QLearning_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# QLearning Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start by importing QLearning class and functions written in QLearning.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from QLearning import *\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First example - Painless QLearning tuto"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First thing to do is to create the model of the system.\n",
    "This is for simulation purpose, in real life it could be given by sensors.\n",
    "The _model_ is given by the state graph and correspond to the possibility of performing an action (columns) from a given state (rows). For further explanations on this example, read [Painless QLearning tutorial](http://mnemstudio.org/path-finding-q-learning-tutorial.htm).\n",
    "\n",
    "This function returns next state from a given state and action. The result of this action will be, by definition of the problem, to move to the room which number is the action provided if this action is feasible. Otherwise the robot stays in his state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def apply_model(state, action):\n",
    "\n",
    "    model = np.array([[0, 0, 0, 0, 1, 0], \n",
    "                      [0, 0, 0, 0, 0, 1], \n",
    "                      [0, 0, 0, 1, 0, 0], \n",
    "                      [0, 0, 1, 0, 1, 0], \n",
    "                      [1, 0, 0, 1, 0, 1], \n",
    "                      [0, 1, 0, 0, 1, 1]])\n",
    "    \n",
    "    if model[state, action]:\n",
    "        \n",
    "        return action\n",
    "    \n",
    "    else:\n",
    "    \n",
    "        return state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the starting and goal states and the reward of any action performed in any state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "R0 = np.array([[0, 0, 0, 0, 0, 0],\n",
    "               [0, 0, 0, 0, 0, 100],\n",
    "               [0, 0, 0, 0, 0, 0],\n",
    "               [0, 0, 0, 0, 0, 0],\n",
    "               [0, 0, 0, 0, 0, 100],\n",
    "               [0, 0, 0, 0, 0, 100]])\n",
    "\n",
    "state = 2\n",
    "goal = 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the QLearning object by providing the states and action lists, reward matrix, learning rate and discount factor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "learning = QLearning(range(0,6), range(0,6), R0, 0.5, 0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we need a training function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def train_model(learning, start, steps, goal = -1, randomize = 0.5):\n",
    "    '''\n",
    "    goal_reached is set to -1 if we want to perform simulation exactly for the specified number of steps\n",
    "    otherwise the value is the state goal and the simulation stops if it is reached \n",
    "    '''\n",
    "    curr_state = start\n",
    "    states_log = [curr_state]\n",
    "    for i in range(steps):\n",
    "        if curr_state != goal:\n",
    "            action = learning.choose_action(state, randomize)\n",
    "            next_state = apply_model(curr_state, action)\n",
    "            learning.update_model(curr_state, action, next_state)\n",
    "            curr_state = next_state\n",
    "            states_log.append(curr_state)\n",
    "        else:\n",
    "            break\n",
    "            \n",
    "    return  states_log"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can perform a training until the robot reach the goal and visualize the path of the robot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "print(train_model(learning, state, 100, goal, 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The effect on Q matrix can be verified:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0.   0.   0.   0.   0.   0.]\n",
      " [  0.   0.   0.   0.   0.   0.]\n",
      " [  0.   0.   0.   0.   0.   0.]\n",
      " [  0.   0.   0.   0.   0.   0.]\n",
      " [  0.   0.   0.   0.   0.  50.]\n",
      " [  0.   0.   0.   0.   0.   0.]]\n"
     ]
    }
   ],
   "source": [
    "print(learning.Q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's train the model 100 simulation of 20 steps by complete semi-random exploration. We do not stop the simulation if the goal is reached. That way we completely explore the world."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2]\n"
     ]
    }
   ],
   "source": [
    "for i in range(100):\n",
    "    path = train_model(learning, state, 20, -1, 0.5)\n",
    "    if np.mod(i, 100) == 0:\n",
    "        print(path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We can now check the Q matrix. For better visualization, we can show it with color scales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 533.  527.  547.  546.  622.  553.]\n",
      " [ 328.  322.  126.  442.  355.  595.]\n",
      " [ 497.  500.  500.  565.  496.  497.]\n",
      " [ 557.  563.  500.  554.  638.  563.]\n",
      " [ 546.  625.  625.  550.  631.  724.]\n",
      " [ 607.  498.  582.  566.  625.  703.]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x228f4291b38>"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x228f444b3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q = np.round(learning.Q)\n",
    "print(Q)\n",
