
        "for iter in range(total_episodes):\n",
        "  epsilon = min_epsilon + (max_epsilon - min_epsilon) * np.exp(-decay_rate * iter) \n",
        "  alpha = min_alpha + (max_alpha - min_alpha) * np.exp(-decay_rate * iter)\n",
        "\n",
        "  episode, episode_steps = episode_generation(policy=policy)\n",
        "  G = 0\n",
        "\n",
        "  state_actions = [(s, a) for (s, a, r) in episode]\n",
        "  episode_reward = np.sum([r for (s, a, r) in episode])\n",
        "\n",
        "  for t, (state, action, reward) in reversed(list(enumerate(episode))):\n",
        "    G = gamma * G + reward\n",
        "    if not (state, action) in state_actions[0:t]:\n",
        "      returns[(state, action)] += G\n",
        "      state_actions_count[(state, action)] += 1\n",
        "      Q[state, action] = returns[(state, action)] / state_actions_count[(state, action)]\n",
        "\n",
        "      A = np.argmax(Q[state], axis=0)\n",
        "      for a in range(env.action_space.n):\n",
        "        if a == A:\n",
        "          policy[state, a] = 1 - epsilon + epsilon / env.action_space.n\n",
        "        else:\n",
        "          policy[state, a] = epsilon / env.action_space.n\n",
        "\n",
        "  on_policy_mc_episode_rewards.append(episode_reward)\n",
        "  on_policy_mc_episode_steps.append(episode_steps)\n",
        "\n",
        "\n",
        "# Plotting Sum of rewards during episode\n",
        "plot(x=np.array(range(total_episodes)), y=on_policy_mc_episode_rewards, color=\"orange\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"Sum of rewards during episode\", title=\"On-policy first-visit Monte Carlo\", moving_avg=True)\n",
        "# Plotting the number of steps during episode\n",
        "plot(x=np.array(range(total_episodes)), y=on_policy_mc_episode_steps, color=\"orange\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"The number of steps during episode\", title=\"On-policy first-visit Monte Carlo\", moving_avg=True)"
      ],
      "execution_count": 142,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IFW4BFfpqNRD",
        "outputId": "45fffa2e-b329-4680-9f2f-439713d47bd4"
      },
      "source": [
        "show_solution(Q)"
      ],
      "execution_count": 143,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[34m ← \u001b[30m ↓ \u001b[30m ↓ \u001b[31m → \u001b[31m → \u001b[30m ↓ \u001b[30m ↓ \u001b[31m → \u001b[31m → \u001b[32m ↑ \n",
            "\u001b[30m ↓ \u001b[30m ↓ \u001b[30m ↓ \u001b[30m ↓ \u001b[31m → \u001b[30m ↓ \u001b[31m → \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \n",
            "\u001b[30m ↓ \u001b[30m ↓ \u001b[30m ↓ \u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[31m → \u001b[34m ← \u001b[31m → \u001b[30m ↓ \u001b[31m → \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[31m → \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G_wIN9RetPt7"
      },
      "source": [
        "## Off-policy Monte Carlo"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "c9pXpcvEtPuC",
        "outputId": "e998bb7c-0197-47b5-afb7-309a81c678ab"
      },
      "source": [
        "Q = np.zeros((env.observation_space.n, env.action_space.n))\n",
        "C = np.zeros((env.observation_space.n, env.action_space.n))\n",
        "off_policy_mc_episode_rewards = []\n",
        "off_policy_mc_episode_steps = []\n",
        "\n",
        "for iter in range(total_episodes):\n",
        "  epsilon = min_epsilon + (max_epsilon - min_epsilon) * np.exp(-decay_rate * iter) \n",
        "  alpha = min_alpha + (max_alpha - min_alpha) * np.exp(-decay_rate * iter)\n",
        "  \n",
        "  b = np.ones((env.observation_space.n, env.action_space.n)) / env.action_space.n\n",
        "  # using epsilon policy based on Q \n",
        "  episode, episode_steps = episode_generation(policy=None, Q=Q, epsilon=epsilon) \n",
        "  # episode, episode_steps = episode_generation(policy=b) \n",
        "  G = 0\n",
        "  W = 1\n",
        "\n",
        "  episode_reward = np.sum([r for (s, a, r) in episode])\n",
        "\n",
        "  for t, (state, action, reward) in reversed(list(enumerate(episode))):\n",
