Reinforcement_Learning_02.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPsWw1iW7y6kyz8FKUvC0GP",
      "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/Yashithi98/Machine-Learning/blob/main/Reinforcement_Learning_02.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RehPoSoVqmEG"
      },
      "source": [
        "#Reinforcement Learning \n",
        "\n",
        " Model the Maze Solving Problem\n",
        "\n",
        "*- Python Code*"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NTcikARQqZ5P"
      },
      "source": [
        "**Importing Packages**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tFsSMIgoqZF_"
      },
      "source": [
        "import numpy as np\n",
        "import pylab as plt\n",
        "import networkx as nx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wIgia_a8qwkc"
      },
      "source": [
        "**Defining Points - Paths of the Maze as coordinates**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yerpbOhvqxdE"
      },
      "source": [
        "mazePaths = [((0,0),(0,1)),((0,1),(0,2)),((0,1),(1,1)),((0,2),(1,2)),((0,2),(-1,2)),((0,2),(0,3)),((-1,3),(-1,2)),((1,1),(2,1)),((-1,-1),(-1,2)),((0,3),(-1,3)),((-1,-1),(2,-1)),\n",
        "((1,1),(1,2)),((2,2),(1,2)),((2,1),(2,2)),((2,1),(3,1)),((2,-1),(2,1)),((2,2),(3,2)),((3,2),(3,3))]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DBybCFO697R2"
      },
      "source": [
        "**Visualizing the Maze Path**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "otrsaoWp-L_1",
        "outputId": "c1f5fe88-9f30-467e-b87a-542b83004b4f"
      },
      "source": [
        "G=nx.Graph()\n",
        "G.add_edges_from(mazePaths)\n",
        "pos = nx.spring_layout(G)\n",
        "nx.draw_networkx_nodes(G,pos)\n",
        "nx.draw_networkx_edges(G,pos)\n",
        "nx.draw_networkx_labels(G,pos)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "voze8oKD-tZK"
      },
      "source": [
        "**Remodelling the Maze Problem**\n",
        "- Here we remodel the above data by substituting data points for coordinates as demonstrated in the figure below :\n",
        "![WhatsApp Image 2021-08-29 at 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)\n",
        "- In order to model this problem to fit the reinforcement learning we create an array which represents the above data points as **states** and the directions as **actions** . \n",
        "Eg : [1,UP] = 3, [1,RIGHT] = 2\n",
        "\n",
        "- Thereby, the states are : {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14}\n",
        "  Directions are : {0,1,2,3} where UP = 0, DOWN = 1, LEFT = 2, RIGHT = 3"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tpGrMf9_-tXO"
      },
      "source": [
        "**Defining the data points - nodes**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7tOjlbW1AckV"
      },
      "source": [
        "pointList = [(0,0),(1,1),(2,2),(1,3),(3,1),(1,0),(7,3),(8,2),(11,1),(8,0),(2,3),(11,2),(9,1),(2,0),(10,1),(11,0),(9,2),(3,3),(10,2),(9,3),(3,2),(6,3),(7,0),(6,1),(5,1),(6,0),(4,1),(3,0),(4,2),(5,3),(10,3),(12,2),(11,3),(14,2),(13,1),(12,0)]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VkQaCzeUO2k6"
      },
      "source": [
        "**Intializing Path Array**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hwdQZFWbO8VW"
      },
      "source": [
        "#Initializing a 2D array of -1's as [STATES,DIRECTIONS] \n",
        "path = [[-1 for i in range(4)] for j in range(15)]\n",
        "\n",
        "\n",
        "#Assigning values to this 2D array as [State,Direction] = Resultant State\n",
        "path[0][0] = 1 \n",
        "path[1][1] = 0 \n",
        "\n",
        "path[3][1] = 1\n",
        "path[1][0] = 3 \n",
        "\n",
        "path[1][3] = 2\n",
