Q_learning_taxi.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Q-learning-taxi.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "metadata": {
        "id": "odNaDE1zyrL2",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# install dependancies, takes around 45 seconds\n",
        "\n",
        "Rendering Dependancies\n",
        "\n"
      ]
    },
    {
      "metadata": {
        "id": "8-AxnvAVyzQQ",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#remove \" > /dev/null 2>&1\" to see what is going on under the hood\n",
        "!pip install gym pyvirtualdisplay > /dev/null 2>&1\n",
        "!apt-get install -y xvfb python-opengl ffmpeg > /dev/null 2>&1"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "8A-1LTSH88EE",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Pacman Dependancies"
      ]
    },
    {
      "metadata": {
        "id": "TCelFzWY9MBI",
        "colab_type": "code",
        "outputId": "c5908c9d-f757-4ab5-f4a3-9a4090dd07a8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "!apt-get update > /dev/null 2>&1\n",
        "!apt-get install cmake > /dev/null 2>&1\n",
        "!pip install --upgrade setuptools 2>&1\n",
        "!pip install ez_setup > /dev/null 2>&1\n",
        "!pip install gym[atari] > /dev/null 2>&1"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already up-to-date: setuptools in /usr/local/lib/python3.6/dist-packages (40.8.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "APXSx7hg19TH",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Imports and Helper functions\n"
      ]
    },
    {
      "metadata": {
        "id": "pdb2JwZy4jGj",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import gym\n",
        "from gym import logger as gymlogger\n",
        "from gym.wrappers import Monitor\n",
        "gymlogger.set_level(40) #error only\n",
        "import tensorflow as tf\n",
        "import numpy as np\n",
        "import random\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "import math\n",
        "import glob\n",
        "import io\n",
        "import base64\n",
        "from IPython.display import HTML\n",
        "\n",
        "from IPython import display as ipythondisplay"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "nQEtc28G4niA",
        "colab_type": "code",
        "outputId": "1b28a5ad-58a6-4376-f4c3-04abc16bc910",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        }
      },
      "cell_type": "code",
      "source": [
        "from pyvirtualdisplay import Display\n",
        "display = Display(visible=0, size=(1400, 900))\n",
        "display.start()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Display cmd_param=['Xvfb', '-br', '-nolisten', 'tcp', '-screen', '0', '1400x900x24', ':1001'] cmd=['Xvfb', '-br', '-nolisten', 'tcp', '-screen', '0', '1400x900x24', ':1001'] oserror=None return_code=None stdout=\"None\" stderr=\"None\" timeout_happened=False>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "metadata": {
        "id": "G9UWeToN4r7D",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "\"\"\"\n",
        "Utility functions to enable video recording of gym environment and displaying it\n",
        "To enable video, just do \"env = wrap_env(env)\"\"\n",
        "\"\"\"\n",
        "\n",
        "def show_video():\n",
        "  mp4list = glob.glob('video/*.mp4')\n",
        "  if len(mp4list) > 0:\n",
        "    mp4 = mp4list[0]\n",
        "    video = io.open(mp4, 'r+b').read()\n",
        "    encoded = base64.b64encode(video)\n",
        "    ipythondisplay.display(HTML(data='''<video alt=\"test\" autoplay \n",
        "                loop controls style=\"height: 400px;\">\n",
        "                <source src=\"data:video/mp4;base64,{0}\" type=\"video/mp4\" />\n",
        "             </video>'''.format(encoded.decode('ascii'))))\n",
        "  else: \n",
        "    print(\"Could not find video\")\n",
        "    \n",
        "\n",
        "def wrap_env(env):\n",
        "  env = Monitor(env, './video', force=True)\n",
        "  return env"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "Dgh6VM5tbPFO",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Q-Learning Implementation"
      ]
    },
    {
      "metadata": {
        "id": "3iiikBR31hRR",
        "colab_type": "code",
        "outputId": "9426b67c-c104-4f34-c501-91aa36e8c9fe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "import gym\n",
        "\n",
        "env = gym.make(\"Taxi-v2\")\n",
        "env.reset()\n",
        "counter = 0\n",
        "reward = 0\n",
        "while reward < 20:\n",
        "  #  print (\"reward : \",reward,\"ittereation : \",counter)\n",
        "    state, reward, done, info = env.step(env.action_space.sample())\n",
        "    counter +=1\n",
        "print('Random Actions Complete the game in ',counter,'iterations')"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Random Actions Complete the game in  2266 iterations\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "tTl42v9hWV2I",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "SeTjPaWegA3o",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Updating Q-Table in every iteration"
      ]
    },
    {
      "metadata": {
        "id": "r_RIQzl4aFLH",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "Q = np.zeros([env.observation_space.n, env.action_space.n])\n",
        "G= 0\n",
        "alpha = 0.2\n",
        "l=[]\n",
        "for episode in range(1000):\n",
        "    done = False\n",
        "    G, reward = 0,0\n",
        "    state = env.reset()\n",
        "    while done != True:\n",
        "            action = np.argmax(Q[state]) #1\n",
        "            state2, reward, done, info = env.step(action) #2\n",
        "            Q[state,action] += alpha * (reward + np.max(Q[state2]) - Q[state,action]) #3\n",
        "            G += reward\n",
        "            state = state2\n",