        "    G = gamma * G + reward\n",
        "    C[state, action] = C[state, action] + W\n",
        "    Q[state, action] = Q[state, action] + (W / C[state, action]) * (G - Q[state, action])\n",
        "\n",
        "    if action != np.argmax(Q[state]):\n",
        "      break\n",
        "    \n",
        "    W = W * (1 / b[state, action])\n",
        "\n",
        "\n",
        "  off_policy_mc_episode_rewards.append(episode_reward)\n",
        "  off_policy_mc_episode_steps.append(episode_steps)\n",
        "\n",
        "\n",
        "# Plotting Sum of rewards during episode\n",
        "plot(x=np.array(range(total_episodes)), y=off_policy_mc_episode_rewards, color=\"c\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"Sum of rewards during episode\", title=\"Off-policy Monte Carlo\", moving_avg=True)\n",
        "# Plotting the number of steps during episode\n",
        "plot(x=np.array(range(total_episodes)), y=off_policy_mc_episode_steps, color=\"c\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"The number of steps during episode\", title=\"Off-policy Monte Carlo\", moving_avg=True)\n"
      ],
      "execution_count": 144,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OgvUnyY7tPuF",
        "outputId": "43a2e2b5-e978-4b6f-cfcf-3e85541712ce"
      },
      "source": [
        "show_solution(Q)"
      ],
      "execution_count": 145,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[31m → \u001b[30m ↓ \u001b[30m ↓ \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[31m → \u001b[31m → \u001b[34m ← \u001b[31m → \u001b[31m → \u001b[31m → \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \u001b[30m ↓ \u001b[31m → \u001b[34m ← \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[34m ← \u001b[30m ↓ \u001b[30m ↓ \u001b[31m → \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[30m ↓ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \n",
            "\u001b[31m → \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \u001b[34m ← \u001b[30m ↓ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[30m ↓ \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \u001b[31m → \u001b[30m ↓ \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[30m ↓ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[30m ↓ \u001b[30m ↓ \u001b[32m ↑ \u001b[32m ↑ \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lMgw-jo928gL"
      },
      "source": [
        "##Double Q-learning"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "Ili0hfgo2i0O",
        "outputId": "ce146289-5e8c-4392-b0f3-1f1454dd82bf"
      },
      "source": [
        "Q_1 = np.zeros((env.observation_space.n, env.action_space.n))\n",
        "Q_2 = np.zeros((env.observation_space.n, env.action_space.n))\n",
        "double_qlearning_episode_rewards = []\n",
        "double_qlearning_episode_steps = []\n",
        "\n",
        "for iter in range(total_episodes):\n",
        "  epsilon = min_epsilon + (max_epsilon - min_epsilon) * np.exp(-decay_rate * iter) \n",
        "  alpha = min_alpha + (max_alpha - min_alpha) * np.exp(-decay_rate * iter)\n",
        "  state = env.reset()\n",
        "\n",
        "  episode_reward = 0\n",
        "  step = 0\n",
        "  while step < max_step: # end of the episode\n",
        "    \n",
        "    action = np.random.choice(env.action_space.n, p=epsilon_greedy(epsilon, np.argmax(Q_1[state] + Q_2[state])))\n",
        "    next_state, reward, done, info = env.step(action)\n",
        "\n",
        "    if np.random.uniform(0,1) < 0.5:\n",
        "      G = reward + gamma * Q_2[next_state, np.argmax(Q_1[next_state], axis=0)]\n",
        "      Q_1[state, action] = Q_1[state, action] + alpha * (G - Q_1[state, action])\n",
        "    else:\n",
        "      G = reward + gamma * Q_1[next_state, np.argmax(Q_2[next_state], axis=0)]\n",
        "      Q_2[state, action] = Q_2[state, action] + alpha * (G - Q_2[state, action])\n",
        "\n",
        "    state = next_state\n",
        "    episode_reward += reward\n",
        "    step += 1\n",
        "    if reward == 10.0:\n",
        "      break\n",
        "\n",
        "  double_qlearning_episode_rewards.append(episode_reward)\n",