        "path[2][2] = 1\n",
        "\n",
        "path[3][2] = 6 \n",
        "path[6][3] = 3 \n",
        "\n",
        "path[4][1] = 3\n",
        "path[3][0] = 4\n",
        "\n",
        "path[9][2] = 3\n",
        "path[3][3] = 9\n",
        "\n",
        "path[9][1] = 2\n",
        "path[2][0] = 9\n",
        "\n",
        "path[10][2] = 9\n",
        "path[9][3] = 10\n",
        "\n",
        "path[2][3] = 11\n",
        "path[11][2] = 2\n",
        "\n",
        "path[10][1] = 11 \n",
        "path[11][0] = 10\n",
        "\n",
        "path[10][3] = 12\n",
        "path[12][2] = 10\n",
        "\n",
        "path[13][1] = 12\n",
        "path[12][0] = 13\n",
        "\n",
        "path[11][1] = 8\n",
        "path[8][0] = 11\n",
        "\n",
        "path[7][3] = 8\n",
        "path[8][2] = 7\n",
        "\n",
        "path[7][0] = 6\n",
        "path[6][1] = 7\n",
        "\n",
        "path[5][1] = 6\n",
        "path[6][0] = 5\n",
        "\n",
        "path[4][2] = 5\n",
        "path[5][3] = 4\n",
        "\n",
        "path[14][2] = 11\n",
        "path[11][3] = 14"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z71Vc4qiV6yZ",
        "outputId": "71ffac18-5b2b-4f85-90a7-57bb1ff98e4d"
      },
      "source": [
        "path"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[[1, -1, -1, -1],\n",
              " [3, 0, -1, 2],\n",
              " [9, -1, 1, 11],\n",
              " [4, 1, 6, 9],\n",
              " [-1, 3, 5, -1],\n",
              " [-1, 6, -1, 4],\n",
              " [5, 7, -1, 3],\n",
              " [6, -1, -1, 8],\n",
              " [11, -1, 7, -1],\n",
              " [-1, 2, 3, 10],\n",
              " [-1, 11, 9, 12],\n",
              " [10, 8, 2, 14],\n",
              " [13, -1, 10, -1],\n",
              " [-1, 12, -1, -1],\n",
              " [-1, -1, 11, -1]]"
            ]
          },
          "metadata": {},
          "execution_count": 205
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2ugphBL9VvRX"
      },
      "source": [
        "**Defining the R Matrix (Rewards Table)**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UePBr8u1V3pH"
      },
      "source": [
        "destination = 14\n",
        "R = np.matrix(np.ones(shape=(15, 4)))\n",
        "R *= -1\n",
        "\n",
        "for i in pointList:\n",
        "  x = i[0]\n",
        "  y = i[1]\n",
        "  if (path[x][y] == destination):\n",
        "    R[i] = 100\n",
        "  else:\n",
        "    R[i] = 0"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7Nw1IpUkWZTh",
        "outputId": "a7f938c1-ce4e-483d-f634-28a41a50a655"
      },
      "source": [
        "R"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "matrix([[  0.,  -1.,  -1.,  -1.],\n",
              "        [  0.,   0.,  -1.,   0.],\n",
              "        [  0.,  -1.,   0.,   0.],\n",
              "        [  0.,   0.,   0.,   0.],\n",
              "        [ -1.,   0.,   0.,  -1.],\n",
              "        [ -1.,   0.,  -1.,   0.],\n",
              "        [  0.,   0.,  -1.,   0.],\n",
              "        [  0.,  -1.,  -1.,   0.],\n",
              "        [  0.,  -1.,   0.,  -1.],\n",
              "        [ -1.,   0.,   0.,   0.],\n",
              "        [ -1.,   0.,   0.,   0.],\n",
              "        [  0.,   0.,   0., 100.],\n",
              "        [  0.,  -1.,   0.,  -1.],\n",
              "        [ -1.,   0.,  -1.,  -1.],\n",
              "        [ -1.,  -1.,   0.,  -1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 207
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nItyJYiOWhAU"
      },
      "source": [
        "**Q-Learning**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jbWsItS3WjqW"
      },
      "source": [
        "Q = np.matrix(np.zeros([15,4]))\n",
