Gridworld_RL.ipynb

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  "metadata": {
    "colab": {
      "name": "Gridworld_RL.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyO1r7FptYii823Q1c7g4aXd",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/samuel-gerstein/gridworld-RL/blob/main/Gridworld_Reinforcement_Learning.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Three Algorithms:\n",
        "\n",
        "\n",
        "*   Q-Learning\n",
        "*   Double Q-Learning\n",
        "*   SARSA(λ)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "2W_WnGIvosfC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Creating Gridworld using OpenAI Gym"
      ],
      "metadata": {
        "id": "OQVAbdg2JvM1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import gym\n",
        "import random\n",
        "import numpy as np\n",
        "import statistics"
      ],
      "metadata": {
        "id": "E6UcHwzOKShN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "custom_map = [\n",
        "    'SFF', #S is initial point of agent\n",
        "    'FFF', #F is safe frozen ice\n",
        "    'FFG'  #G is goal (reward = 1)\n",
        "]"
      ],
      "metadata": {
        "id": "eXOwimfJUGpU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "env = gym.make(\"FrozenLake-v0\", is_slippery = False, desc = custom_map).env\n",
        "env.reset()\n",
        "env.render()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O9ZxFIApJ8km",
        "outputId": "5d874663-db66-44c4-8a92-fdacb3744637"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\u001b[41mS\u001b[0mFF\n",
            "FFF\n",
            "FFG\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Action Mapping:\n",
        "*   0 - Left\n",
        "*   1 - Down\n",
        "*   2 - Right\n",
        "*   3 - Up"
      ],
      "metadata": {
        "id": "ARASeEWQSDiP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Ground Truth V-Table for gamma = 0.8\n",
        "true_v = np.array([0.512, 0.64   , 0.512   , 0.64 , 0.8   , 0.64   , 0.8  , 1.   , 0.   ])\n",
        "true_v.reshape((3,3))\n",
        "\n",
        "#Need to calculate q table by hand because some states go unexplored"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MNjI8w4r3koV",
        "outputId": "9e01a6d0-7d03-4582-ff3c-7e7aeef055b7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.512, 0.64 , 0.512],\n",
              "       [0.64 , 0.8  , 0.64 ],\n",
              "       [0.8  , 1.   , 0.   ]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Q-Learning"
      ],
      "metadata": {
        "id": "S3tx5UPYNeYB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def q_learning(env, epochs, alpha, epsilon, gamma):\n",
        "  q_table = np.zeros([env.observation_space.n, env.action_space.n])\n",
        "  v_table = np.zeros(env.observation_space.n)\n",
        "  steps_to_goal = []\n",
        "  sum_squared_error = []\n",
        "  for i in range (0,epochs):\n",
        "    v_error = []\n",
        "    state = env.reset()\n",
        "    done = False\n",
        "    steps = 0 \n",
        "    while not done:\n",
        "      if np.random.random() < epsilon:  #Epsilon Greedy Action\n",
        "        action = env.action_space.sample()\n",
        "      else:\n",
        "        action = np.argmax(q_table[state])\n",
        "      \n",
        "      next_state, reward, done, info = env.step(action)\n",
        "      \n",
        "      old_q = q_table[state, action]\n",
        "      next_q = np.max(q_table[next_state])\n",
        "\n",
        "      updated_q = (1 - alpha) * old_q + alpha * (reward + gamma * next_q) #TD Step\n",
        "      q_table[state, action] = updated_q\n",
        "\n",
        "      v_table[state] = reward + gamma * v_table[next_state] #Bellman Equation for V\n",
        "\n",
        "      state = next_state\n",
        "      steps += 1\n",
        "    steps_to_goal.append(steps)\n",
        "    \n",
        "    zip_object = zip(true_v, v_table)\n",
        "    for v_true, v_current in zip_object:\n",
        "      v_error.append(v_current - v_true)  #Change in V\n",
        "    v_error = np.square(v_error)\n",
        "    v_error = np.sum(v_error)\n",
        "    sum_squared_error.append(v_error)\n",
        "  return(sum_squared_error, steps_to_goal, v_table)"
      ],
      "metadata": {
        "id": "fWyvaY26NhmH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "alpha = 1\n",