        "    l.append(G)  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "UZoFfrtS-Byc",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "Q = np.zeros([env.observation_space.n, env.action_space.n])\n",
        "alphalist = np.linspace(0.01,0.99,20)\n",
        "l=[]\n",
        "i=0\n",
        "while i<len(alphalist):\n",
        "      count = 0\n",
        "      alpha = alphalist[i]\n",
        "      G= 0\n",
        "      while G<10:\n",
        "          done = False\n",
        "          G, reward = 0,0\n",
        "          state = env.reset()\n",
        "          while done != True:\n",
        "                  action = np.argmax(Q[state]) #1\n",
        "                  state2, reward, done, info = env.step(action) #2\n",
        "\n",
        "                  Q[state,action] += alpha * (reward + np.max(Q[state2]) - Q[state,action]) #3\n",
        "                  G += reward\n",
        "                  state = state2\n",
        "          count += 1\n",
        "      l.append(count)\n",
        "      i += 1 "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "O-GiWTWygLxi",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Plotting the reward obtained"
      ]
    },
    {
      "metadata": {
        "id": "_snCjyQHaFIt",
        "colab_type": "code",
        "outputId": "6700e548-1b1b-4523-e798-b94a0c80fb39",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 328
        }
      },
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "from google.colab import files\n",
        "%matplotlib inline\n",
        "l = np.array(l)\n",
        "#l_avg = np.mean(l.reshape(-1, 10), axis=1)   # Average reward over every 10 iterations\n",
        "plt.scatter(np.arange(len(l)),l)\n",
        "plt.xlabel('Number of Episode')\n",
        "plt.ylabel('Cumulative Reward')\n",
        "plt.title('Using Q table')\n",
        "print('Maximum available Reward = 20')\n",
        "print('Maximum Reward Obtained = ', np.max(l))\n",
        "#plt.savefig('Reward vs Iteration.png')\n",
        "#files.download(\"Reward vs Iteration.png\") "
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Maximum available Reward = 20\n",
            "Maximum Reward Obtained =  802\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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w7gJgQZJYRESk+pIkg+uAxcDk6Mqgw4CLUo1KRERqKskcyD8ys4eBI4Es8CF3X5l6ZCIi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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "-4xzlOv-qfPa",
        "colab_type": "code",
        "outputId": "99cf4c51-ce76-4ec6-d481-a232cda72dd5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        }
      },
      "cell_type": "code",
      "source": [
        "plt.hist(l)\n",
        "plt.ylabel('Number of Episodes')\n",
        "plt.xlabel('Cumulative Reward')\n",
        "plt.title('Using Q Table');\n"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "nxTVQBYevppK",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "6Sjp0_wtqlCa",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        ""
      ]
    },
    {
      "metadata": {
        "id": "4Wsj02WZa-f8",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "[link text](https://)### Goal increases progressively as it should be in case of Q-Learning.\n",
        "### Optimization over increasing Reward"
      ]
    },
    {
      "metadata": {
        "id": "MwfFRuGSaFFD",
        "colab_type": "code",
        "outputId": "3576aa39-9952-47e8-d401-df3dda9b538b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "Q.shape"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(500, 6)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "metadata": {
        "id": "uBSgXpMkgoNm",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### The number of states are represented by rows and number of possible actions by columns"
      ]
    },
    {
      "metadata": {
        "id": "vtaR2sKGbtgr",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### use updated Q table"
      ]
    },
    {
      "metadata": {
        "id": "99uxfg9aaPeS",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# using the updated Q values\n",
        "import numpy as np\n",
        "G= 0\n",
        "alpha = 0.618\n",
        "l=[]\n",
        "for episode in range(1,1001):\n",
        "    done = False\n",
        "    G, reward = 0,0\n",
        "    state = env.reset()\n",
        "    while done != True:\n",
        "            action = np.argmax(Q[state]) #1\n",
        "            state, reward, done, info = env.step(action) #2\n",
        "            #Q[state,action] += alpha * (reward + np.max(Q[state2]) - Q[state,action]) #3\n",
        "            G += reward\n",
        "            #state = state2\n",
        "    l.append(G)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "xC_6c_QJabq6",
        "colab_type": "code",
        "outputId": "111a9707-8fff-4342-b6eb-566499d07a7b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 311
        }
      },
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "l = np.array(l)\n",
        "l_avg = np.mean(l.reshape(-1, 10), axis=1)   # Average reward over every 10 iterations\n",
        "plt.scatter(np.arange(len(l_avg)),l_avg)\n",
        "plt.xlabel('Iteration Number')\n",
        "plt.ylabel('Average Reward over 10 iterations')\n",
        "plt.title('Reward in Basic Q-Learning')"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Reward in Basic Q-Learning')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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qkXmTa19s6erx3S9RZ7wlJcsliKCxBjneg2Y65crsq2RGYpBjJtXV0/c5eHLpm+hrHSVl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\nBsIYY4wvayCMMcb4+v8C3j1ynlHO/AAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "z5B_s5kidSv2",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### goal not fix which mean the agent has not learnt the environment yet. Still the values are positive we should appretiate that."
