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  {
   "source": [
    "## CartPole Skating\n",
    "\n",
    "> **Problem**: If Peter wants to escape from the wolf, he needs to be able to move faster than him. We will see how Peter can learn to skate, in particular, to keep balance, using Q-Learning.\n",
    "\n",
    "First, let's install the gym and import required libraries:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Collecting gym\n",
      "  Downloading gym-0.18.3.tar.gz (1.6 MB)\n",
      "\u001b[K     |████████████████████████████████| 1.6 MB 2.3 MB/s \n",
      "\u001b[?25hRequirement already satisfied: scipy in /Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages (from gym) (1.4.1)\n",
      "Requirement already satisfied: numpy>=1.10.4 in /Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages (from gym) (1.19.2)\n",
      "Collecting pyglet<=1.5.15,>=1.4.0\n",
      "  Downloading pyglet-1.5.15-py3-none-any.whl (1.1 MB)\n",
      "\u001b[K     |████████████████████████████████| 1.1 MB 3.7 MB/s \n",
      "\u001b[?25hRequirement already satisfied: Pillow<=8.2.0 in /Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages (from gym) (7.0.0)\n",
      "Collecting cloudpickle<1.7.0,>=1.2.0\n",
      "  Downloading cloudpickle-1.6.0-py3-none-any.whl (23 kB)\n",
      "Building wheels for collected packages: gym\n",
      "  Building wheel for gym (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25h  Created wheel for gym: filename=gym-0.18.3-py3-none-any.whl size=1657514 sha256=578c789ab75e603e58dd1152b2bd60d9a5adc6a057559cf8b5bdd6ee8b80abf2\n",
      "  Stored in directory: /Users/jenlooper/Library/Caches/pip/wheels/1a/ec/6d/705d53925f481ab70fd48ec7728558745eeae14dfda3b49c99\n",
      "Successfully built gym\n",
      "Installing collected packages: pyglet, cloudpickle, gym\n",
      "Successfully installed cloudpickle-1.6.0 gym-0.18.3 pyglet-1.5.15\n",
      "\u001b[33mWARNING: You are using pip version 20.2.3; however, version 21.1.2 is available.\n",
      "You should consider upgrading via the '/Library/Frameworks/Python.framework/Versions/3.7/bin/python3.7 -m pip install --upgrade pip' command.\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "!{sys.executable} -m pip install gym \n",
    "\n",
    "import gym\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random"
   ]
  },
  {
   "source": [
    "## Create a cartpole environment"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "env = gym.make(\"CartPole-v1\")\n",
    "print(env.action_space)\n",
    "print(env.observation_space)\n",
    "print(env.action_space.sample())"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": 2,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Discrete(2)\nBox(-3.4028234663852886e+38, 3.4028234663852886e+38, (4,), float32)\n1\n"
     ]
    }
   ]
  },
  {
   "source": [
    "To see how the environment works, let's run a short simulation for 100 steps."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "env.reset()\n",
    "\n",
    "for i in range(100):\n",
    "   env.render()\n",
    "   env.step(env.action_space.sample())\n",
    "env.close()"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": 3,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/gym/logger.py:30: UserWarning: \u001b[33mWARN: You are calling 'step()' even though this environment has already returned done = True. You should always call 'reset()' once you receive 'done = True' -- any further steps are undefined behavior.\u001b[0m\n  warnings.warn(colorize('%s: %s'%('WARN', msg % args), 'yellow'))\n"
     ]
    }
   ]
  },
  {
   "source": [
    "During simulation, we need to get observations in order to decide how to act. In fact, `step` function returns us back current observations, reward function, and the `done` flag that indicates whether it makes sense to continue the simulation or not:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "env.reset()\n",