        "  double_qlearning_episode_steps.append(step)\n",
        "\n",
        "\n",
        "# Plotting Sum of rewards during episode\n",
        "plot(x=np.array(range(total_episodes)), y=double_qlearning_episode_rewards, color=\"r\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"Sum of rewards during episode\", title=\"Double Q-learning\", moving_avg=True)\n",
        "# Plotting the number of steps during episode\n",
        "plot(x=np.array(range(total_episodes)), y=double_qlearning_episode_steps, color=\"r\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"The number of steps during episode\", title=\"Double Q-learning\", moving_avg=True)\n"
      ],
      "execution_count": 146,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3GsSjPd82i0R",
        "outputId": "9d30c7a0-5546-4a65-cca0-fadd4a2a98b2"
      },
      "source": [
        "show_solution(Q_1)"
      ],
      "execution_count": 147,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[34m ← \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[31m → \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oJelUcFntdCU",
        "outputId": "90e0b37d-11e2-47a3-d4d4-be86485d931f"
      },
      "source": [
        "show_solution(Q_2)"
      ],
      "execution_count": 148,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[30m ↓ \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Se-jhW619TPq"
      },
      "source": [
        "## 2-Step Tree Back-up"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "gyQ9d4FD9VTu",
        "outputId": "169478c7-df31-4da2-a316-e64982c3f62c"
      },
      "source": [
        "Q = np.zeros((env.observation_space.n, env.action_space.n))\n",
        "two_step_tree_backup_episode_rewards = []\n",
        "two_step_tree_backup_episode_steps = []\n",
        "\n",
        "for iter in range(total_episodes):\n",
        "  epsilon = min_epsilon + (max_epsilon - min_epsilon) * np.exp(-decay_rate * iter) \n",
        "  alpha = min_alpha + (max_alpha - min_alpha) * np.exp(-decay_rate * iter)\n",
        "  \n",
        "  state = env.reset()\n",
        "  action = np.random.choice(env.action_space.n, p=epsilon_greedy(epsilon, np.argmax(Q[state])))\n",
        "  next_state_1, reward_1, done_1, info_1 = env.step(action)\n",
        "  p=epsilon_greedy(epsilon, np.argmax(Q[next_state_1]))\n",
        "  next_action_1 = np.random.choice(env.action_space.n, p=p)\n",
        "\n",
        "  episode_reward = 0\n",
        "  step = 0\n",
        "  while step < max_step: # end of the episode\n",
        "\n",
        "    next_state_2, reward_2, done_2, info_2 = env.step(next_action_1)\n",
        "    next_action_2 = np.random.choice(env.action_space.n, p=epsilon_greedy(epsilon, np.argmax(Q[next_state_2])))\n",
        "\n",
        "    p_1 = epsilon_greedy(epsilon, np.argmax(Q[next_state_1]))\n",
        "    p_2 = epsilon_greedy(epsilon, np.argmax(Q[next_state_2]))\n",
        "\n",
        "    G = reward_1 + gamma * np.sum(p_1[p_1 != next_action_1] * Q[next_state_1][p_1 != next_action_1]) + gamma * p_1[next_action_1] * (reward_2 + gamma * np.sum(p_2 * Q[next_state_2]))\n",
        "\n",
        "    Q[state, action] = Q[state, action] + alpha * (G - Q[state, action])\n",
        "\n",
        "    \n",
        "    state = next_state_1\n",
        "    next_state_1 = next_state_2\n",
        "    next_action_1 = next_action_2\n",
        "    reward_1 = reward_2\n",
        "    episode_reward += reward_2\n",
        "    step += 1\n",
        "    if reward_2 == 10.0:\n",
        "      break\n",
        "\n",
        "  two_step_tree_backup_episode_rewards.append(episode_reward)\n",
        "  two_step_tree_backup_episode_steps.append(step)\n",
        "\n",
        "# Plotting Sum of rewards during episode\n",
        "plot(x=np.array(range(total_episodes)), y=two_step_tree_backup_episode_rewards, color=\"g\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"Sum of rewards during episode\", title=\"2-Step Tree Back-up\", moving_avg=True)\n",
        "# Plotting the number of steps during episode\n",
