8-Reinforcement/1-QLearning/notebook.ipynb

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   "source": [
    "# Peter and the Wolf: Reinforcement Learning Primer\n",
    "\n",
    "In this tutorial, we will learn how to apply Reinforcement learning to a problem of path finding. The setting is inspired by [Peter and the Wolf](https://en.wikipedia.org/wiki/Peter_and_the_Wolf) musical fairy tale by Russian composer [Sergei Prokofiev](https://en.wikipedia.org/wiki/Sergei_Prokofiev). It is a story about young pioneer Peter, who bravely goes out of his house to the forest clearing to chase a wolf. We will train machine learning algorithms that will help Peter to explore the surrounding area and build an optimal navigation map.\n",
    "\n",
    "First, let's import a bunch of useful libraries:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random\n",
    "import math"
   ]
  },
  {
   "source": [
    "## Overview of Reinforcement Learning\n",
    "\n",
    "**Reinforcement Learning** (RL) is a learning technique that allows us to learn an optimal behaviour of an **agent** in some **environment** by running many experiments. An agent in this environment should have some **goal**, defined by a **reward function**.\n",
    "\n",
    "## The Environment\n",
    "\n",
    "For simplicity, let's consider Peter's world to be a square board of size `width` x `height`. Each cell in this board can either be:\n",
    "* **ground**, on which Peter and other creatures can walk\n",
    "* **water**, on which you obviously cannot walk\n",
    "* **a tree** or **grass** - a place where you can rest\n",
    "* **an apple**, which represents something Peter would be glad to find in order to feed himself\n",
    "* **a wolf**, which is dangerous and should be avoided\n",
    "\n",
    "To work with the environment, we will define a class called `Board`. In order not to clutter this notebook too much, we have moved all code to work with the board into separate `rlboard` module, which we will now import. You may look inside this module to get more details about the internals of the implementation."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "Let's now create a random board and see how it looks:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# code block 1"
   ]
  },
  {
   "source": [
    "## Actions and Policy\n",
    "\n",
    "In our example, Peter's goal would be to find an apple, while avoiding the wolf and other obstacles. Define those actions as a dictionary, and map them to pairs of corresponding coordinate changes."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# code block 2"
   ]
  },
  {
   "source": [
    "The strategy of our agent (Peter) is defined by a so-called **policy**. Let's consider the simplest policy called **random walk**.\n",
    "\n",
    "## Random walk\n",
    "\n",
    "Let's first solve our problem by implementing a random walk strategy."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "# Let's run a random walk experiment several times and see the average number of steps taken: code block 3"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# code block 4"
   ]
  },
  {
   "source": [
    "## Reward Function\n",
    "\n",
    "To make our policy more intelligent, we need to understand which moves are \"better\" than others.\n",
    "\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#code block 5"
   ]
  },
  {
   "source": [
    "## Q-Learning\n",
    "\n",
    "Build a Q-Table, or multi-dimensional array. Since our board has dimentions `width` x `height`, we can represent Q-Table by a numpy array with shape `width` x `height` x `len(actions)`:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# code block 6"
   ]
  },
  {
   "source": [
