Week_9/Day_3/Find_Best_Path_for_Jerry_Solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib as matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating random route map cell to cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "points_list = [(0,1), (0,3), (1,2), (1,4), (1,5), (1,8), (2,7), (5,6), (5,9), (7,9), (4,7), (3,8), (3,4), (8,9)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Jerry will start at point 0 and has to race to point 9 before other mouse and avoid cat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "mouse = [3,5]\n",
    "cat = [4,6,8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing the route"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "cheese = 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "G=nx.Graph()\n",
    "G.add_edges_from(points_list)\n",
    "mapping={0:'Jerry', 1:'1', 2:'2', 3:'3 - Mouse',\n",
    "    4:'4 - Cat', 5:'5 - Mouse', 6:'6 - Cat', 7:'7', 8:'8 - Cat', 9:'9 - Cheese'}\n",
    "H=nx.relabel_nodes(G,mapping)\n",
    "pos = nx.spring_layout(H)\n",
    "nx.draw_networkx_nodes(H,pos,\n",
    "    node_size=[500,500,500,500,500,500,500,500,500,500])\n",
    "nx.draw_networkx_edges(H,pos)\n",
    "nx.draw_networkx_labels(H,pos)\n",
    "matplotlib.pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The map shows the cell to cell route that Jerry has to scout while dealing with other mouse and avoiding cat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "MATRIX_SIZE = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "Initial_Cheese_Path_Matrix = np.matrix(np.ones(shape=(MATRIX_SIZE, MATRIX_SIZE)))\n",
    "Initial_Cheese_Path_Matrix *= -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Define values of viable path = 0 and for path leading to cheese = 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 0)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0,1)[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(0,1)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 1)\n",
      "(0, 3)\n",
      "(1, 2)\n",
      "(1, 4)\n",
      "(1, 5)\n",
      "(1, 8)\n",
      "(2, 7)\n",
      "(5, 6)\n",
      "(5, 9)\n",
      "(7, 9)\n",
      "(4, 7)\n",
      "(3, 8)\n",
      "(3, 4)\n",
      "(8, 9)\n"
     ]
    }
   ],
   "source": [
    "for point in points_list:\n",
    "    print(point)\n",
    "    if point[1] == cheese:\n",
    "        Initial_Cheese_Path_Matrix[point] = 100\n",
    "    else:\n",
    "        Initial_Cheese_Path_Matrix[point] = 0\n",
    "\n",
    "    if point[0] == cheese:\n",
    "        Initial_Cheese_Path_Matrix[point[::-1]] = 100\n",
    "    else:\n",
    "        # reverse of point\n",
    "        Initial_Cheese_Path_Matrix[point[::-1]]= 0\n",
    "\n",
    "Initial_Cheese_Path_Matrix[cheese,cheese]= 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ -1.,   0.,  -1.,   0.,  -1.,  -1.,  -1.,  -1.,  -1.,  -1.],\n",
       "        [  0.,  -1.,   0.,  -1.,   0.,   0.,  -1.,  -1.,   0.,  -1.],\n",
       "        [ -1.,   0.,  -1.,  -1.,  -1.,  -1.,  -1.,   0.,  -1.,  -1.],\n",
       "        [  0.,  -1.,  -1.,  -1.,   0.,  -1.,  -1.,  -1.,   0.,  -1.],\n",
       "        [ -1.,   0.,  -1.,   0.,  -1.,  -1.,  -1.,   0.,  -1.,  -1.],\n",
       "        [ -1.,   0.,  -1.,  -1.,  -1.,  -1.,   0.,  -1.,  -1., 100.],\n",
       "        [ -1.,  -1.,  -1.,  -1.,  -1.,   0.,  -1.,  -1.,  -1.,  -1.],\n",
       "        [ -1.,  -1.,   0.,  -1.,   0.,  -1.,  -1.,  -1.,  -1., 100.],\n",
       "        [ -1.,   0.,  -1.,   0.,  -1.,  -1.,  -1.,  -1.,  -1., 100.],\n",
       "        [ -1.,  -1.,  -1.,  -1.,  -1.,   0.,  -1.,   0.,   0., 100.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Initial_Cheese_Path_Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# To read the above matrix, the vertical values in the first column are the states or where Jerry is currently located, and the horizontal values are your possible next actions. We will use this matrix to update the values as Jerry learns which path it should take and which one to avoid."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We have assigned nodes 3 & 5 as mouse with which Jerry has to race and nodes 5,6,8 as cat that Jerry has to avoid. Jerry doesn’t know yet that there are other mouse or cats nor does it know that cats are bad as they will eat Jerry. Jerry needs to explore the environment, but this time it needs to deal with environment also."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "matrix = np.matrix(np.zeros([MATRIX_SIZE,MATRIX_SIZE]))\n",
    "gamma = 0.8\n",
    "mouse_present = np.matrix(np.zeros([MATRIX_SIZE,MATRIX_SIZE]))\n",
    "cat_present = np.matrix(np.zeros([MATRIX_SIZE,MATRIX_SIZE]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_state = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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     ]
    }
   ],
   "source": [
    "def available_actions(state):\n",
    "    current_state_row = Initial_Cheese_Path_Matrix[state,]\n",
    "    av_act = np.where(current_state_row >= 0)[1]\n",
    "    return av_act\n",
    "\n",
    "def sample_next_action(available_actions_range):\n",
    "    next_action = int(np.random.choice(available_act,1))\n",
    "    return next_action\n",
    "\n",