        "plot(x=np.array(range(total_episodes)), y=two_step_tree_backup_episode_steps, color=\"g\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"The number of steps during episode\", title=\"2-Step Tree Back-up\", moving_avg=True)\n"
      ],
      "execution_count": 149,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Yr0tN1zq9U6_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eb393f23-22d2-47ef-a2d2-fcdd3c26ba7d"
      },
      "source": [
        "show_solution(Q)"
      ],
      "execution_count": 150,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[30m ↓ \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[30m ↓ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[30m ↓ \n",
            "\u001b[34m ← \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[31m → \u001b[31m → \u001b[31m → \u001b[30m ↓ \n",
            "\u001b[34m ← \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[30m ↓ \u001b[32m ↑ \u001b[30m ↓ \u001b[30m ↓ \n",
            "\u001b[34m ← \u001b[30m ↓ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[30m ↓ \u001b[34m ← \u001b[30m ↓ \u001b[30m ↓ \u001b[30m ↓ \n",
            "\u001b[32m ↑ \u001b[30m ↓ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[30m ↓ \u001b[30m ↓ \u001b[32m ↑ \n",
            "\u001b[30m ↓ \u001b[30m ↓ \u001b[30m ↓ \u001b[30m ↓ \u001b[30m ↓ \u001b[34m ← \u001b[30m ↓ \u001b[34m ← \u001b[30m ↓ \u001b[30m ↓ \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[30m ↓ \u001b[34m ← \u001b[34m ← \u001b[31m → \u001b[34m ← \u001b[34m ← \u001b[30m ↓ \n",
            "\u001b[30m ↓ \u001b[34m ← \u001b[30m ↓ \u001b[30m ↓ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \u001b[30m ↓ \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[30m ↓ \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[30m ↓ \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xolgpN-H2tOQ"
      },
      "source": [
        "##SARSA"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "FshLVK1EcGJ3",
        "outputId": "aad3c02b-25be-47ba-a88d-d46ea2ff77c8"
      },
      "source": [
        "Q = np.zeros((env.observation_space.n, env.action_space.n))\n",
        "v = np.zeros(env.observation_space.n)\n",
        "sarsa_episode_rewards = []\n",
        "sarsa_episode_steps = []\n",
        "\n",
        "for iter in range(total_episodes):\n",
        "  epsilon = min_epsilon + (max_epsilon - min_epsilon) * np.exp(-decay_rate * iter) \n",
        "  alpha = min_alpha + (max_alpha - min_alpha) * np.exp(-decay_rate * iter)\n",
        "\n",
        "  state = env.reset()\n",
        "  action = np.random.choice(env.action_space.n, p=epsilon_greedy(epsilon, np.argmax(Q[state])))\n",
        "\n",
        "  episode_reward = 0\n",
        "  step = 0\n",
        "  while step < max_step: # end of the episode\n",
        "    \n",
        "    next_state, reward, done, info = env.step(action)\n",
        "    next_action = np.random.choice(env.action_space.n, p=epsilon_greedy(epsilon, np.argmax(Q[next_state])))\n",
        "\n",
        "    G = reward + gamma * Q[next_state, next_action]\n",
        "    Q[state, action] = Q[state, action] + alpha * (G - Q[state, action])\n",
        "    v[state]+=1\n",
        "\n",
        "    state = next_state\n",
        "    action = next_action\n",
        "    episode_reward += reward\n",
        "    step += 1\n",
        "    if reward == 10.0:\n",
        "      break\n",
        "\n",
        "  sarsa_episode_rewards.append(episode_reward)\n",
        "  sarsa_episode_steps.append(step)\n",
        "\n",
        "# Plotting Sum of rewards during episode\n",
        "plot(x=np.array(range(total_episodes)), y=sarsa_episode_rewards, color=\"b\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"Sum of rewards during episode\", title=\"SARSA\", moving_avg=True)\n",
        "# Plotting the number of steps during episode\n",
        "plot(x=np.array(range(total_episodes)), y=sarsa_episode_steps, color=\"b\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"The number of steps during episode\", title=\"SARSA\", moving_avg=True)\n"
      ],
      "execution_count": 151,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BomyVo_3owty",
        "outputId": "40814c72-b010-4dbe-c9f3-c74a8edbf234"