    "Pass the Q-Table to the `plot` function in order to visualize the table on the board:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 'm' is not defined",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-10-8b8a9e4cb2b8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mQ\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'm' is not defined"
     ]
    }
   ],
   "source": [
    "m.plot(Q)"
   ]
  },
  {
   "source": [
    "\n",
    "## Essence of Q-Learning: Bellman Equation and  Learning Algorithm\n",
    "\n",
    "Write a pseudo-code for our leaning algorithm:\n",
    "\n",
    "* Initialize Q-Table Q with equal numbers for all states and actions\n",
    "* Set learning rate $\\alpha\\leftarrow 1$\n",
    "* Repeat simulation many times\n",
    "   1. Start at random position\n",
    "   1. Repeat\n",
    "        1. Select an action $a$ at state $s$\n",
    "        2. Exectute action by moving to a new state $s'$\n",
    "        3. If we encounter end-of-game condition, or total reward is too small - exit simulation  \n",
    "        4. Compute reward $r$ at the new state\n",
    "        5. Update Q-Function according to Bellman equation: $Q(s,a)\\leftarrow (1-\\alpha)Q(s,a)+\\alpha(r+\\gamma\\max_{a'}Q(s',a'))$\n",
    "        6. $s\\leftarrow s'$\n",
    "        7. Update total reward and decrease $\\alpha$.\n",
    "\n",
    "## Exploit vs. Explore\n",
    "\n",
    "The best approach is to balance between exploration and exploitation. As we learn more about our environment, we would be more likely to follow the optimal route, however, choosing the unexplored path once in a while.\n",
    "\n",
    "## Python Implementation\n",
    "\n",
    "Now we are ready to implement the learning algorithm. Before that, we also need some function that will convert arbitrary numbers in the Q-Table into a vector of probabilities for corresponding actions:"
   ],
   "cell_type": "markdown",
   "metadata": {}
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  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# code block 7"
   ]
  },
  {
   "source": [
    "We add a small amount of `eps` to the original vector in order to avoid division by 0 in the initial case, when all components of the vector are identical.\n",
    "\n",
    "The actual learning algorithm we will run for 5000 experiments, also called **epochs**: "
   ],
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   "cell_type": "code",
   "execution_count": 56,
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    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      ""
     ]
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   ],
   "source": [
    "\n",
    "from IPython.display import clear_output\n",
    "\n",
    "lpath = []\n",
    "\n",
    "# code block 8"
   ]
  },
  {
   "source": [
    "After executing this algorithm, the Q-Table should be updated with values that define the attractiveness of different actions at each step. Visualize the table here:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "m.plot(Q)"
   ]
  },
  {
   "source": [
    "## Checking the Policy\n",
    "\n",
    "Since Q-Table lists the \"attractiveness\" of each action at each state, it is quite easy to use it to define the efficient navigation in our world. In the simplest case, we can just select the action corresponding to the highest Q-Table value:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "# code block 9"
   ]
  },
  {
   "source": [
    "If you try the code above several times, you may notice that sometimes it just \"hangs\", and you need to press the STOP button in the notebook to interrupt it. \n",
    "\n",
    "> **Task 1:** Modify the `walk` function to limit the maximum length of path by a certain number of steps (say, 100), and watch the code above return this value from time to time.\n",