    "def collect_environmental_data(action):\n",
    "    found = []\n",
    "    if action in mouse:\n",
    "        found.append('m')\n",
    "\n",
    "    if action in cat:\n",
    "        found.append('c')\n",
    "    return (found)\n",
    "\n",
    "available_act = available_actions(initial_state)\n",
    "\n",
    "action = sample_next_action(available_act)\n",
    "\n",
    "def update(current_state, action, gamma):\n",
    "    max_index = np.where(matrix[action,] == np.max(matrix[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 = matrix[action, max_index]\n",
    "\n",
    "    matrix[current_state, action] = Initial_Cheese_Path_Matrix[current_state, action] + gamma * max_value\n",
    "    print('max_value', Initial_Cheese_Path_Matrix[current_state, action] + gamma * max_value)\n",
    "\n",
    "    environment = collect_environmental_data(action)\n",
    "    if 'm' in environment:\n",
    "        mouse_present[current_state, action] += 1\n",
    "\n",
    "    if 'c' in environment:\n",
    "        cat_present[current_state, action] += 1\n",
    "\n",
    "    if (np.max(matrix) > 0):\n",
    "        return(np.sum(matrix/np.max(matrix)*100))\n",
    "    else:\n",
    "        return (0)\n",
    "\n",
    "update(initial_state,action,gamma)\n",
    "\n",
    "scores = []\n",
    "for i in range(700):\n",
    "    current_state = np.random.randint(0, int(matrix.shape[0]))\n",
    "    available_act = available_actions(current_state)\n",
    "    action = sample_next_action(available_act)\n",
    "    score = update(current_state,action,gamma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Print where other mouse and cat were found"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mouse Found\n",
      "[[ 0.  0.  0. 32.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0. 12.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0. 25.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0. 55.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0. 23.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0. 26.  0.  0.  0.  0.]]\n",
      "Cat Found\n",
      "[[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0. 17.  0.  0.  0. 14.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0. 23.  0.  0.  0. 22.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0. 18.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0. 25.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0. 19.  0.]]\n"
     ]
    }
   ],
   "source": [
    "print('Mouse Found')\n",
    "print(mouse_present)\n",
    "print('Cat Found')\n",
    "print(cat_present)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Giving a negative value to cat so that Jerry avoids that route"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "enviro_matrix = mouse_present - cat_present"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Get possible actions in the current state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "available_act = available_actions(initial_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sample next action to be performed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "action = sample_next_action(available_act)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Updating the initial cheese path matrix according to the path selected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max_value 316.31065118525817\n"
     ]
    }
   ],
   "source": [
    "def update(current_state, action, gamma):\n",
    "\n",
    "    max_index = np.where(matrix[action,] == np.max(matrix[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 = matrix[action, max_index]\n",
    "\n",
    "    matrix[current_state, action] = Initial_Cheese_Path_Matrix[current_state, action] + gamma * max_value\n",
    "    print('max_value', Initial_Cheese_Path_Matrix[current_state, action] + gamma * max_value)\n",
    "\n",
    "    environment = collect_environmental_data(action)\n",
    "    if 'b' in environment:\n",
    "        enviro_matrix[current_state, action] += 1\n",
    "    if 's' in environment:\n",
    "        enviro_matrix[current_state, action] -= 1\n",
    "\n",
    "    return(np.sum(matrix/np.max(matrix)*100))\n",
    "\n",
    "update(initial_state,action,gamma)\n",
    "\n",
    "enviro_matrix_snap = enviro_matrix.copy()\n",
    "\n",
    "def available_actions_with_enviro_help(state):\n",
    "    current_state_row = Initial_Cheese_Path_Matrix[state,]\n",
    "    av_act = np.where(current_state_row >= 0)[1]\n",
    "    # Jerry will not take any route with even a single negative value as Jerry does not want to be in danger\n",
    "    env_pos_row = enviro_matrix_snap[state,av_act]\n",
    "    if (np.sum(env_pos_row < 0)):\n",
    "        temp_av_act = av_act[np.array(env_pos_row)[0]>=0]\n",
    "        if len(temp_av_act) > 0:\n",
    "            print('going from:',av_act)\n",
    "            print('to:',temp_av_act)\n",
    "            av_act = temp_av_act\n",
    "    return av_act"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training for 1500 iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max_value 313.58687413062455\n",
      "Score: 2096.7054267577437\n",
      "max_value 313.58687413062455\n",
      "Score: 2096.7054267577437\n",
      "max_value 494.86949930449964\n",