        "gamma = 0.8\n",
        "epsilon = 0.01"
      ],
      "metadata": {
        "id": "sqBHMxq5Ng5x"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "q_mse = []\n",
        "q_avg_steps = []\n",
        "q_v_table = []"
      ],
      "metadata": {
        "id": "dZe4qk2Q8G9H"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(0,100):\n",
        "  print(\"-------- Starting Round: \", (i+1))\n",
        "  sum_squared_error, steps_to_goal, v_table = q_learning(env, 100, alpha, epsilon, gamma)\n",
        "  q_mse.append(sum_squared_error)\n",
        "  q_avg_steps.append(steps_to_goal)\n",
        "  q_v_table.append(v_table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NS8XjAfK4act",
        "outputId": "53988d11-e8a6-44cb-adf3-064ec63a2607"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-------- Starting Round:  1\n",
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          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "q_mse = [statistics.mean(k) for k in zip(*q_mse)]\n",
        "q_avg_steps = [statistics.mean(k) for k in zip(*q_avg_steps)]\n",
        "q_v_table = np.mean(q_v_table, axis = 0)"
      ],
      "metadata": {
        "id": "58H_JVel8isJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "XddsMiWuxure"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.axhline(y=4, color='red')\n",
        "plt.plot(q_avg_steps)\n",
        "plt.ylim(0,30)\n",
        "plt.xlabel(\"Episode\")\n",
        "plt.ylabel(\"Steps to Goal\")\n",
        "plt.title(\"Average Steps to Goal for 100 Rounds of $\\epsilon$ Q-Learning\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        },
        "id": "iM0s_u_iwrC9",
        "outputId": "39e40699-74e7-4b92-edb5-75aad8fb6a9f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Average Steps to Goal for 100 Rounds of $\\\\epsilon$ Q-Learning')"
            ]
          },
          "metadata": {},
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(q_mse)\n",
        "plt.xlabel(\"Episode\")\n",
        "plt.ylabel(\"Mean Squared Error\")\n",
        "plt.title(\"MSE for 100 Rounds of $\\epsilon$ Q-Learning\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        },
        "id": "kAmveWqu7seV",
        "outputId": "d87a2565-ca9d-4b59-8493-4db2cf42a505"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'MSE for 100 Rounds of $\\\\epsilon$ Q-Learning')"
            ]
          },
          "metadata": {},
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Double Q-Learning"
      ],
      "metadata": {
        "id": "KQ0aKJ1ah2Eo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def double_q_learning(env, epochs, alpha, epsilon, gamma):\n",
        "  qa_table = np.zeros([env.observation_space.n, env.action_space.n])\n",
        "  qb_table = np.zeros([env.observation_space.n, env.action_space.n])\n",
        "  va_table = np.zeros(env.observation_space.n)\n",
        "  vb_table = np.zeros(env.observation_space.n)\n",
        "  steps_to_goal = []\n",
        "  sum_squared_error = []\n",
        "  for i in range (0,epochs):\n",
        "    v_error = []\n",
        "    state = env.reset()\n",
        "    done = False\n",
        "    steps = 0 \n",
        "    while not done:\n",
        "      q_sum_table = qa_table + qb_table\n",
        "      if np.random.random() < epsilon:  #Epsilon Greedy Action\n",
        "        action = env.action_space.sample()\n",
        "      else:\n",
        "        action = np.argmax(q_sum_table[state])\n",
        "      \n",
        "      next_state, reward, done, info = env.step(action)\n",
        "      \n",
        "      if np.random.random() < 0.5:  #Q_A Table Case\n",
        "        old_q = qa_table[state,action]\n",
        "        next_action = np.argmax(qa_table[next_state])\n",
        "        updated_q = (1 - alpha) * old_q + alpha * (reward + gamma * qb_table[next_state,next_action]) #TD Step\n",
        "        qa_table[state, action] = updated_q\n",
        "        zip_object = zip(true_v, va_table)\n",
        "        va_table[state] = reward + gamma * va_table[next_state] #Bellman Equation for V\n",
        "      else:                          #Q_B Table Case\n",
        "        old_q = qb_table[state,action]\n",
        "        next_action = np.argmax(qb_table[next_state])\n",
        "        updated_q = (1 - alpha) * old_q + alpha * (reward + gamma * qa_table[next_state,next_action]) #TD Step\n",
        "        qb_table[state, action] = updated_q\n",