    "\n",
    "> **Task 2:** Modify the `walk` function so that it does not go back to the places where is has already been previously. This will prevent `walk` from looping, however, the agent can still end up being \"trapped\" in a location from which it is unable to escape."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Average path length = 5.31, eaten by wolf: 0 times\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# code block 10"
   ]
  },
  {
   "source": [
    "## Investigating the Learning Process"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x26dab295a48>]"
      ]
     },
     "metadata": {},
     "execution_count": 57
    },
    {
     "output_type": "display_data",
     "data": {
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115.016451 213.43645 \r\nL 115.046891 214.46305 \r\nL 115.07733 207.339708 \r\nL 115.168648 209.66527 \r\nL 115.229527 213.268842 \r\nL 115.290406 211.215644 \r\nL 115.320845 205.642677 \r\nL 115.351285 214.756364 \r\nL 115.381724 209.749074 \r\nL 115.533921 214.756364 \r\nL 115.564361 213.687862 \r\nL 115.655679 206.606423 \r\nL 115.746997 214.756364 \r\nL 115.716558 193.700604 \r\nL 115.777436 214.735413 \r\nL 115.838315 193.763457 \r\nL 115.868755 193.910114 \r\nL 115.899194 214.756364 \r\nL 115.990512 212.346998 \r\nL 116.051391 210.754722 \r\nL 116.11227 214.756364 \r\nL 116.142709 211.76037 \r\nL 116.203588 214.756364 \r\nL 116.234027 214.756364 \r\nL 116.264467 213.478352 \r\nL 116.294906 214.756364 \r\nL 116.325346 184.670721 \r\nL 116.386225 214.756364 \r\nL 116.416664 214.044029 \r\nL 116.447103 214.756364 \r\nL 116.477543 196.047117 \r\nL 116.538422 212.786969 \r\nL 116.5993 210.964232 \r\nL 116.690619 214.756364 \r\nL 116.812376 200.404926 \r\nL 116.903694 214.756364 \r\nL 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200.090661 \r\nL 122.595864 211.927978 \r\nL 122.687182 211.383252 \r\nL 122.717621 214.756364 \r\nL 122.7785 214.756364 \r\nL 122.80894 210.335702 \r\nL 122.900258 212.493655 \r\nL 122.930697 214.756364 \r\nL 123.022015 183.958387 \r\nL 123.052455 208.533915 \r\nL 123.082894 214.756364 \r\nL 123.113334 201.703888 \r\nL 123.143773 210.482359 \r\nL 123.174212 210.419506 \r\nL 123.265531 200.48873 \r\nL 123.29597 214.756364 \r\nL 123.326409 214.735413 \r\nL 123.356849 187.017234 \r\nL 123.417728 214.756364 \r\nL 123.569925 191.291239 \r\nL 123.691682 214.756364 \r\nL 123.722122 214.735413 \r\nL 123.783001 205.579824 \r\nL 123.81344 189.279942 \r\nL 123.874319 214.735413 \r\nL 123.935198 214.735413 \r\nL 123.996076 214.756364 \r\nL 124.026516 206.669276 \r\nL 124.148273 214.756364 \r\nL 124.178713 214.756364 \r\nL 124.239592 209.581466 \r\nL 124.270031 211.96988 \r\nL 124.300471 214.023078 \r\nL 124.33091 201.201064 \r\nL 124.422228 208.471062 \r\nL 124.513546 214.756364 \r\nL 124.543986 212.326047 \r\nL 124.604865 199.818297 \r\nL 124.635304 207.360659 \r\nL 124.726622 214.756364 \r\nL 124.787501 174.467582 \r\nL 124.81794 214.756364 \r\nL 124.909259 214.735413 \r\nL 124.939698 211.173742 \r\nL 124.970137 186.283949 \r\nL 125.031016 211.907027 \r\nL 125.091895 214.756364 \r\nL 125.152774 214.735413 \r\nL 125.274532 173.252424 \r\nL 125.36585 214.756364 \r\nL 125.396289 214.127834 \r\nL 125.426729 214.735413 \r\nL 125.457168 198.267923 \r\nL 125.518047 214.106882 \r\nL 125.548486 210.775673 \r\nL 125.609365 214.756364 \r\nL 125.639804 211.006134 \r\nL 125.731123 214.735413 \r\nL 125.761562 214.421148 \r\nL 125.822441 214.735413 \r\nL 125.913759 173.399081 \r\nL 125.974638 214.756364 \r\nL 126.035517 206.648325 \r\nL 126.065956 206.585472 \r\nL 126.187714 214.756364 \r\nL 126.248593 214.756364 \r\nL 126.309471 213.562156 \r\nL 126.339911 205.852187 \r\nL 126.37035 214.735413 \r\nL 126.40079 212.996479 \r\nL 126.431229 214.756364 \r\nL 126.461668 214.588756 \r\nL 126.522547 198.41458 \r\nL 126.552987 213.059332 \r\nL 126.705184 214.756364 \r\nL 126.735623 192.192132 \r\nL 126.796502 213.750715 \r\nL 126.91826 214.756364 \r\nL 126.979138 210.021437 \r\nL 127.009578 214.756364 \r\nL 127.040017 214.756364 \r\nL 127.131335 210.461408 \r\nL 127.192214 207.402561 \r\nL 127.253093 214.756364 \r\nL 127.283532 210.377604 \r\nL 127.344411 214.735413 \r\nL 127.374851 214.756364 \r\nL 127.40529 214.46305 \r\nL 127.466169 214.756364 \r\nL 127.527048 199.524983 \r\nL 127.557487 214.735413 \r\nL 127.587927 211.404203 \r\nL 127.618366 177.673086 \r\nL 127.648805 214.756364 \r\nL 127.679245 184.251701 \r\nL 127.801002 214.756364 \r\nL 127.861881 214.756364 \r\nL 127.953199 207.612071 \r\nL 128.014078 214.756364 \r\nL 128.044518 204.532273 \r\nL 128.074957 198.309825 \r\nL 128.105396 214.756364 \r\nL 128.166275 214.756364 \r\nL 128.257593 210.105241 \r\nL 128.348912 214.756364 \r\nL 128.501109 186.430606 \r\nL 128.531548 210.314751 \r\nL 128.592427 206.459766 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214.693511 \r\nL 130.236155 214.735413 \r\nL 130.297034 204.972245 \r\nL 130.388352 214.756364 \r\nL 130.449231 190.620806 \r\nL 130.47967 213.331695 \r\nL 130.540549 214.756364 \r\nL 130.601428 214.358295 \r\nL 130.692746 203.547576 \r\nL 130.753625 197.953658 \r\nL 130.814504 214.756364 \r\nL 130.844943 210.649967 \r\nL 130.905822 211.425154 \r\nL 130.936261 214.756364 \r\nL 130.99714 214.546854 \r\nL 131.058019 203.945645 \r\nL 131.088458 213.939274 \r\nL 131.149337 214.756364 \r\nL 131.179777 207.653973 \r\nL 131.240655 214.756364 \r\nL 131.51461 214.756364 \r\nL 131.54505 182.827033 \r\nL 131.605928 214.106882 \r\nL 131.636368 214.756364 \r\nL 131.758125 205.998844 \r\nL 131.788565 214.756364 \r\nL 131.819004 200.111612 \r\nL 131.849444 213.813568 \r\nL 131.879883 194.643399 \r\nL 131.910322 214.756364 \r\nL 131.940762 212.849822 \r\nL 131.971201 214.756364 \r\nL 132.092959 153.16041 \r\nL 132.184277 214.756364 \r\nL 132.214716 191.752161 \r\nL 132.306035 214.756364 \r\nL 132.336474 205.475069 \r\nL 132.397353 203.568527 \r\nL 132.458232 214.400197 \r\nL 132.488671 202.122908 \r\nL 132.519111 214.714462 \r\nL 132.54955 209.749074 \r\nL 132.671308 214.756364 \r\nL 132.701747 214.735413 \r\nL 132.732186 181.046197 \r\nL 132.793065 214.756364 \r\nL 132.884383 214.756364 \r\nL 132.914823 212.870773 \r\nL 132.945262 214.756364 \r\nL 132.975702 195.942362 \r\nL 133.03658 209.895731 \r\nL 133.06702 213.918323 \r\nL 133.097459 196.214725 \r\nL 133.127899 214.756364 \r\nL 133.158338 199.797346 \r\nL 133.280096 214.735413 \r\nL 133.310535 208.63867 \r\nL 133.340975 209.225298 \r\nL 133.371414 167.260436 \r\nL 133.401853 214.756364 \r\nL 133.432293 214.756364 \r\nL 133.462732 202.730487 \r\nL 133.55405 210.08429 \r\nL 133.645369 214.756364 \r\nL 133.614929 205.600775 \r\nL 133.675808 213.876421 \r\nL 133.736687 214.756364 \r\nL 133.767126 214.735413 \r\nL 133.888884 201.515329 \r\nL 133.828005 214.756364 \r\nL 133.919323 203.861841 \r\nL 133.980202 214.735413 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168.589809 199.88115 \r\nL 168.650687 214.756364 \r\nL 168.772445 205.056049 \r\nL 168.833324 207.255904 \r\nL 168.955081 214.756364 \r\nL 169.076839 204.720832 \r\nL 169.168157 214.756364 \r\nL 169.198597 212.912675 \r\nL 169.289915 214.756364 \r\nL 169.320354 214.735413 \r\nL 169.442112 194.287232 \r\nL 169.56387 214.756364 \r\nL 169.685627 181.884238 \r\nL 169.807385 214.756364 \r\nL 169.837824 200.048758 \r\nL 169.898703 208.072993 \r\nL 169.959582 214.756364 \r\nL 169.990021 207.695875 \r\nL 170.020461 210.189045 \r\nL 170.111779 214.756364 \r\nL 170.142218 187.059136 \r\nL 170.203097 