    "plt.imshow(Q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We can check that the resulting policy allows to find a direct path to the goal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def planer(learning, start, goal):\n",
    "    curr_state = start\n",
    "    path = [curr_state]\n",
    "    i = 0\n",
    "    while (curr_state != goal) and i < 1000:\n",
    "        action = learning.choose_best_action(curr_state)\n",
    "        next_state = apply_model(curr_state, action)\n",
    "        curr_state = next_state\n",
    "        path.append(curr_state)\n",
    "        i += 1\n",
    "    return path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "print(planer(learning, state, goal))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Secound example - Grid World Path Finding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example we will try to find a path linking 2 points avoiding randomly generated obstacles in a grid world where posiible actions are the 4-neighbourhood of the cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from QLearning import *\n",
    "import GridWorld as gw\n",
    "import matplotlib.pylab as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some functions are needed to manage easily the grid map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mapper(x, dim):\n",
    "    \n",
    "    return [x//dim[1], np.mod(x, dim[1])]\n",
    "\n",
    "def unmapper(x, dim):\n",
    "    \n",
    "    return x[0] * dim[1] + x[1]\n",
    "\n",
    "dim = [20, 20]\n",
    "model = np.zeros(dim)\n",
    "model[np.where(np.random.rand(dim[0], dim[1]) > 0.6)] = 1 \n",
    "\n",
    "def find_free(model):\n",
    "    \n",
    "    free = np.where(model == 0)\n",
    "    rand_pos = np.random.randint(len(free[0]))\n",
    "\n",
    "    return unmapper([free[0][rand_pos], free[1][rand_pos]], dim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in last example, I define a model for the simulation, assuming edged are obstacles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def apply_model(state, action):\n",
    "    \n",
    "    cord = mapper(state, dim)\n",
    "    \n",
    "    if (cord[0] == 0 and action == 1) or (cord[0] == dim[0] - 1 and action == 3) or (cord[1] == 0 and action == 2) or (cord[1] == dim[1] - 1 and action == 0):\n",
    "        \n",
    "        return state\n",
    "    \n",
    "    elif (action == 0 and model[cord[0], cord[1] + 1]) or (action == 1 and model[cord[0] - 1, cord[1]]) or (action == 2 and model[cord[0], cord[1] - 1]) or (action == 3 and model[cord[0] + 1, cord[1]]):\n",
    "        \n",
    "        return state\n",
    "    \n",
    "    else:   \n",
    "        \n",
    "        if action == 0:\n",
    "            \n",
    "            return unmapper([cord[0], cord[1] + 1], dim)\n",
    "                           \n",
    "        elif action == 1:\n",
    "            \n",
    "            return unmapper([cord[0] - 1, cord[1]], dim)\n",
    "                           \n",
    "        elif action == 2:\n",
    "            \n",
    "            return unmapper([cord[0], cord[1] - 1], dim)\n",
    "                           \n",
    "        else:\n",
    "            \n",
    "            return unmapper([cord[0] + 1, cord[1]], dim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Define a reward function, a random goal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [],
   "source": [
    "R0 = np.zeros([dim[0] * dim[1], 4])\n",
    "goal = find_free(model)\n",
    "R0[goal, 0] = 100\n",
    "s0 = goal\n",
    "while np.sum(np.abs(s0 - goal)) < np.sum(dim) * 0.8:\n",
    "    s0 = find_free(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the learning object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [],
   "source": [
    "learning = QLearning(range(0,dim[0] * dim[1]), range(0,4), R0, 0.5, 0.99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [],
   "source": [
    "preview = np.zeros(dim)\n",
    "\n",
    "for _ in range(500):\n",
    "            \n",
    "    state = s0\n",
    "    \n",
    "    for _ in range(500):\n",
    "        \n",
    "        action = learning.choose_action(state,0.5)\n",
    "        next_state = apply_model(state, action)\n",
    "        learning.update_model(state, action, next_state)        \n",
    "        state = next_state\n",
    "        \n",
    "    s = s0\n",
    "    \n",
    "for _ in range(dim[0] * dim[1]):\n",
    "\n",
    "    s = apply_model(s, learning.choose_best_action(s))\n",
    "    preview[tuple(mapper(s, dim))] = 0.5\n",
    "\n",
    "    if s == goal:\n",
    "        break\n",
    "        \n",
    "preview[tuple(mapper(s0, dim))] = 1\n",
    "preview[tuple(mapper(goal, dim))] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We can now visualize Q matrix and the learned path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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521EgIQIAANbrlgkRAABwUCfcZVbvbPM+R0IEAACsR0IEAIBlOuMuMxIiAAAAP0NCBACA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x228f4499588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(dim[1]/2,dim[0]),facecolor='w') \n",
    "plt.clf()\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.title('Q matrix coefficients')\n",
    "gw.DrawMap(np.reshape(np.max(learning.Q, 1), dim), model)\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.title('Simulated learned path')\n",
    "gw.DrawMap(preview, model)\n",
    "plt.pause(0.01)"
   ]
  }
 ],
 "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}