        "        zip_object = zip(true_v, vb_table) \n",
        "        vb_table[state] = reward + gamma * vb_table[next_state] #Bellman Equation for V\n",
        "\n",
        "\n",
        "      state = next_state\n",
        "      steps += 1\n",
        "    steps_to_goal.append(steps)\n",
        "    for v_true, v_current in zip_object:\n",
        "      v_error.append(v_current - v_true)  #Change in V\n",
        "    v_error = np.square(v_error)\n",
        "    v_error = np.sum(v_error)\n",
        "    sum_squared_error.append(v_error)\n",
        "  return(sum_squared_error, steps_to_goal, v_table)"
      ],
      "metadata": {
        "id": "cWBYf1JGh4Mg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "dq_mse = []\n",
        "dq_avg_steps = []\n",
        "dq_v_table = []"
      ],
      "metadata": {
        "id": "mrb9P1d2f4oo"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(0,100):\n",
        "  print(\"-------- Starting Round: \", (i+1))\n",
        "  sum_squared_error, steps_to_goal, v_table = double_q_learning(env, 100, alpha, epsilon, gamma)\n",
        "  dq_mse.append(sum_squared_error)\n",
        "  dq_avg_steps.append(steps_to_goal)\n",
        "  dq_v_table.append(v_table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "m4c9i6LefUt2",
        "outputId": "1a38dd2b-6b82-44a8-8dd2-b9f516ae8ca6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-------- Starting Round:  1\n",
            "-------- Starting Round:  2\n",
            "-------- Starting Round:  3\n",
            "-------- Starting Round:  4\n",
            "-------- Starting Round:  5\n",
            "-------- Starting Round:  6\n",
            "-------- Starting Round:  7\n",
            "-------- Starting Round:  8\n",
            "-------- Starting Round:  9\n",
            "-------- Starting Round:  10\n",
            "-------- Starting Round:  11\n",
            "-------- Starting Round:  12\n",
            "-------- Starting Round:  13\n",
            "-------- Starting Round:  14\n",
            "-------- Starting Round:  15\n",
            "-------- Starting Round:  16\n",
            "-------- Starting Round:  17\n",
            "-------- Starting Round:  18\n",
            "-------- Starting Round:  19\n",
            "-------- Starting Round:  20\n",
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            "-------- Starting Round:  24\n",
            "-------- Starting Round:  25\n",
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            "-------- Starting Round:  27\n",
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            "-------- Starting Round:  30\n",
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            "-------- Starting Round:  97\n",
            "-------- Starting Round:  98\n",
            "-------- Starting Round:  99\n",
            "-------- Starting Round:  100\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dq_mse = [statistics.mean(k) for k in zip(*dq_mse)]\n",
        "dq_avg_steps = [statistics.mean(k) for k in zip(*dq_avg_steps)]\n",
        "dq_v_table = np.mean(dq_v_table, axis = 0)"
      ],
      "metadata": {
        "id": "ghuoR0Wfgg4X"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.axhline(y=4, color='red')\n",
        "plt.plot(dq_avg_steps)\n",
        "plt.ylim(0,30)\n",
        "plt.xlabel(\"Episode\")\n",
        "plt.ylabel(\"Steps to Goal\")\n",
        "plt.title(\"Average Steps to Goal for 100 Rounds of Double Q-Learning\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "6pIUDRN-ffsc",
        "outputId": "6518a479-4610-4963-eab4-410daf39efd8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Average Steps to Goal for 100 Rounds of Double Q-Learning')"
            ]
          },
          "metadata": {},
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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ZUaupe7OIZFs7e0mtjCWL+nAg/4PQEn894WEuCONHXd2uNHSKfM6o6nkYEcm4dlZJrQGuiO0YOeAqd7/GzG4jDH72bkJ3rk+2MQ0dIWdGtdnAHiIiGdG2gOHuNxN+Y2D+9HuAJ7Vru50on0NVUiKSeV39pHdWqEpKRDqBAkYGqNFbRDqBAkYGqIQhIp1AASMD8jmjqhKGiGScAkYG5E0BQ0SyTwEjA1TCEJFOoICRAbmcUVMbhohknAJGBqhKSkQ6gQJGBqhKSkQ6gQJGBuTMULwQkaxTwMiAfA6VMEQk8xQwMiCnB/dEpAMoYGRAIaehQUQk+xQwMiBvRkUBQ0QyTgEjA3I5AzTEuYhkmwJGBuQtBAy1Y4hIlilgZEC9hKGeUiKSZQoYGZCvV0mphCEiGaaAkQH7q6RUwhCRDFPAyIC5Ru+UEyIisgAFjAzIh3ihRm8RyTQFjAzI50M2qEpKRLJMASMD1IYhIp1AASMDYgFDVVIikmkKGBmQMz3pLSLZp4CRAXk9uCciHUABIwP2BwxVSYlIhrUtYJjZOjO73sxuM7NbzezNcfolZrbVzG6Kf89rVxo6haqkRKQTFNq47grwNnf/LzMbADaZ2bfivEvd/X1t3HZHUQlDRDpB2wKGu28DtsXXo2Z2O7C2XdvrZDl1qxWRDrAobRhmth54AnBjnPQGM7vZzC43s+WLkYYsy2toEBHpAG0PGGa2DPgy8Cfuvg/4KHAycBahBPL+Jp+70Mw2mtnGnTt3tjuZqSrEgFFRxBCRDGtrwDCzIiFYfM7dvwLg7g+6e9Xda8DHgSc1+qy7X+buG9x9w8qVK9uZzNTlNLy5iHSAdvaSMuCTwO3u/oHE9DWJxX4XuKVdaegUc0ODpJwQEZEFtLOX1NOBVwA/N7Ob4rS3A+eb2VmAA5uB17UxDR0hVx8aRI3eIpJh7ewl9QPAGsz6t3Zts1PVSxiqkhKRLNOT3hmgoUFEpBMoYGRATg/uiUgHUMDIgLyGBhGRDqCAkQGqkhKRTqCAkQEKGCLSCRQwMkCDD4pIJ1DAyAANPiginUABIwPyGhpERDqAAkYGaGgQEekEChgZUB8aRN1qRSTLFDAyQI3eItIJFDAyIK9GbxHpAAoYGaDfwxCRTqCAkQH7f3GvqoAhItmlgJEBKmGISCdQwMgAtWGISCdQwMgA9ZISkU6ggJEBOQ1vLiIdQAEjA+ZGq005ISIiC1DAyIAYL1QlJSKZpoCRAWZGzlQlJSLZpoCREfmcqYQhIpmmgJEROTN1qxWRTFPAyIhCTgFDRLJNASMjcgoYIpJxChgZkc+ZhgYRkUxTwMiIvNowRCTjFDAyIqcShohkXNsChpmtM7Przew2M7vVzN4cp68ws2+Z2V3x//J2paGTqIQhIlnXzhJGBXibu58GPAV4vZmdBlwMXOfupwLXxfddL58zDQ0iIpnWtoDh7tvc/b/i61HgdmAt8ELgirjYFcCL2pWGTpLL6fcwRCTbFqUNw8zWA08AbgRWu/u2OGs7sLrJZy40s41mtnHnzp2LkcxU5c2oqEpKRDKs7QHDzJYBXwb+xN33Jee5uwMNr5Lufpm7b3D3DStXrmx3MlOXz5nGkhKRTGtrwDCzIiFYfM7dvxInP2hma+L8NcCOdqahU+T14J6IZFw7e0kZ8Engdnf/QGLW14EL4usLgKvblYZOkjMNPigi2VZo47qfDrwC+LmZ3RSnvR14L3CVmb0G2AK8pI1p6BiqkhKRrGsaMMzsGzRpXwBw999ZaMXu/gPAmsw+t6XUdRENby4iWbdQCeN9i5YK0fDmIpJ5TQOGu9+wmAnpdhp8UESy7qBtGGZ2KvC3wGlAb326u5/UxnR1HQ0NIiJZ10ovqX8GPkoY6uM3gE8Dn21norpRLgc1DQ0iIhnWSsDoc/frAHP3Le5+CfD89iar+xRyOSqKGCKSYa10q502sxxwl5m9AdgKLGtvsrpPLmdUVSMlIhnWSgnjzUAZeBNwNuHZigsW/IQcsryh5zBEJNMOWsJw958ChAe3eaO7j7U7Ud1IQ4OISNYdtIRhZo83s58BtwK3mtkmM3tc+5PWXXLWuFvtzfeP8JKP/Yip2WoKqRIRmdNKldTHgLe6+wnufgLwNuCy9iar+zQrYWzcvIef3PsQ2/dOpZAqEZE5rQSMfne/vv7G3b8L9LctRV0q12RokLHpCgATMyphiEi6WukldY+Z/SXwmfj+D4F72pek7pS3xoMPjk7NAjA5W1nsJImIHKCVEsargZXAV+LfyjhNjqBmgw+qhCEiWdFKL6k9hC610kb5nFFt8CDGvikFDBHJhqYlDDN7hpm9MvH+S2b2nfj3m4uTvO6Rb/IDSmMxYEwqYIhIyhYqYbwTeGPi/aOBPyI0eL8d+E77ktV9cjmj2mBkkHobhkoYIpK2hdowBt39tsT7u9x9k7t/Dxhoc7q6Tj5Hw+cw5tow1OgtIulaKGAMJ9+4++8l3q5uT3K6V7PhzVUlJSJZsVDA+IWZPWxUWjN7AXBH+5LUnXJNftN7NAaMcQUMEUnZQm0YbwH+1cxeDPxXnHY28DTgBe1OWLdp1OhdqzljM/UShqqkRCRdTUsY7n43cAbwfWB9/PsecIa737kYiesmfaU8U7PVA0oZ4zMV6jFEjd4ikrYFn8Nw92ng8kVKS1cb6itScxidrjDUVwTmGrwBJjT4oIikrJUnvWURDJdLAOydmN0/rd5+AWr0FpH0KWBkxHAsVeyZmNk/LRkw1K1WRNLWyuCDmFkJeFR8e4e7zy60vBy64XIIGCOTyRJGeD3QW1AJQ0RSd9CAYWbnAFcAmwED1pnZBfEBPjlC6lVSI4kSRr0NY9VAjxq9RSR1rZQw3g/8lrvfAWBmjwKuJHSxlSOkXsLYmyhh1B/aWz3Yy5bdE6mkS0SkrpU2jGI9WADELrXFg33IzC43sx1mdkti2iVmttXMbop/zzu8ZC899Z5RIw0avUMJQ20YIpKuVgLGRjP7hJmdE/8+Dmxs4XOfAp7TYPql7n5W/Pu3Q0nsUlbM51jWUziw0Xu6ghmsVJWUiGRAKwHjfwK3EX4T403x9UUH+1Bs43joEaWuywz1Fed1q51lWalAf0+B6Uqt4VhTIiKLpZWAcZG7f8Ddfy/+XUoIIofrDWZ2c6yyWt5sITO70Mw2mtnGnTt3PoLNdY7l/cUDekmNTVVY1lugXMoDMKmH90QkRa0EjAsaTPujw9zeR4GTgbOAbYQG9Ybc/TJ33+DuG1auXHmYm+ssw32lA3pJjU5VGOgt0FcKfRPUjiEiaWraS8rMzgdeBpxoZl9PzBrgMKua3P3BxPo/DlxzOOtZqobKRR7YO7n//dh0hWU9BcrFWMJQO4aIpGihbrU/JJQCjubAksAocPPhbMzM1rj7tvj2d4FbFlq+2wz3Fef1kppluFzaXyWlhm8RSVPTgOHuW4AtwFMPZ8VmdiVwDnC0md0P/DVwjpmdBTjhQcDXHc66l6rhcpGRiRlqNSeXM0anKxy3okyfAoaIZEBLQ4McDnc/v8HkT7Zre0vB8nKJmsPYTIXB3iKjUxUGewuU1YYhIhmgwQczpP7wXr1r7dhUbMNQCUNEMuCQAoaZLTezM9qVmG5XH09qz8QMlWqNydkqA73FuW61ChgikqKDBgwz+66ZDZrZCsJPtX7czD7Q/qR1n/0j1k7M7h94MJQw6lVSChgikp5WShhD7r4P+D3g0+7+ZODZ7U1Wd6r/JsbI5Oz+caTCcxj1Kim1YYhIeloJGAUzWwO8BD030VZzv7o3c0DAUJWUiGRBKwHjXcB/AL9095+a2UnAXe1NVndKjlg7VyVVpJjPUcybftdbRFJ10G617v5F4IuJ9/cAv9/ORHWrUiFHfynPnonZA35tD6CvmFcJQ0RS1Uqj90lm9g0z2xl/3+LqWMqQNhgulxiZnJkrYcSAUS4V1IYhIqlqpUrq88BVwBrgWEJp48p2JqqbDZfDEOf7Em0YAOVSnnGVMEQkRa0EjLK7f8bdK/Hvs0BvuxPWrYbLYYjz+s+zDvSEdo1yj6qkRCRdrQSMfzezi81svZmdYGZ/Bvybma2Iz2bIETTcV2LPxAxj07MUckZvMWRRuagqKRFJVytjSb0k/p8/UOBLCYMIqj3jCBqKVVKj8ceTzAyAvlL+gN/KEBFZbK30kjpxMRIiwXBfcf+De/X2CwhtGA+MqEpKRNLTSi+pspm9w8wui+9PNbMXtD9p3Wl5uUS15mzbO8my2H4BoYShoUFEJE2ttGH8MzADPC2+3wq8u20p6nJDcTyp+/dMPqyEod/0FpE0tRIwTnb3vwdmAdx9ArC2pqqL1ceT2rZ3ioGeZMBQo7eIpKuVgDFjZn2EBm7M7GRguq2p6mL18aSqNT+ghNFXzDM1W6Na87SSJiJdrpVeUpcA3wTWmdnngKcDr2pnorpZfYhzmHvKG5gbgHC2yrKetv1QoohIU630krrWzDYBTyFURb3Z3Xe1PWVdKhkwBnrnXpd75n6mVQFDRNLQSi+p69x9t7v/q7tf4+67zOy6xUhcN6qPWAscEBjKRQ1xLiLpanqrama9QBk42syWM9fQPQisXYS0daWeQp5y7EI72KBKSl1rRSQtC9VtvA74E8KAg5uYCxj7gA+3OV1dbbivyMRM9YA2jD4FDBFJWdOA4e4fBD5oZm90939cxDR1vaFyiQf2Tu0feBDY/7veqpISkbQ0bcMws18zs2PqwcLMXhl/C+NDGnSwvZbHhu9GvaT0LIaIpGWhRu+PEZ7wxsx+HXgv8GlgL3BZ+5PWveo9pZKN3n2JbrUiImlYqA0j7+4PxdfnAZe5+5eBL5vZTe1PWvca6gsP7w0mu9XGgDE+rYAhIulYqISRN7N6QDkX+E5inh4EaKPhhlVSc89hiIikYaGAcSVwg5ldDUwC3wcws1MI1VILMrPL42+A35KYtsLMvmVmd8X/yx9h+pekM9YOceqqZQ271arRW0TS0jRguPt7gLcBnwKe4e6e+MwbW1j3p4DnzJt2MXCdu58KXBffyzzPffwavvXWZ1HIz2VPMZ+jmDcm1IYhIilZsGrJ3X/cYNqdrazY3b9nZuvnTX4hcE58fQXwXeDPW1mfhAEIVcIQkbS0MlrtkbTa3bfF19uB1c0WNLMLzWyjmW3cuXPn4qQu4zTEuYikabEDxn6xiqvpWN3ufpm7b3D3DStXrlzElGVXWb+6JyIpWuyA8aCZrQGI/3cs8vY7Wl9JVVIikp7FDhhfBy6Iry8Arl7k7Xc0lTBEJE1tCxhmdiXwI+DRZna/mb2G8LT4/zCzu4Bnx/fSoj61YYhIitr2AJ67n99k1rnt2uZS11/Ks21EJQwRSUdqjd5y6PpUJSUiKVLA6CDlUl6DD4pIahQwOoiewxCRNClgdJC+Yp6p2Rq1WtPHV0RE2kYBo4OU9ZsYIpIiBYwOUtbveotIihQwOkifftdbRFKkgNFBlvWEEsbo9GzKKRGRbqSA0UGOXtYDwK6xmZRTIiLdSAGjg6we7AXgwX1TKadERLqRAkYHWTkQShg7FDBEJAUKGB2kt5hnebnIg/um006KiHQhBYwOs3qwl+0qYYhIChQwOsyqwV5VSYlIKhQwOszqgR5VSYlIKhQwOszqwV52jk1T1XhSIrLIFDA6zOrBHqo1Z/e4ShkisrgUMDrM/mcx9ipgiMjiUsDoMHp4T0TSooDRYfYHjFEFDBFZXAoYHeboZSXMUE8pEVl0ChgdppDPcfSyHj2LISKLTgGjAx0z2Ks2DBFZdAoYHWj1YA/bVSUlIotMAaMDaXgQEUmDAkYHWj3Qy+7xGWYqtbSTIiJdRAGjA60eDL+LsXNM1VIisngKaWzUzDYDo0AVqLj7hjTS0amSD++tHe5LOTUi0i1SCRjRb7j7rhS337HmhgdRO4aILB5VSXWgepWUutaKyGJKK2A4cK2ZbTKzC1NKQ8daXi5RzBsPjqoNQ0QWT1pVUs9w961mtgr4lpn9wt2/l1wgBpILAY4//vg00phZuZyxakAP74nI4kqlhOHuW+P/HcBXgSc1WOYyd9/g7htWrly52EnMvFWDPezQw3sisogWPWCYWb+ZDdRfA78F3LLY6eh0q1XCEJFFlm5GSFsAAA1BSURBVEYJYzXwAzP7b+AnwL+6+zdTSEdHO2aol+0KGCKyiBa9DcPd7wHOXOztLjWrBnsYnaowMVOhXEqzd7Q0M1Op4Tg9hXzaSRE5InSl6VCrB8KzGDfcsZOaw47RKfqKeYbLRYbLpfC/r8Sy3gJ3PjjKxs0PsWnLHqYrNfpLBcqlPGuG+zh11TIetXoAgHt3jbNl9zgPTcwwW3FmqzWq7vu3WcwZQ+USw31FBnoLlAo5ivkcpXyOck+e/lKBmju3bN3LTfft5d5dYzxmzSBPWr+Cs9YNkzNjfKbCxEyVfM4o5IxiPkfNw7ZmKjUmZ6uMT1eZmKlQrc1tu1TIUS4V6C/l6SnmKeVzFAtG3gyzsMzYdJUHRiZ5YGSS0akKQ31FhstFlveXWDvcx7HDfZSLebbvm2Lz7nG2752it5inr5Snt5BnbLrCyMQMD43PcN+eCbbsnmDrnklOWtnP004+mqeefBQrB0KXZnfYOznLjtEpdsbeauV4XH+5c4wb7tjJD3+5GzP4jces4vmPX8Pj1w6xb2qWvROzTMxUKRZyFPMGcV0jk7OMT1co5sNx7S3mOGaol7XDfawe7KWQCzs6W3Xu3TXOXTtG2bJ7guX9JU48qp/jV5SpujMyMcPI5Cx5M/p78pRLBXrqeVXIsW9ylq0jkzwwMsWeiRnGp0Oe1NM2MjlLIWeccdwQZ64bZkW5xKYte/jplj1s3TPBo1YPcNqaQU5ZtYy+UsiLQj5HpVpjplqjUnXyeaMnbm95f4mVAz0M9BSoOexL7OvYdLjp6S3kGSoXGeorUqvByOQMIxOzVN1Z1hOOaymf25/XZhbOgXw4hsVCOA/zOcMafF+q7kzOVBmfqTI9W2WgN2yrkDPu2TXGTfft5fZt+1jWU9h/rvQWQwWMA5WqMxPP0QdGJrlrxyh3PTjG1Gw1nJc9BdYM9XLmumHOWjfEscN9TMxUmZiuMjlbZbZaC9+nxDldqdXTVGFyprp/+nSlxi93jnH3jjHuenCMD7/sCWxYv+LwLxZHkHnigpBVGwYGfOPZZ6edjEz50eA6zj/tpYf0mfWTexisTjGeLzGeK7Gj1E/NHl4rWapV6KlVKXqVXOL8mMnlGc334NboK3mgo2bHOXFyD3eUVzJa6DmkdLZToValkjv4Hf/w7CQnTO9hzfQYvyivZHPf8kPazvFTI5wzcg8Vy3Ht8lPZVeo/3CS3XaFWpVybZVl1huHKJMsrU4znitzWv4qZ3Nw95aMndrJuaoS7+44+5OMB4bxKri8LkudDb3WW6VyhpfN7oDLFqZO7GahOM5ErMZYvcV/PEGNH6Fzvq85w6uRuTpnczWu3beS0iZ2HtR674YZNR3IkjWzlnrTsSfvu54N3fYNl1RmOnRll1cwYU7kCI4U+Rgq97C307v+/fmqEDaP3s3J24oB1TFmee/tWcGffURhw4tQejp8aYajavPdVFWM038NooYcZyzFreaZzBSbyRSZyRaqW47TxHayd2YfF5X9RXskt/aspeI3+6gy9tVncjBnLU7EceXeKXqXgNcq1WcrVWcq1GQpeH1zRmLEcE/nwxZy2PLO5PBXLU0l8ufuqFY6d2cfa6X0sq84wli8xUuhjV7HM1p5BHigNsrfQw3HT+1g/tYc1M6PMWp7xfJGpXIGB6gzDlSmGK5MMVGcO2O/7S4P8dPA4xvKl/dMGK9OsnB1n5ew4Oa8xkS8xnityzMwY66dH9i/3f+79Nj8ZPI77eoYYqkwxXJmirzbLrOWZiRer+nbL1VlqZvvTta00wNaeQXYUl1GL+5pz5/jpEU6d2M36qT3sKfaxuXc59/UMUapVGapOMVSZwrFwcxCP2Uwuz4zlGajOsHZ6H8fO7OOo2Ql6vEojM5bjF+WV7Cn0cebYdoarc21mY7kim3uXM50rMGs5Kpan6NX9+Vi1HLOWYypX5KFCHztL/ewqlumtVRiuhPQNVKfpr85Srs4wnSswUuhlpNBH3mssr0wyVJkmR42JXInxfHH/sQKoEdY/G/ep/rrS4AYIwBzKtRn6q7OUvBrPjV7G8iVOmdzNWWPbOXlyNxXL8WBpgAdKAwdsr+A1SrWwb8fMjLJqdvxhJZkqxj19K/jZsjXsLpb371tvrUIpHpu8O0a4Ccu7U67O0F+bpbdWgTi9WKuxanYsk09Vd0YJY8MG37hxY9rJEBHpKGZ2REsYWQxiIiKSQQoYIiLSEgUMERFpiQKGiIi0RAFDRERaooAhIiItUcAQEZGWKGCIiEhLFDBERKQlChgiItISBQwREWmJAoaIiLREAUNERFqigCEiIi1RwBARkZYoYIiISEsUMEREpCUKGCIi0hIFDBERaYkChoiItEQBQ0REWqKAISIiLVHAEBGRlihgiIhIS1IJGGb2HDO7w8zuNrOL00iDiIgcmkUPGGaWBz4CPBc4DTjfzE5b7HSIiMihSaOE8STgbne/x91ngC8AL0whHSIicggKKWxzLXBf4v39wJPnL2RmFwIXxrdjZnbHYW7vaGDXYX62k3XjfnfjPkN37nc37jMc+n6fcCQ3nkbAaIm7XwZc9kjXY2Yb3X3DEUhSR+nG/e7GfYbu3O9u3GdIf7/TqJLaCqxLvD8uThMRkQxLI2D8FDjVzE40sxLwUuDrKaRDREQOwaJXSbl7xczeAPwHkAcud/db27jJR1yt1aG6cb+7cZ+hO/e7G/cZUt5vc/c0ty8iIh1CT3qLiEhLFDBERKQlSzpgdMMQJGa2zsyuN7PbzOxWM3tznL7CzL5lZnfF/8vTTuuRZmZ5M/uZmV0T359oZjfG/P6X2KliSTGzYTP7kpn9wsxuN7OnLvW8NrO3xHP7FjO70sx6l2Jem9nlZrbDzG5JTGuYtxZ8KO7/zWb2xMVI45INGF00BEkFeJu7nwY8BXh93M+Lgevc/VTguvh+qXkzcHvi/d8Bl7r7KcAe4DWppKq9Pgh8090fA5xJ2P8lm9dmthZ4E7DB3R9H6CjzUpZmXn8KeM68ac3y9rnAqfHvQuCji5HAJRsw6JIhSNx9m7v/V3w9SriArCXs6xVxsSuAF6WTwvYws+OA5wOfiO8N+E3gS3GRpbjPQ8CvA58EcPcZdx9hiec1oTdnn5kVgDKwjSWY1+7+PeCheZOb5e0LgU978GNg2MzWtDuNSzlgNBqCZG1KaVkUZrYeeAJwI7Da3bfFWduB1Sklq13+AfgzoBbfHwWMuHslvl+K+X0isBP451gV9wkz62cJ57W7bwXeB/yKECj2AptY+nld1yxvU7m+LeWA0VXMbBnwZeBP3H1fcp6HvtNLpv+0mb0A2OHum9JOyyIrAE8EPuruTwDGmVf9tATzejnhbvpE4Fign4dX23SFLOTtUg4YXTMEiZkVCcHic+7+lTj5wXoRNf7fkVb62uDpwO+Y2WZCVeNvEur2h2O1BSzN/L4fuN/db4zvv0QIIEs5r58N3OvuO919FvgKIf+Xel7XNcvbVK5vSzlgdMUQJLHu/pPA7e7+gcSsrwMXxNcXAFcvdtraxd3/wt2Pc/f1hHz9jru/HLgeeHFcbEntM4C7bwfuM7NHx0nnArexhPOaUBX1FDMrx3O9vs9LOq8TmuXt14FXxt5STwH2Jqqu2mZJP+ltZs8j1HXXhyB5T8pJOuLM7BnA94GfM1ef/3ZCO8ZVwPHAFuAl7j6/Qa3jmdk5wJ+6+wvM7CRCiWMF8DPgD919Os30HWlmdhahob8E3AO8inDjt2Tz2szeCZxH6BH4M+C1hPr6JZXXZnYlcA5hCPMHgb8GvkaDvI3B88OE6rkJ4FXuvrHtaVzKAUNERI6cpVwlJSIiR5AChoiItEQBQ0REWqKAISIiLVHAEBGRlihgSFcys6qZ3ZT4W3DAPjO7yMxeeQS2u9nMjn6k6xFJg7rVSlcyszF3X5bCdjcTRl7dtdjbFnmkVMIQSYglgL83s5+b2U/M7JQ4/RIz+9P4+k3x90duNrMvxGkrzOxrcdqPzeyMOP0oM7s2/p7DJwBLbOsP4zZuMrOPxSH5RTJLAUO6Vd+8KqnzEvP2uvvjCU/S/kODz14MPMHdzwAuitPeCfwsTns78Ok4/a+BH7j76cBXCU/sYmaPJTy9/HR3PwuoAi8/srsocmQVDr6IyJI0GS/UjVyZ+H9pg/k3A58zs68Rhm4AeAbw+wDu/p1Yshgk/H7F78Xp/2pme+Ly5wJnAz8NozzQx9IaNFCWIAUMkYfzJq/rnk8IBL8N/G8ze/xhbMOAK9z9Lw7jsyKpUJWUyMOdl/j/o+QMM8sB69z9euDPgSFgGWEAyJfHZc4BdsXfJfke8LI4/blA/fe2rwNebGar4rwVZnZCG/dJ5BFTCUO6VZ+Z3ZR4/013r3etXW5mNwPTwPnzPpcHPht/LtWAD7n7iJldAlwePzfB3JDU7wSuNLNbgR8ShuvG3W8zs3cA18YgNAu8njAiqUgmqVutSIK6vYo0pyopERFpiUoYIiLSEpUwRESkJQoYIiLSEgUMERFpiQKGiIi0RAFDRERa8v8A/mIN4RNi6GoAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(dq_mse)\n",
        "plt.xlabel(\"Episode\")\n",
        "plt.ylabel(\"Mean Squared Error\")\n",
        "plt.title(\"MSE for 100 Rounds of Double Q-Learning\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "zI1ez-K4fiol",
        "outputId": "e5bbdf47-61a3-4ef5-86fe-5fadfc8c2b08"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'MSE for 100 Rounds of Double Q-Learning')"
            ]
          },
          "metadata": {},
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# SARSA(λ)"
      ],
      "metadata": {
        "id": "eOvBdHHN_vLZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def SARSA(env, epochs, alpha, epsilon, gamma, lmbda):\n",
        "  q_table = np.zeros([env.observation_space.n, env.action_space.n])\n",
        "  v_table = np.zeros(env.observation_space.n)\n",
        "  e_table = np.zeros([env.observation_space.n, env.action_space.n]) #Eligibility Trace Table\n",
        "  steps_to_goal = []\n",
        "  sum_squared_error = []\n",
        "  for i in range (0,epochs):\n",
        "    v_error = []\n",
        "    state = env.reset()\n",
        "    done = False\n",
        "    steps = 0 \n",
        "    if np.random.random() < epsilon:  #Epsilon Greedy Initial Action\n",
        "      action = env.action_space.sample()\n",
        "    else:\n",
        "      action = np.argmax(q_table[state])\n",
        "\n",
        "    while not done:\n",
        "      next_state, reward, done, info = env.step(action)\n",
        "      if np.random.random() < epsilon:  #Epsilon Greedy (s', a')\n",
        "        next_action = env.action_space.sample()\n",
        "      else:\n",
        "        next_action = np.argmax(q_table[next_state])\n",
        "\n",
        "      delta = reward + gamma * q_table[next_state, next_action] - q_table[state, action]\n",
        "      e_table[state,action] = e_table[state,action] + 1 #Accumulating Eligibility Traces\n",
        "\n",
        "      q_table = q_table + (alpha * delta) * e_table\n",
        "      e_table = (gamma * lmbda) * e_table\n",
        "      v_table[state] = reward + gamma * v_table[next_state] #Bellman Equation for V\n",
        "\n",
        "      state = next_state\n",
        "      action = next_action\n",
        "      steps += 1\n",
        "  \n",
        "    steps_to_goal.append(steps)\n",
        "    zip_object = zip(true_v, v_table)\n",
        "    for v_true, v_current in zip_object:\n",
        "      v_error.append(v_current - v_true)  #Change in V\n",
        "    v_error = np.square(v_error)\n",
        "    v_error = np.sum(v_error)\n",
        "    sum_squared_error.append(v_error)\n",
        "  return(sum_squared_error, steps_to_goal, v_table)"
      ],
      "metadata": {
        "id": "Lpwt8VpPA2Ib"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "sarsa_mse = []\n",
        "sarsa_avg_steps = []\n",
        "sarsa_v_table = []"
      ],
      "metadata": {
        "id": "-oTgQA1aIZCe"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(0,100):\n",
        "  print(\"-------- Starting Round: \", (i+1))\n",
        "  sum_squared_error, steps_to_goal, v_table = SARSA(env, 100, alpha, epsilon, gamma, 0.9) #lambda = 0.9\n",
        "  sarsa_mse.append(sum_squared_error)\n",
        "  sarsa_avg_steps.append(steps_to_goal)\n",
        "  sarsa_v_table.append(v_table)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6BfKeZcsIdbR",