        "\n",
        "# Learning Rate\n",
        "gamma = 0.8\n",
        "\n",
        "initial_state = 0\n",
        "\n",
        "def sample_next_action(current_state, direction_value):\n",
        "    next_action = path[current_state][direction_value]\n",
        "    return next_action\n",
        "\n",
        "\n",
        "def update(current_state, action, gamma, direction_value):\n",
        "    max_index = np.where(Q[action,] == np.max(Q[action,]))[1]\n",
        "\n",
        "    if max_index.shape[0] > 1:\n",
        "        max_index = int(np.random.choice(max_index, size = 1))\n",
        "    else:\n",
        "        max_index = int(max_index)\n",
        "    max_value = Q[action, max_index]\n",
        "    print(max_value)\n",
        "\n",
        "    Q[current_state, direction_value] = R[current_state, direction_value] + gamma * max_value\n",
        "    print('max_value', R[current_state, direction_value] + gamma * max_value)\n",
        "\n",
        "    if (np.max(Q) > 0):\n",
        "      return(np.sum(Q/np.max(Q)*100))\n",
        "    else:\n",
        "      return (0)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P9-8CFGnfkxG"
      },
      "source": [
        "**Training**\n",
        "\n",
        "- The Possible Direction Sequences are as follows :\n",
        "\n",
        "**1. STARTING FROM (0,0) [STATE : 0]**\n",
        "\n",
        "Sequence1  = 0 -> 3 -> 3 -> 3 \n",
        "\n",
        "**2. STARTING FROM (1,1) [STATE : 2]**\n",
        "\n",
        "Sequence2  = 3 -> 3 \n",
        "\n",
        "**3. STARTING FROM (1,2) [STATE : 9]**\n",
        "\n",
        "Sequence3  = 1 -> 3 -> 3 \n",
        "\n",
        "**4. STARTING FROM (2,-1) [STATE : 8]**\n",
        "\n",
        "Sequence4  = 0 -> 3\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "l_WdtjQ0fsE-",
        "outputId": "5d6b3466-8510-40ac-8d40-cd1d83ea0ed9"
      },
      "source": [
        "scores = []\n",
        "\n",
        "# SEQUENCE 01\n",
        "seq1 = [0, 3, 3, 3]\n",
        "current_state = 0\n",
        "for i in seq1:\n",
        "    direction_value = i\n",
        "    action = sample_next_action(current_state, direction_value)\n",
        "    print(current_state, action, direction_value)\n",
        "    score = update(current_state, action, gamma, direction_value)\n",
        "    scores.append(score)\n",
        "    print ('Score:', str(score))\n",
        "    current_state = action\n",
        "\n",
        "# SEQUENCE 02\n",
        "seq2 = [3, 3]\n",
        "current_state = 2\n",
        "for i in seq2:\n",
        "    direction_value = i\n",
        "    action = sample_next_action(current_state, direction_value)\n",
        "    print(current_state, action, direction_value)\n",
        "    score = update(current_state, action, gamma, direction_value)\n",
        "    scores.append(score)\n",
        "    print ('Score:', str(score))\n",
        "    current_state = action\n",
        "\n",
        "# SEQUENCE 03\n",
        "seq3 = [1, 3, 3]\n",
        "current_state = 9\n",
        "for i in seq3:\n",
        "    direction_value = i\n",
        "    action = sample_next_action(current_state, direction_value)\n",
        "    print(current_state, action, direction_value)\n",
        "    score = update(current_state, action, gamma, direction_value)\n",
        "    scores.append(score)\n",
        "    print ('Score:', str(score))\n",
        "    current_state = action\n",
        "\n",
        "# SEQUENCE 04\n",
        "seq4 = [0, 3]\n",
        "current_state = 8\n",
        "for i in seq4:\n",
        "    direction_value = i\n",
        "    action = sample_next_action(current_state, direction_value)\n",