213.059332 \r\nL 170.233537 210.796624 \r\nL 170.263976 213.331695 \r\nL 170.324855 211.404203 \r\nL 170.385734 214.756364 \r\nL 170.446612 214.756364 \r\nL 170.477052 210.733771 \r\nL 170.537931 214.735413 \r\nL 170.629249 214.756364 \r\nL 170.659688 204.406567 \r\nL 170.720567 208.21965 \r\nL 170.842325 214.756364 \r\nL 170.933643 196.298529 \r\nL 170.964082 211.446105 \r\nL 170.994522 214.756364 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213.960225 \r\nL 177.082403 214.756364 \r\nL 177.112843 194.769105 \r\nL 177.173721 214.316393 \r\nL 177.204161 214.756364 \r\nL 177.2346 195.271929 \r\nL 177.295479 198.058413 \r\nL 177.386797 214.756364 \r\nL 177.417237 204.46942 \r\nL 177.447676 214.756364 \r\nL 177.538994 208.869131 \r\nL 177.569434 208.785327 \r\nL 177.660752 214.756364 \r\nL 177.630313 206.96259 \r\nL 177.691191 214.735413 \r\nL 177.721631 207.214002 \r\nL 177.78251 214.756364 \r\nL 177.812949 214.756364 \r\nL 177.873828 182.575621 \r\nL 177.904267 213.960225 \r\nL 177.934707 214.735413 \r\nL 177.965146 211.383252 \r\nL 177.995585 188.420951 \r\nL 178.026025 213.583107 \r\nL 178.056464 196.424235 \r\nL 178.117343 214.756364 \r\nL 178.178222 214.735413 \r\nL 178.239101 214.756364 \r\nL 178.26954 177.819743 \r\nL 178.360858 214.756364 \r\nL 178.391298 211.383252 \r\nL 178.421737 214.756364 \r\nL 178.452177 212.954577 \r\nL 178.482616 197.765099 \r\nL 178.573934 205.726481 \r\nL 178.604374 206.019795 \r\nL 178.695692 214.756364 \r\nL 178.726131 205.077 \r\nL 178.78701 214.693511 \r\nL 178.847889 214.756364 \r\nL 178.878328 214.421148 \r\nL 178.908768 214.714462 \r\nL 178.939207 211.844174 \r\nL 178.969647 193.051123 \r\nL 179.030525 214.756364 \r\nL 179.060965 207.255904 \r\nL 179.121844 214.756364 \r\nL 179.213162 211.027085 \r\nL 179.274041 192.548299 \r\nL 179.30448 213.750715 \r\nL 179.334919 214.756364 \r\nL 179.426238 214.358295 \r\nL 179.456677 214.756364 \r\nL 179.487116 214.609707 \r\nL 179.547995 189.887521 \r\nL 179.578435 214.756364 \r\nL 179.639313 214.756364 \r\nL 179.669753 214.504952 \r\nL 179.700192 205.349363 \r\nL 179.730632 214.756364 \r\nL 179.761071 214.756364 \r\nL 179.882829 200.237318 \r\nL 179.913268 214.756364 \r\nL 180.004586 206.564521 \r\nL 180.065465 205.097951 \r\nL 180.095905 195.062419 \r\nL 180.126344 208.994837 \r\nL 180.156783 203.715184 \r\nL 180.278541 214.756364 \r\nL 180.400299 206.145501 \r\nL 180.430738 214.756364 \r\nL 180.461177 208.114895 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200.551583 \r\nL 184.266103 214.756364 \r\nL 184.296543 214.756364 \r\nL 184.387861 203.191409 \r\nL 184.509619 214.756364 \r\nL 184.540058 208.994837 \r\nL 184.600937 214.756364 \r\nL 184.631376 214.756364 \r\nL 184.661816 195.523342 \r\nL 184.722695 214.756364 \r\nL 184.783573 214.756364 \r\nL 184.93577 200.404926 \r\nL 184.96621 214.735413 \r\nL 185.057528 213.541205 \r\nL 185.118407 214.044029 \r\nL 185.240164 192.275936 \r\nL 185.331483 187.373401 \r\nL 185.361922 214.756364 \r\nL 185.392362 203.882792 \r\nL 185.45324 213.981176 \r\nL 185.48368 214.756364 \r\nL 185.544559 180.103402 \r\nL 185.574998 214.756364 \r\nL 185.605437 214.756364 \r\nL 185.757634 190.599855 \r\nL 185.788074 192.171181 \r\nL 185.818513 181.695679 \r\nL 185.909831 214.756364 \r\nL 185.940271 203.149507 \r\nL 185.97071 214.756364 \r\nL 186.031589 202.16481 \r\nL 186.062028 213.22694 \r\nL 186.092468 195.271929 \r\nL 186.153347 207.130198 \r\nL 186.214226 214.756364 \r\nL 186.244665 207.402561 \r\nL 186.305544 213.981176 \r\nL 186.396862 211.236595 \r\nL 186.427301 207.758728 \r\nL 186.457741 214.756364 \r\nL 186.48818 212.661263 \r\nL 186.51862 210.733771 \r\nL 186.609938 214.756364 \r\nL 186.640377 168.035624 \r\nL 186.701256 210.461408 \r\nL 186.762135 208.303454 \r\nL 186.792574 195.942362 \r\nL 186.823014 214.756364 \r\nL 186.853453 198.184119 \r\nL 186.975211 214.756364 \r\nL 187.00565 191.668357 \r\nL 187.066529 209.476711 \r\nL 187.096968 214.756364 \r\nL 187.188287 170.486891 \r\nL 187.310044 214.756364 \r\nL 187.340484 214.756364 \r\nL 187.431802 200.928701 \r\nL 187.462241 214.316393 \r\nL 187.492681 199.294522 \r\nL 187.553559 208.84818 \r\nL 187.614438 210.901379 \r\nL 187.644878 194.978615 \r\nL 187.705756 212.80792 \r\nL 187.736196 210.042388 \r\nL 187.857954 183.853632 \r\nL 187.827514 210.92233 \r\nL 187.888393 186.996283 \r\nL 187.949272 214.756364 \r\nL 187.979711 214.735413 \r\nL 188.010151 192.024524 \r\nL 188.04059 214.756364 \r\nL 188.071029 214.756364 \r\nL 188.162348 206.648325 \r\nL 188.192787 164.432051 \r\nL 188.253666 208.701523 \r\nL 188.284105 207.653973 \r\nL 188.314545 213.897372 \r\nL 188.344984 202.332418 \r\nL 188.405863 210.000486 \r\nL 188.436302 214.756364 \r\nL 188.466742 190.055129 \r\nL 188.52762 214.756364 \r\nL 188.55806 214.044029 \r\nL 188.588499 214.756364 \r\nL 188.710257 204.993196 \r\nL 188.801575 214.756364 \r\nL 188.832015 214.735413 \r\nL 188.862454 214.567805 \r\nL 188.892893 199.105963 \r\nL 188.984212 206.585472 \r\nL 189.136409 214.756364 \r\nL 189.166848 164.369198 \r\nL 189.227727 214.756364 \r\nL 189.319045 200.048758 \r\nL 189.440803 214.756364 \r\nL 189.471242 214.023078 \r\nL 189.501682 204.322763 \r\nL 189.56256 212.724116 \r\nL 189.623439 214.756364 \r\nL 189.653879 194.475791 \r\nL 189.714757 214.756364 \r\nL 189.836515 194.203428 \r\nL 189.866954 205.894089 \r\nL 189.927833 194.894811 \r\nL 189.958273 214.756364 \r\nL 189.988712 193.931065 \r\nL 190.049591 214.274491 \r\nL 190.08003 214.756364 \r\nL 190.11047 202.772389 \r\nL 190.201788 207.59112 \r\nL 190.323546 214.756364 \r\nL 190.353985 214.421148 \r\nL 190.384424 214.756364 \r\nL 190.414864 197.953658 \r\nL 190.475743 209.183396 \r\nL 190.62794 214.756364 \r\nL 190.658379 214.756364 \r\nL 190.688818 189.824668 \r\nL 190.749697 214.714462 \r\nL 190.810576 214.756364 \r\nL 190.932334 201.578182 \r\nL 191.023652 214.756364 \r\nL 191.084531 211.802272 \r\nL 191.175849 214.756364 \r\nL 191.236728 206.836884 \r\nL 191.267167 213.771666 \r\nL 191.328046 214.756364 \r\nL 191.419364 208.680572 \r\nL 191.480243 214.756364 \r\nL 191.541122 214.735413 \r\nL 191.571561 214.756364 \r\nL 191.63244 180.962393 \r\nL 191.662879 212.3889 \r\nL 191.693319 214.756364 \r\nL 191.815077 180.627177 \r\nL 191.936834 214.756364 \r\nL 191.967274 214.756364 \r\nL 191.997713 214.190687 \r\nL 192.028152 179.831039 \r\nL 192.058592 214.756364 \r\nL 192.089031 214.756364 \r\nL 192.14991 210.2938 \r\nL 192.180349 213.331695 \r\nL 192.271668 214.756364 \r\nL 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200.520747 199.441179 \r\nL 200.612065 203.023801 \r\nL 200.703384 214.67256 \r\nL 200.672944 201.368672 \r\nL 200.733823 208.533915 \r\nL 200.764262 205.077 \r\nL 200.794702 214.756364 \r\nL 200.825141 195.104321 \r\nL 200.855581 160.87038 \r\nL 200.88602 214.756364 \r\nL 200.916459 207.423512 \r\nL 200.977338 214.735413 \r\nL 201.038217 177.777841 \r\nL 201.129535 212.17939 \r\nL 201.159975 210.126192 \r\nL 201.251293 214.232589 \r\nL 201.281732 184.545015 \r\nL 201.40349 213.604058 \r\nL 201.464369 208.911033 \r\nL 201.494808 198.393629 \r\nL 201.525248 214.756364 \r\nL 201.555687 214.756364 \r\nL 201.586126 214.421148 \r\nL 201.738323 146.89606 \r\nL 201.829642 214.756364 \r\nL 201.860081 208.63867 \r\nL 201.89052 206.040746 \r\nL 201.92096 212.053684 \r\nL 201.951399 212.493655 \r\nL 201.981839 214.756364 \r\nL 202.012278 214.735413 \r\nL 202.042717 142.140182 \r\nL 202.103596 159.843781 \r\nL 202.164475 214.756364 \r\nL 202.225354 211.844174 \r\nL 202.255793 157.664876 \r\nL 