        "outputId": "dba13e6c-2165-4de8-ac3d-21324f13414c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-------- Starting Round:  1\n",
            "-------- Starting Round:  2\n",
            "-------- Starting Round:  3\n",
            "-------- Starting Round:  4\n",
            "-------- Starting Round:  5\n",
            "-------- Starting Round:  6\n",
            "-------- Starting Round:  7\n",
            "-------- Starting Round:  8\n",
            "-------- Starting Round:  9\n",
            "-------- Starting Round:  10\n",
            "-------- Starting Round:  11\n",
            "-------- Starting Round:  12\n",
            "-------- Starting Round:  13\n",
            "-------- Starting Round:  14\n",
            "-------- Starting Round:  15\n",
            "-------- Starting Round:  16\n",
            "-------- Starting Round:  17\n",
            "-------- Starting Round:  18\n",
            "-------- Starting Round:  19\n",
            "-------- Starting Round:  20\n",
            "-------- Starting Round:  21\n",
            "-------- Starting Round:  22\n",
            "-------- Starting Round:  23\n",
            "-------- Starting Round:  24\n",
            "-------- Starting Round:  25\n",
            "-------- Starting Round:  26\n",
            "-------- Starting Round:  27\n",
            "-------- Starting Round:  28\n",
            "-------- Starting Round:  29\n",
            "-------- Starting Round:  30\n",
            "-------- Starting Round:  31\n",
            "-------- Starting Round:  32\n",
            "-------- Starting Round:  33\n",
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            "-------- Starting Round:  35\n",
            "-------- Starting Round:  36\n",
            "-------- Starting Round:  37\n",
            "-------- Starting Round:  38\n",
            "-------- Starting Round:  39\n",
            "-------- Starting Round:  40\n",
            "-------- Starting Round:  41\n",
            "-------- Starting Round:  42\n",
            "-------- Starting Round:  43\n",
            "-------- Starting Round:  44\n",
            "-------- Starting Round:  45\n",
            "-------- Starting Round:  46\n",
            "-------- Starting Round:  47\n",
            "-------- Starting Round:  48\n",
            "-------- Starting Round:  49\n",
            "-------- Starting Round:  50\n",
            "-------- Starting Round:  51\n",
            "-------- Starting Round:  52\n",
            "-------- Starting Round:  53\n",
            "-------- Starting Round:  54\n",
            "-------- Starting Round:  55\n",
            "-------- Starting Round:  56\n",
            "-------- Starting Round:  57\n",
            "-------- Starting Round:  58\n",
            "-------- Starting Round:  59\n",
            "-------- Starting Round:  60\n",
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            "-------- Starting Round:  63\n",
            "-------- Starting Round:  64\n",
            "-------- Starting Round:  65\n",
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            "-------- Starting Round:  84\n",
            "-------- Starting Round:  85\n",
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            "-------- Starting Round:  90\n",
            "-------- Starting Round:  91\n",
            "-------- Starting Round:  92\n",
            "-------- Starting Round:  93\n",
            "-------- Starting Round:  94\n",
            "-------- Starting Round:  95\n",
            "-------- Starting Round:  96\n",
            "-------- Starting Round:  97\n",
            "-------- Starting Round:  98\n",
            "-------- Starting Round:  99\n",
            "-------- Starting Round:  100\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sarsa_mse = [statistics.mean(k) for k in zip(*sarsa_mse)]\n",
        "sarsa_avg_steps = [statistics.mean(k) for k in zip(*sarsa_avg_steps)]\n",
        "sarsa_v_table = np.mean(sarsa_v_table, axis = 0)"
      ],
      "metadata": {
        "id": "zVPa2k8ZIgvq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.axhline(y=4, color='red')\n",
        "plt.plot(sarsa_avg_steps)\n",
        "plt.ylim(0,100)\n",
        "plt.xlabel(\"Episode\")\n",
        "plt.ylabel(\"Steps to Goal\")\n",
        "plt.title(\"Average Steps to Goal for 100 Rounds of SARSA($\\lambda$)\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        },
        "id": "Hdonpfm0IjZo",