        "    print(current_state, action, direction_value)\n",
        "    score = update(current_state, action, gamma, direction_value)\n",
        "    scores.append(score)\n",
        "    print ('Score:', str(score))\n",
        "    current_state = action\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0 1 0\n",
            "0.0\n",
            "max_value 0.0\n",
            "Score: 0\n",
            "1 2 3\n",
            "0.0\n",
            "max_value 0.0\n",
            "Score: 0\n",
            "2 11 3\n",
            "0.0\n",
            "max_value 0.0\n",
            "Score: 0\n",
            "11 14 3\n",
            "0.0\n",
            "max_value 100.0\n",
            "Score: 100.0\n",
            "2 11 3\n",
            "100.0\n",
            "max_value 80.0\n",
            "Score: 180.0\n",
            "11 14 3\n",
            "0.0\n",
            "max_value 100.0\n",
            "Score: 180.0\n",
            "9 2 1\n",
            "80.0\n",
            "max_value 64.0\n",
            "Score: 244.0\n",
            "2 11 3\n",
            "100.0\n",
            "max_value 80.0\n",
            "Score: 244.0\n",
            "11 14 3\n",
            "0.0\n",
            "max_value 100.0\n",
            "Score: 244.0\n",
            "8 11 0\n",
            "100.0\n",
            "max_value 80.0\n",
            "Score: 324.0\n",
            "11 14 3\n",
            "0.0\n",
            "max_value 100.0\n",
            "Score: 324.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ukkID6S1ka9_",
        "outputId": "436358fb-08a4-4137-fade-c35f3c959a1f"
      },
      "source": [
        "print(\"Trained Q matrix:\")\n",
        "print(Q/np.max(Q)*100)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Trained Q matrix:\n",
            "[[  0.   0.   0.   0.]\n",
            " [  0.   0.   0.   0.]\n",
            " [  0.   0.   0.  80.]\n",
            " [  0.   0.   0.   0.]\n",
            " [  0.   0.   0.   0.]\n",
            " [  0.   0.   0.   0.]\n",
            " [  0.   0.   0.   0.]\n",
            " [  0.   0.   0.   0.]\n",
            " [ 80.   0.   0.   0.]\n",
            " [  0.  64.   0.   0.]\n",
            " [  0.   0.   0.   0.]\n",
            " [  0.   0.   0. 100.]\n",
            " [  0.   0.   0.   0.]\n",
            " [  0.   0.   0.   0.]\n",
            " [  0.   0.   0.   0.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C8K08ANqki21"
      },
      "source": [
        "**Results**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kDFlJ2HDkky_",
        "outputId": "c3156806-1618-4012-c372-8d6d18a64350"
      },
      "source": [
        "initial_state = 0\n",
        "steps = [initial_state]\n",
        "\n",
        "while initial_state != 14:\n",
        "    next_step_index = np.where(Q[initial_state,] == np.max(Q[initial_state,]))[1]\n",
        "\n",
        "    if next_step_index.shape[0] > 1:\n",
        "        index = (np.random.choice(next_step_index, size = 1))\n",
        "        next_step_index = path[initial_state][index[0]]\n",
        "    else:\n",
        "        index = int(next_step_index)\n",
        "        next_step_index = path[initial_state][index]\n",
        "\n",
        "    steps.append(next_step_index)\n",
        "    initial_state = next_step_index\n",
        "\n",
        "print(\"Most efficient path:\")\n",
        "print(steps)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Most efficient path:\n",
            "[0, 1, 2, 11, 14]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YnVEr7y1lhIw",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 264
        },
        "outputId": "b3d10ee4-876f-4cef-9113-5889ec0d40c8"
      },
      "source": [
        "plt.plot(scores)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}