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207.308735 213.268842 \r\nL 207.339174 214.756364 \r\nL 207.369614 198.498384 \r\nL 207.430493 211.048036 \r\nL 207.521811 214.609707 \r\nL 207.58269 214.756364 \r\nL 207.613129 199.126914 \r\nL 207.704447 214.756364 \r\nL 207.734887 214.442099 \r\nL 207.765326 208.806278 \r\nL 207.795765 214.735413 \r\nL 207.826205 214.232589 \r\nL 207.856644 214.756364 \r\nL 207.887084 200.509681 \r\nL 207.947963 214.46305 \r\nL 208.008841 214.756364 \r\nL 208.06972 210.314751 \r\nL 208.10016 176.164613 \r\nL 208.130599 212.493655 \r\nL 208.161038 212.200341 \r\nL 208.221917 195.271929 \r\nL 208.252357 213.394548 \r\nL 208.282796 214.756364 \r\nL 208.313235 214.735413 \r\nL 208.343675 204.280861 \r\nL 208.374114 214.756364 \r\nL 208.404554 214.756364 \r\nL 208.465432 214.756364 \r\nL 208.495872 209.623368 \r\nL 208.526311 159.257153 \r\nL 208.556751 214.756364 \r\nL 208.617629 180.0615 \r\nL 208.648069 214.735413 \r\nL 208.739387 213.583107 \r\nL 208.769827 214.756364 \r\nL 208.800266 191.584553 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257.807712 211.927978 \r\nL 257.838152 214.735413 \r\nL 257.868591 214.756364 \r\nL 257.89903 210.817575 \r\nL 257.92947 136.839578 \r\nL 257.990349 213.059332 \r\nL 258.020788 186.954381 \r\nL 258.112106 197.660344 \r\nL 258.142546 214.756364 \r\nL 258.233864 214.735413 \r\nL 258.264303 214.756364 \r\nL 258.325182 177.12836 \r\nL 258.386061 208.952935 \r\nL 258.4165 205.852187 \r\nL 258.477379 214.169736 \r\nL 258.507819 178.783489 \r\nL 258.629576 214.756364 \r\nL 258.660016 209.686221 \r\nL 258.690455 184.272652 \r\nL 258.751334 211.634664 \r\nL 258.781773 200.719191 \r\nL 258.873091 214.714462 \r\nL 258.903531 191.584553 \r\nL 258.994849 202.206712 \r\nL 259.025288 214.714462 \r\nL 259.116607 214.316393 \r\nL 259.207925 214.756364 \r\nL 259.268804 200.677289 \r\nL 259.299243 206.313109 \r\nL 259.390561 214.756364 \r\nL 259.421001 213.101234 \r\nL 259.45144 210.859477 \r\nL 259.48188 212.409851 \r\nL 259.512319 214.756364 \r\nL 259.542758 195.753803 \r\nL 259.634077 203.00285 \r\nL 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272.449067 214.756364 \r\nL 272.509946 210.147143 \r\nL 272.570825 209.707172 \r\nL 272.631704 214.756364 \r\nL 272.753461 199.839248 \r\nL 272.844779 214.756364 \r\nL 272.875219 209.728123 \r\nL 272.936098 202.101957 \r\nL 272.996977 214.756364 \r\nL 273.057855 212.011782 \r\nL 273.149174 214.735413 \r\nL 273.179613 213.22694 \r\nL 273.240492 214.756364 \r\nL 273.301371 214.735413 \r\nL 273.362249 209.853829 \r\nL 273.392689 212.430802 \r\nL 273.423128 214.756364 \r\nL 273.453568 213.185038 \r\nL 273.484007 203.903743 \r\nL 273.514446 214.756364 \r\nL 273.544886 209.078641 \r\nL 273.575325 214.504952 \r\nL 273.605765 204.218008 \r\nL 273.636204 210.838526 \r\nL 273.666643 209.66527 \r\nL 273.697083 212.074635 \r\nL 273.818841 214.756364 \r\nL 273.879719 214.735413 \r\nL 273.910159 214.442099 \r\nL 273.971038 214.756364 \r\nL 274.031916 205.831236 \r\nL 274.092795 214.756364 \r\nL 274.123235 214.46305 \r\nL 274.153674 172.623894 \r\nL 274.184113 214.756364 \r\nL 274.214553 213.834519 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210.608065 \r\nL 276.193114 214.756364 \r\nL 276.223554 196.989912 \r\nL 276.284433 214.46305 \r\nL 276.314872 214.714462 \r\nL 276.375751 214.756364 \r\nL 276.43663 213.038381 \r\nL 276.467069 214.756364 \r\nL 276.497508 204.825588 \r\nL 276.588827 206.878786 \r\nL 276.619266 204.888441 \r\nL 276.649705 213.750715 \r\nL 276.741024 210.230947 \r\nL 276.801902 206.250256 \r\nL 276.832342 214.756364 \r\nL 276.862781 205.789334 \r\nL 276.92366 214.67256 \r\nL 277.014978 205.056049 \r\nL 277.075857 214.756364 \r\nL 277.106297 200.27922 \r\nL 277.136736 191.437896 \r\nL 277.167175 214.756364 \r\nL 