      ]
    },
    {
      "metadata": {
        "id": "Dk121CsNadZQ",
        "colab_type": "code",
        "outputId": "946b4dd7-8db7-43db-8979-13f37441a83f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 153
        }
      },
      "cell_type": "code",
      "source": [
        "np.array(l).shape\n",
        "\n",
        "env.render()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "+---------+\n",
            "|\u001b[43mR\u001b[0m: | : :\u001b[34;1mG\u001b[0m|\n",
            "| : : : : |\n",
            "| : : : : |\n",
            "| | : | : |\n",
            "|\u001b[35mY\u001b[0m| : |B: |\n",
            "+---------+\n",
            "  (North)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "yxwy01u8ciS4",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### just random steps. No Q table."
      ]
    },
    {
      "metadata": {
        "id": "Dme5fey6av_6",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "l=[]\n",
        "for episode in range(1000):\n",
        "    done = False\n",
        "    G, reward = 0,0\n",
        "    state = env.reset()\n",
        "    while reward < 20:\n",
        "            action = env.action_space.sample() #1\n",
        "            state, reward, done, info = env.step(action) #2\n",
        "            G += reward\n",
        "    #if episode % 10 == 0:\n",
        "#        print('Episode {} Total Reward: {}'.format(episode,G))\n",
        "    l.append(G)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "CB1TLrQTcdbt",
        "colab_type": "code",
        "outputId": "d6ff09ac-dcac-4c02-be0b-889aa1a64f5c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 311
        }
      },
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "plt.scatter(np.arange(len(l)),l)\n",
        "plt.xlabel('Number of Episodes')\n",
        "plt.ylabel('Cumulative Reward')\n",
        "plt.title('Random action')\n",
        "print(reward)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "20\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3PfEKuw+epqtvlKDfw2jkDYKsTj5rqg0yf1Y1Q6MxuvtGaawtY+mCRsuZ9n1D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\ngg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "3EE85Uifu6wC",
        "colab_type": "code",
        "outputId": "e031bde4-15e3-47e0-fa21-5df7df481ebf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 311
        }
      },
      "cell_type": "code",
      "source": [
        "plt.hist(l);\n",
        "plt.xlabel('Cumulative Reward')\n",
        "plt.ylabel('Number of Episodes')\n",
        "plt.title('Random Agent');\n",
        "max(l)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-120"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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B6wH7RMQewBO8efcswCO5EGybf0c7Ax8H3l7w92NDlHsG1mxeJz2Jri8eiogX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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "mjMFo4g3r_E6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b1a1919c-2d31-4cf4-e8fd-f8a1adbfb138"
      },
      "cell_type": "code",
      "source": [
        "import gym\n",
        "\n",
        "env = gym.make(\"Taxi-v2\")\n",
        "env.reset()\n",
        "counter = 0\n",
        "reward = 0\n",
        "while reward < 20:\n",
        "  #  print (\"reward : \",reward,\"ittereation : \",counter)\n",
        "    state, reward, done, info = env.step(env.action_space.sample())\n",
        "    counter +=1\n",
        "print('Random Actions Complete the game in ',counter,'iterations')"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Random Actions Complete the game in  766 iterations\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "d8jx38Afco7Z",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Goal values are extremely negetive which tell that to complete the game the taxi has taken n number of wrong steps, silly!\n",
        "### the agent is not only poor but it not wrong to say that it is of use"
      ]
    }
  ]
}