        "outputId": "8a6fdce3-022c-4e38-a031-5a71c7b437cf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Average Steps to Goal for 100 Rounds of SARSA($\\\\lambda$)')"
            ]
          },
          "metadata": {},
          "execution_count": 23
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(sarsa_mse)\n",
        "plt.xlabel(\"Episode\")\n",
        "plt.ylabel(\"Mean Squared Error\")\n",
        "plt.title(\"MSE for 100 Rounds of SARSA($\\lambda$)\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        },
        "id": "c_pIc2MjImvk",
        "outputId": "359da9a7-b1db-4d20-ca52-9e4e72ac08f8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'MSE for 100 Rounds of SARSA($\\\\lambda$)')"
            ]
          },
          "metadata": {},
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Comparison\n"
      ],
      "metadata": {
        "id": "KIuT0xm9J6n1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "opt = ax.hlines(4, xmin=0, xmax=50, color='red', label='Optimal')\n",
        "exp1, = ax.plot(q_avg_steps, label='Q-Learning')\n",
        "exp2, = ax.plot(dq_avg_steps, label='Double Q-Learning')\n",
        "exp3, = ax.plot(sarsa_avg_steps, label='SARSA($\\lambda$)')\n",
        "ax.legend(handles=[exp1,exp2,exp3, opt])\n",
        "ax.set_ylabel(\"Steps to Goal\")\n",
        "ax.set_xlabel(\"Episode\")\n",
        "plt.ylim(0,500)\n",
        "ax.set_title(\"Average Steps to Goal for 100 Trials of TD Learning\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "TYxNNyFYlzEb",
        "outputId": "35146587-e3b9-4354-ee16-6286a0a25fd6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Average Steps to Goal for 100 Trials of TD Learning')"
            ]
          },
          "metadata": {},
          "execution_count": 25
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "exp1, = ax.plot(q_mse, label='Q-Learning')\n",
        "exp2, = ax.plot(dq_mse, label='Double Q-Learning')\n",
        "exp3, = ax.plot(sarsa_mse, label='SARSA($\\lambda$)')\n",
        "ax.legend(handles=[exp1,exp2,exp3])\n",
        "ax.set_ylabel(\"Mean Squared Error\")\n",
        "ax.set_xlabel(\"Episode\")\n",
        "ax.set_title(\"MSE for 100 Trials of TD Learning\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "K1m4C9OimFQG",
        "outputId": "ed4511fd-fc52-4ac2-bc07-f91b1dc6fe30"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'MSE for 100 Trials of TD Learning')"
            ]
          },
          "metadata": {},
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Can be modified to find convergent v-table, but inaccurate as some states go unexplored.\n",
        "# v_tables = []\n",
        "# step_curves = []\n",
        "# avg_v = np.zeros(env.observation_space.n)\n",
        "# avg_steps = []\n",
        "# not_converged = True\n",
        "\n",
        "# while not_converged:\n",
        "#   gradient_v = []\n",
        "#   v_table, steps_to_goal = ep_q_learning(env, 50, alpha, epsilon, gamma)\n",
        "#   v_tables.append(v_table)\n",
        "#   step_curves.append(steps_to_goal)\n",
        "\n",
        "#   new_avg_v = [statistics.mean(k) for k in zip(*v_tables)]\n",
        "#   zip_object = zip(new_avg_v, avg_v)\n",
        "#   for v_new, v_old in zip_object:\n",
        "#     gradient_v.append(v_new - v_old)  #Change in V\n",
        "#   avg_v = new_avg_v\n",
        "#   max_gradient = np.max(gradient_v)\n",
        "#   print(max_gradient)\n",
        "#   if max_gradient < 0.05: #Tolerance Value for Convergence\n",
        "#     not_converged = False"
      ],
      "metadata": {
        "id": "Y2Y9b2T5ZmqE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "q_v_table"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "U-wyTceDRwbt",
        "outputId": "831d92a7-bcb4-45fa-a80d-530bb63611ea"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.4999168, 0.       , 0.       , 0.64     , 0.118784 , 0.01     ,\n",
              "       0.8      , 1.       , 0.       ])"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dq_v_table"
      ],
      "metadata": {
        "id": "KBbhZGoS7F_2"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "sarsa_v_table"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2ihQArjZjg54",
        "outputId": "2645926e-424e-4954-dfdb-c5719d2692b7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.4888576 , 0.1781038 , 0.05302976, 0.50529901, 0.31623875,\n",
              "       0.1056    , 0.67987143, 0.96707614, 0.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    }
  ]
}