      },
      "source": [
        "show_solution(Q)"
      ],
      "execution_count": 152,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[34m ← \u001b[34m ← \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \n",
            "\u001b[30m ↓ \u001b[32m ↑ \u001b[30m ↓ \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[31m → \u001b[30m ↓ \u001b[30m ↓ \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[34m ← \n",
            "\u001b[34m ← \u001b[34m ← \u001b[31m → \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[32m ↑ \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qJWxXjG_2zLj"
      },
      "source": [
        "##2-Step Expected SARSA"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "-U1ujTP6p6px",
        "outputId": "81a6c0ce-61cc-469f-98fc-7fad874e85aa"
      },
      "source": [
        "Q = np.zeros((env.observation_space.n, env.action_space.n))\n",
        "two_step_expected_sarsa_episode_rewards = []\n",
        "two_step_expected_sarsa_episode_steps = []\n",
        "\n",
        "for iter in range(total_episodes):\n",
        "  epsilon = min_epsilon + (max_epsilon - min_epsilon) * np.exp(-decay_rate * iter) \n",
        "  alpha = min_alpha + (max_alpha - min_alpha) * np.exp(-decay_rate * iter)\n",
        "  \n",
        "  state = env.reset()\n",
        "  action = np.random.choice(env.action_space.n, p=epsilon_greedy(epsilon, np.argmax(Q[state])))\n",
        "  next_state_1, reward_1, done_1, info_1 = env.step(action)\n",
        "  p=epsilon_greedy(epsilon, np.argmax(Q[next_state_1]))\n",
        "  next_action_1 = np.random.choice(env.action_space.n, p=p)\n",
        "\n",
        "  episode_reward = 0\n",
        "  step = 0\n",
        "  while step < max_step: # end of the episode\n",
        "\n",
        "    next_state_2, reward_2, done_2, info_2 = env.step(next_action_1)\n",
        "    next_action_2 = np.random.choice(env.action_space.n, p=epsilon_greedy(epsilon, np.argmax(Q[next_state_2])))\n",
        "\n",
        "    p = epsilon_greedy(epsilon, np.argmax(Q[next_state_2]))\n",
        "    G = reward_1 + gamma * reward_2 + np.square(gamma) * np.sum(p * Q[next_state_2, :])\n",
        "    Q[state, action] = Q[state, action] + alpha * (G - Q[state, action])\n",
        "\n",
        "    state = next_state_1\n",
        "    next_state_1 = next_state_2\n",
        "    next_action_1 = next_action_2\n",
        "    reward_1 = reward_2\n",
        "    episode_reward += reward_2\n",
        "    step += 1\n",
        "    if reward_2 == 10.0:\n",
        "      break\n",
        "\n",
        "  two_step_expected_sarsa_episode_rewards.append(episode_reward)\n",
        "  two_step_expected_sarsa_episode_steps.append(step)\n",
        "\n",
        "# Plotting Sum of rewards during episode\n",
        "plot(x=np.array(range(total_episodes)), y=two_step_expected_sarsa_episode_rewards, color=\"m\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"Sum of rewards during episode\", title=\"2-Step Expected SARSA\", moving_avg=True)\n",
        "# Plotting the number of steps during episode\n",
        "plot(x=np.array(range(total_episodes)), y=two_step_expected_sarsa_episode_steps, color=\"m\", yscale=\"linear\", xlabel=\"Episodes\", ylabel=\"The number of steps during episode\", title=\"2-Step Expected SARSA\", moving_avg=True)\n"
      ],
      "execution_count": 153,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GassXp1UzqBR",
        "outputId": "4e1c6e37-42b9-43a3-f171-893cf95e2602"
      },
      "source": [
        "show_solution(Q)"
      ],
      "execution_count": 154,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[32m ↑ \u001b[30m ↓ \u001b[34m ← \u001b[31m → \u001b[34m ← \u001b[34m ← \u001b[30m ↓ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \n",
            "\u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[34m ← \u001b[31m → \u001b[32m ↑ \u001b[34m ← \n",
            "\u001b[30m ↓ \u001b[30m ↓ \u001b[34m ← \u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[30m ↓ \u001b[30m ↓ \u001b[30m ↓ \n",
            "\u001b[30m ↓ \u001b[34m ← \u001b[30m ↓ \u001b[32m ↑ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[30m ↓ \u001b[34m ← \u001b[34m ← \n",