277.228054 203.882792 \r\nL 277.258494 214.756364 \r\nL 277.349812 214.756364 \r\nL 277.380251 206.187403 \r\nL 277.44113 209.644319 \r\nL 277.471569 214.756364 \r\nL 277.532448 213.666911 \r\nL 277.562888 199.67164 \r\nL 277.623766 214.756364 \r\nL 277.684645 214.756364 \r\nL 277.775964 204.0504 \r\nL 277.867282 214.756364 \r\nL 277.9586 196.151872 \r\nL 277.989039 214.756364 \r\nL 278.080358 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279.571889 200.530632 \r\nL 279.602328 213.541205 \r\nL 279.663207 208.554866 \r\nL 279.693646 214.756364 \r\nL 279.724086 204.113253 \r\nL 279.754525 200.509681 \r\nL 279.784964 214.756364 \r\nL 279.845843 197.639393 \r\nL 280.058919 214.756364 \r\nL 280.119798 195.565244 \r\nL 280.150237 207.528267 \r\nL 280.180677 213.708813 \r\nL 280.241556 213.059332 \r\nL 280.332874 214.588756 \r\nL 280.363313 201.913398 \r\nL 280.51551 214.756364 \r\nL 280.54595 200.404926 \r\nL 280.606828 214.756364 \r\nL 280.637268 214.756364 \r\nL 280.667707 203.400919 \r\nL 280.728586 214.756364 \r\nL 280.789465 213.205989 \r\nL 280.819904 206.878786 \r\nL 280.880783 214.756364 \r\nL 280.911222 213.792617 \r\nL 280.972101 214.756364 \r\nL 281.002541 214.756364 \r\nL 281.03298 205.181755 \r\nL 281.124298 206.564521 \r\nL 281.154738 213.478352 \r\nL 281.185177 208.177748 \r\nL 281.215617 190.243688 \r\nL 281.276495 214.756364 \r\nL 281.306935 214.735413 \r\nL 281.337374 214.546854 \r\nL 281.398253 205.49602 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288.855908 210.377604 \r\nL 288.916787 214.735413 \r\nL 289.008105 210.042388 \r\nL 289.038544 212.933626 \r\nL 289.099423 214.756364 \r\nL 289.129863 214.67256 \r\nL 289.25162 206.774031 \r\nL 289.28206 214.756364 \r\nL 289.312499 214.169736 \r\nL 289.342938 195.879509 \r\nL 289.403817 214.756364 \r\nL 289.434257 211.886076 \r\nL 289.464696 173.294326 \r\nL 289.495135 214.756364 \r\nL 289.525575 211.529909 \r\nL 289.556014 210.754722 \r\nL 289.586454 214.756364 \r\nL 289.616893 208.994837 \r\nL 289.647332 203.652331 \r\nL 289.677772 214.756364 \r\nL 289.708211 214.756364 \r\nL 289.799529 209.078641 \r\nL 289.829969 214.756364 \r\nL 289.921287 214.400197 \r\nL 290.012605 214.756364 \r\nL 290.043045 211.76037 \r\nL 290.134363 212.954577 \r\nL 290.164802 211.446105 \r\nL 290.195242 214.756364 \r\nL 290.225681 211.613713 \r\nL 290.256121 200.342073 \r\nL 290.28656 214.756364 \r\nL 290.316999 214.756364 \r\nL 290.347439 214.756364 \r\nL 290.408318 209.581466 \r\nL 290.469196 213.960225 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212.284145 \r\nL 307.210871 214.756364 \r\nL 307.24131 200.593485 \r\nL 307.332628 209.225298 \r\nL 307.363068 212.242243 \r\nL 307.393507 193.260633 \r\nL 307.454386 214.756364 \r\nL 307.484825 200.174465 \r\nL 307.545704 214.756364 \r\nL 307.606583 214.002127 \r\nL 307.637022 214.756364 \r\nL 307.667462 189.196138 \r\nL 307.728341 211.006134 \r\nL 307.789219 212.472704 \r\nL 307.880538 203.505674 \r\nL 307.910977 210.587114 \r\nL 307.971856 209.602417 \r\nL 308.093613 214.756364 \r\nL 308.124053 214.085931 \r\nL 308.184932 202.898095 \r\nL 308.215371 209.916682 \r\nL 308.306689 209.183396 \r\nL 308.337129 214.756364 \r\nL 308.458886 206.145501 \r\nL 308.580644 214.651609 \r\nL 308.732841 203.023801 \r\nL 308.854599 214.274491 \r\nL 308.885038 206.501668 \r\nL 308.945917 213.85547 \r\nL 308.976356 214.756364 \r\nL 309.006796 195.816656 \r\nL 309.067674 214.756364 \r\nL 309.098114 214.756364 \r\nL 309.28075 195.942362 \r\nL 309.372069 214.756364 \r\nL 309.341629 192.024524 \r\nL 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(lpath)"
   ]
  },
  {
   "source": [
    "## Exercise\n",
    "## A more realistic Peter and the Wolf world\n",
    "\n",
    "\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
 ]
}