      "Score: 2092.259231714177\n",
      "going from: [0 4 8]\n",
      "to: [0]\n",
      "max_value 250.86949930449964\n",
      "Score: 2092.259231714177\n",
      "going from: [2 4 9]\n",
      "to: [2 9]\n",
      "max_value 313.58687413062455\n",
      "Score: 2092.988188197976\n",
      "max_value 313.58687413062455\n",
      "Score: 2092.988188197976\n",
      "max_value 313.58687413062455\n",
      "Score: 2093.717144681775\n",
      "max_value 313.58687413062455\n",
      "Score: 2094.446101165574\n",
      "max_value 313.58687413062455\n",
      "Score: 2094.446101165574\n",
      "max_value 313.58687413062455\n",
      "Score: 2094.446101165574\n",
      "max_value 313.58687413062455\n",
      "Score: 2094.446101165574\n",
      "max_value 313.58687413062455\n",
      "Score: 2094.446101165574\n",
      "max_value 313.58687413062455\n",
      "Score: 2094.446101165574\n",
      "going from: [0 2 4 5 8]\n",
      "to: [0 2 5]\n",
      "max_value 391.98359266328066\n",
      "Score: 2095.3572967703226\n",
      "going from: [0 4 8]\n",
      "to: [0]\n",
      "max_value 250.86949930449964\n",
      "Score: 2095.3572967703226\n",
      "max_value 313.58687413062455\n",
      "Score: 2095.3572967703226\n",
      "max_value 391.98359266328066\n",
      "Score: 2095.3572967703226\n",
      "max_value 391.98359266328066\n",
      "Score: 2095.3572967703226\n",
      "going from: [0 4 8]\n",
      "to: [0]\n",
      "max_value 250.86949930449964\n",
      "Score: 2095.3572967703226\n",
      "max_value 391.98359266328066\n",
      "Score: 2095.3572967703226\n",
      "going from: [1 6 9]\n",
      "to: [1 9]\n",
      "max_value 494.86949930449964\n",
      "Score: 2096.3454377816943\n",
      "max_value 313.58687413062455\n",
      "Score: 2096.3454377816943\n",
      "going from: [2 4 9]\n",
      "to: [2 9]\n",
      "max_value 313.58687413062455\n",
      "Score: 2096.3454377816943\n",
      "going from: [1 6 9]\n",
      "to: [1 9]\n",
      "max_value 494.86949930449964\n",
      "Score: 2096.3454377816943\n",
      "max_value 313.58687413062455\n",
      "Score: 2096.3454377816943\n",
      "going from: [2 4 9]\n",
      "to: [2 9]\n",
      "max_value 494.86949930449964\n",
      "Score: 2097.3335787930664\n",
      "max_value 313.58687413062455\n",
      "Score: 2098.062535276865\n",
      "going from: [2 4 9]\n",
      "to: [2 9]\n",
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      "Score: 2102.4491415501525\n",
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      "Score: 2102.4476041261837\n",
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      "Score: 2102.4476873736635\n",
      "going from: [5 7 8 9]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "to: [5 7 9]\n",
      "max_value 399.9983350573348\n",
      "Score: 2102.4477706211433\n",
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      "Score: 2102.4479579279728\n",
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      "Score: 2102.4480411754525\n",
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      "max_value 319.9983350573348\n",
      "Score: 2102.4480411754525\n",
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      "Score: 2102.4480411754525\n",
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      "Score: 2102.4480411754525\n",
      "max_value 319.9979188216685\n",
      "Score: 2102.4481452348023\n",
      "max_value 319.9979188216685\n",
      "Score: 2102.4481452348023\n",
      "max_value 313.58687413062455\n",
      "Score: 2102.4481452348023\n"
     ]
    }
   ],
   "source": [
    "scores = []\n",
    "for i in range(1500):\n",
    "    current_state = np.random.randint(0, int(matrix.shape[0]))\n",
    "    available_act = available_actions_with_enviro_help(current_state)\n",
    "    action = sample_next_action(available_act)\n",
    "    score = update(current_state,action,gamma)\n",
    "    scores.append(score)\n",
    "    print ('Score:', str(score))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best path to get to cheese before the other mouse while avoiding the cats is:\n",
      "[0, 1, 5, 9]\n"
     ]
    }
   ],
   "source": [
    "current_state = 0\n",
    "steps = [current_state]\n",
    "\n",
    "while current_state != 9:\n",
    "\n",
    "    next_step_index = np.where(matrix[current_state,]\n",
    "        == np.max(matrix[current_state,]))[1]\n",
    "\n",
    "    if next_step_index.shape[0] > 1:\n",
    "        next_step_index = int(np.random.choice(next_step_index, size = 1))\n",
    "        \n",
    "    else:\n",
    "        next_step_index = int(next_step_index)\n",
    "\n",
    "    steps.append(next_step_index)\n",
    "    current_state = next_step_index\n",
    "\n",
    "print(\"The best path to get to cheese before the other mouse while avoiding the cats is:\")\n",
    "print(steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20cbdb6f0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "matplotlib.pyplot.plot(scores)\n",
    "matplotlib.pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The above plot shows the convergence of the model or after how many iterations Jerry learnt the best path i.e. after approximately 900 iterations."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}