Model_Answer_of_Q_No_1_Assignment_Module_6_.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "5KhwpV5M1ppt"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pylab as pl\n",
        "import networkx as nx"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "edges = [(0, 5), (0, 1), (2, 3), (5, 4), (1, 2),\n",
        "\t\t(1, 3), (9, 10), (2, 4), (2, 6), (6, 7),\n",
        "\t\t(5, 9), (2, 9), (3, 8), (3, 10)]\n",
        "\n",
        "goal = 7\n",
        "G = nx.Graph()\n",
        "G.add_edges_from(edges)\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",
        "pl.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        },
        "id": "ChIx3cgl1x60",
        "outputId": "150751f2-d624-4a53-c14f-745481c5f58c"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "MATRIX_SIZE = 11\n",
        "M = np.matrix(np.ones(shape =(MATRIX_SIZE, MATRIX_SIZE)))\n",
        "M *= -1\n",
        "\n",
        "for point in edges:\n",
        "\tprint(point)\n",
        "\tif point[1] == goal:\n",
        "\t\tM[point] = 100\n",
        "\telse:\n",
        "\t\tM[point] = 0\n",
        "\n",
        "\tif point[0] == goal:\n",
        "\t\tM[point[::-1]] = 100\n",
        "\telse:\n",
        "\t\tM[point[::-1]]= 0\n",
        "\t\t# reverse of point\n",
        "M[goal, goal]= 100\n",
        "print(M)\n",
        "# add goal point round trip"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OLqJiyRl2Hdj",
        "outputId": "3aeda671-4d8c-498d-c87f-22f4373ec4c5"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(0, 5)\n",
            "(0, 1)\n",
            "(2, 3)\n",
            "(5, 4)\n",
            "(1, 2)\n",
            "(1, 3)\n",
            "(9, 10)\n",
            "(2, 4)\n",
            "(2, 6)\n",
            "(6, 7)\n",
            "(5, 9)\n",
            "(2, 9)\n",
            "(3, 8)\n",
            "(3, 10)\n",
            "[[ -1.   0.  -1.  -1.  -1.   0.  -1.  -1.  -1.  -1.  -1.]\n",
            " [  0.  -1.   0.   0.  -1.  -1.  -1.  -1.  -1.  -1.  -1.]\n",
            " [ -1.   0.  -1.   0.   0.  -1.   0.  -1.  -1.   0.  -1.]\n",
            " [ -1.   0.   0.  -1.  -1.  -1.  -1.  -1.   0.  -1.   0.]\n",
            " [ -1.  -1.   0.  -1.  -1.   0.  -1.  -1.  -1.  -1.  -1.]\n",
            " [  0.  -1.  -1.  -1.   0.  -1.  -1.  -1.  -1.   0.  -1.]\n",
            " [ -1.  -1.   0.  -1.  -1.  -1.  -1. 100.  -1.  -1.  -1.]\n",
            " [ -1.  -1.  -1.  -1.  -1.  -1.   0. 100.  -1.  -1.  -1.]\n",
            " [ -1.  -1.  -1.   0.  -1.  -1.  -1.  -1.  -1.  -1.  -1.]\n",
            " [ -1.  -1.   0.  -1.  -1.   0.  -1.  -1.  -1.  -1.   0.]\n",
            " [ -1.  -1.  -1.   0.  -1.  -1.  -1.  -1.  -1.   0.  -1.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Q = np.matrix(np.zeros([MATRIX_SIZE, MATRIX_SIZE]))\n",
        "\n",
        "gamma = 0.75\n",
        "# learning parameter\n",
        "initial_state = 1\n",
        "\n",
        "# Determines the available actions for a given state\n",
        "def available_actions(state):\n",
        "\tcurrent_state_row = M[state, ]\n",
        "\tavailable_action = np.where(current_state_row >= 0)[1]\n",
        "\treturn available_action\n",
        "\n",
        "available_action = available_actions(initial_state)\n",
        "\n",
        "# Chooses one of the available actions at random\n",
        "def sample_next_action(available_actions_range):\n",
        "\tnext_action = int(np.random.choice(available_action, 1))\n",
        "\treturn next_action\n",
        "\n",
        "\n",
        "action = sample_next_action(available_action)\n",
        "\n",
        "def update(current_state, action, gamma):\n",
        "\n",
        "  max_index = np.where(Q[action, ] == np.max(Q[action, ]))[1]\n",
        "  if max_index.shape[0] > 1:\n",
        "\t   max_index = int(np.random.choice(max_index, size = 1))\n",
        "  else:\n",
        "\t     max_index = int(max_index)\n",
        "  max_value = Q[action, max_index]\n",
        "  Q[current_state, action] = M[current_state, action] + gamma * max_value\n",
        "  if (np.max(Q) > 0):\n",
        "\t  return(np.sum(Q / np.max(Q)*100))\n",
        "  else:\n",
        "\t  return (0)\n",
        "# Updates the Q-Matrix according to the path chosen\n",
        "\n",
        "update(initial_state, action, gamma)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hljZJF4o2kwz",
        "outputId": "a69a8252-b56c-411b-d294-c0ed745c90bb"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "scores = []\n",
        "for i in range(1000):\n",
        "\tcurrent_state = np.random.randint(0, int(Q.shape[0]))\n",
        "\tavailable_action = available_actions(current_state)\n",
        "\taction = sample_next_action(available_action)\n",
        "\tscore = update(current_state, action, gamma)\n",
        "\tscores.append(score)\n",
        "\n",
        "# print(\"Trained Q matrix:\")\n",
        "# print(Q / np.max(Q)*100)\n",
        "# You can uncomment the above two lines to view the trained Q matrix\n",
        "\n",
        "# Testing\n",
        "current_state = 0\n",
        "steps = [current_state]\n",
        "\n",
        "while current_state != 7:\n",
        "\n",
        "\tnext_step_index = np.where(Q[current_state, ] == np.max(Q[current_state, ]))[1]\n",
        "\tif next_step_index.shape[0] > 1:\n",
        "\t\tnext_step_index = int(np.random.choice(next_step_index, size = 1))\n",
        "\telse:\n",
        "\t\tnext_step_index = int(next_step_index)\n",
        "\tsteps.append(next_step_index)\n",
        "\tcurrent_state = next_step_index\n",
        "\n",
        "print(\"Most efficient path:\")\n",
        "print(steps)\n",
        "\n",
        "pl.plot(scores)\n",
        "pl.xlabel('No of iterations')\n",
        "pl.ylabel('Reward gained')\n",
        "pl.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484
        },
        "id": "_VF68Or523Rf",
        "outputId": "1b21ba23-1a5d-4e3b-979e-4b9777fcbfd5"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Most efficient path:\n",
            "[0, 1, 2, 6, 7]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}