            "\u001b[30m ↓ \u001b[32m ↑ \u001b[30m ↓ \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[30m ↓ \u001b[34m ← \u001b[34m ← \u001b[34m ← \n",
            "\u001b[32m ↑ \u001b[31m → \u001b[30m ↓ \u001b[32m ↑ \u001b[32m ↑ \u001b[31m → \u001b[30m ↓ \u001b[32m ↑ \u001b[30m ↓ \u001b[34m ← \n",
            "\u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[31m → \u001b[30m ↓ \u001b[30m ↓ \n",
            "\u001b[34m ← \u001b[32m ↑ \u001b[30m ↓ \u001b[30m ↓ \u001b[32m ↑ \u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[30m ↓ \n",
            "\u001b[34m ← \u001b[34m ← \u001b[34m ← \u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[30m ↓ \u001b[34m ← \u001b[30m ↓ \n",
            "\u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[31m → \u001b[30m ↓ \u001b[34m ← \u001b[30m ↓ \u001b[30m ↓ \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7HAaY2g3EVCN"
      },
      "source": [
        "## Comparison"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "rVe0o9L0EWdr",
        "outputId": "5790b227-70bd-4a3e-c930-06764911ed65"
      },
      "source": [
        "# @title Comparison of sum of reward\n",
        "W = 512\n",
        "episodes = np.array(range(total_episodes))\n",
        "episodes = episodes[:len(episodes)-W+1]\n",
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "ax.plot(episodes, np.convolve(on_policy_mc_episode_rewards, np.ones(W), 'valid') / W, color=\"orange\", label='On-policy Monte-Carlo')\n",
        "ax.plot(episodes, np.convolve(off_policy_mc_episode_rewards, np.ones(W), 'valid') / W, color=\"c\", label='Off-policy Monte-Carlo')\n",
        "ax.plot(episodes, np.convolve(double_qlearning_episode_rewards, np.ones(W), 'valid') / W, color=\"r\", label='Double Q-learning')\n",
        "ax.plot(episodes, np.convolve(sarsa_episode_rewards, np.ones(W), 'valid') / W, color=\"b\", label='SARSA')\n",
        "ax.plot(episodes, np.convolve(two_step_expected_sarsa_episode_rewards, np.ones(W), 'valid') / W, color=\"m\", label='Two-Step Expected SARSA')\n",
        "ax.plot(episodes, np.convolve(two_step_tree_backup_episode_rewards, np.ones(W), 'valid') / W, color=\"g\", label='Two-Step Tree Back-up')\n",
        "\n",
        "legend = ax.legend()\n",
        "plt.yscale(\"symlog\")\n",
        "plt.xlabel(\"Episodes\")\n",
        "plt.ylabel(\"Sum of rewards during episode\")\n",
        "plt.title(\"Comparison of algorithms w.r.t. sum of rewards\")\n",
        "plt.show()"
      ],
      "execution_count": 155,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "n1J5xwBQdIZw",
        "outputId": "f2a91d38-7da2-4515-8695-9d0eb8b98724"
      },
      "source": [
        "# @title Comparison of number of steps\r\n",
        "W = 64\r\n",
        "episodes = np.array(range(total_episodes))\r\n",
        "episodes = episodes[:len(episodes)-W+1]\r\n",
        "fig, ax = plt.subplots(figsize=(12,8))\r\n",
        "ax.plot(episodes, np.convolve(on_policy_mc_episode_steps, np.ones(W), 'valid') / W, color=\"orange\", label='On-policy Monte-Carlo')\r\n",
        "ax.plot(episodes, np.convolve(off_policy_mc_episode_steps, np.ones(W), 'valid') / W, color=\"c\", label='Off-policy Monte-Carlo')\r\n",
        "ax.plot(episodes, np.convolve(double_qlearning_episode_steps, np.ones(W), 'valid') / W, color=\"r\", label='Double Q-learning')\r\n",
        "ax.plot(episodes, np.convolve(sarsa_episode_steps, np.ones(W), 'valid') / W, color=\"b\", label='SARSA')\r\n",
        "ax.plot(episodes, np.convolve(two_step_expected_sarsa_episode_steps, np.ones(W), 'valid') / W, color=\"m\", label='Two-Step Expected SARSA')\r\n",
        "ax.plot(episodes, np.convolve(two_step_tree_backup_episode_steps, np.ones(W), 'valid') / W, color=\"g\", label='Two-Step Tree Back-up')\r\n",
        "\r\n",
        "legend = ax.legend()\r\n",
        "plt.xlabel(\"Episodes\")\r\n",
        "plt.ylabel(\"The number of steps during episode\")\r\n",
        "plt.title(\"Comparison of algorithms w.r.t. number of steps\")\r\n",
        "plt.show()"
      ],
      "execution_count": 156,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}