    "\n",
    "done = False\n",
    "while not done:\n",
    "   env.render()\n",
    "   obs, rew, done, info = env.step(env.action_space.sample())\n",
    "   print(f\"{obs} -> {rew}\")\n",
    "env.close()"
   ],
   "cell_type": "code",
   "metadata": {},
   "execution_count": 4,
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[-0.035025    0.21201857 -0.010404   -0.3300738 ] -> 1.0\n",
      "[-0.03078463  0.40728707 -0.01700547 -0.62601941] -> 1.0\n",
      "[-0.02263889  0.21240657 -0.02952586 -0.3387403 ] -> 1.0\n",
      "[-0.01839076  0.01771693 -0.03630067 -0.05551247] -> 1.0\n",
      "[-0.01803642  0.21334007 -0.03741092 -0.35942391] -> 1.0\n",
      "[-0.01376962  0.40897331 -0.0445994  -0.66366469] -> 1.0\n",
      "[-0.00559015  0.21449925 -0.05787269 -0.38535156] -> 1.0\n",
      "[-0.00130017  0.410393   -0.06557972 -0.69570532] -> 1.0\n",
      "[ 0.00690769  0.21623893 -0.07949383 -0.42436686] -> 1.0\n",
      "[ 0.01123247  0.02232776 -0.08798116 -0.15776523] -> 1.0\n",
      "[ 0.01167903  0.21859198 -0.09113647 -0.47685598] -> 1.0\n",
      "[ 0.01605087  0.02486705 -0.10067359 -0.21423159] -> 1.0\n",
      "[ 0.01654821  0.22127341 -0.10495822 -0.53689749] -> 1.0\n",
      "[ 0.02097368  0.02777162 -0.11569617 -0.27904318] -> 1.0\n",
      "[ 0.02152911 -0.16552613 -0.12127703 -0.02497378] -> 1.0\n",
      "[ 0.01821859 -0.35871897 -0.12177651  0.22711886] -> 1.0\n",
      "[ 0.01104421 -0.16208621 -0.11723413 -0.10135989] -> 1.0\n",
      "[ 0.00780248 -0.35534992 -0.11926133  0.15215788] -> 1.0\n",
      "[ 0.00069548 -0.15874009 -0.11621817 -0.17564179] -> 1.0\n",
      "[-0.00247932  0.03783674 -0.11973101 -0.50260923] -> 1.0\n",
      "[-0.00172258  0.23442478 -0.12978319 -0.83049704] -> 1.0\n",
      "[ 0.00296591  0.04129289 -0.14639313 -0.58128481] -> 1.0\n",
      "[ 0.00379177  0.23812991 -0.15801883 -0.9162682 ] -> 1.0\n",
      "[ 0.00855437  0.04545686 -0.17634419 -0.67712384] -> 1.0\n",
      "[ 0.00946351  0.24253346 -0.18988667 -1.01973114] -> 1.0\n",
      "[ 0.01431417  0.05037919 -0.21028129 -0.7921723 ] -> 1.0\n"
     ]
    }
   ]
  },
  {
   "source": [
    "We can get min and max value of those numbers:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[-4.8000002e+00 -3.4028235e+38 -4.1887903e-01 -3.4028235e+38]\n[4.8000002e+00 3.4028235e+38 4.1887903e-01 3.4028235e+38]\n"
     ]
    }
   ],
   "source": [
    "print(env.observation_space.low)\n",
    "print(env.observation_space.high)"
   ]
  },
  {
   "source": [
    "## State Discretization"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def discretize(x):\n",
    "    return tuple((x/np.array([0.25, 0.25, 0.01, 0.1])).astype(np.int))"
   ]
  },
  {
   "source": [
    "Let's also explore other discretization method using bins:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Sample bins for interval (-5,5) with 10 bins\n [-5. -4. -3. -2. -1.  0.  1.  2.  3.  4.  5.]\n"
     ]
    }
   ],
   "source": [
    "def create_bins(i,num):\n",
    "    return np.arange(num+1)*(i[1]-i[0])/num+i[0]\n",
    "\n",
    "print(\"Sample bins for interval (-5,5) with 10 bins\\n\",create_bins((-5,5),10))\n",
    "\n",
    "ints = [(-5,5),(-2,2),(-0.5,0.5),(-2,2)] # intervals of values for each parameter\n",
    "nbins = [20,20,10,10] # number of bins for each parameter\n",
    "bins = [create_bins(ints[i],nbins[i]) for i in range(4)]\n",
    "\n",
    "def discretize_bins(x):\n",
    "    return tuple(np.digitize(x[i],bins[i]) for i in range(4))"
   ]
  },
  {
   "source": [
    "Let's now run a short simulation and observe those discrete environment values."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "(0, 0, -1, -3)\n(0, 0, -2, 0)\n(0, 0, -2, -3)\n(0, 1, -3, -6)\n(0, 0, -4, -3)\n(0, 1, -5, -6)\n(0, 2, -6, -9)\n(0, 1, -8, -6)\n(0, 2, -9, -9)\n(0, 2, -11, -13)\n(0, 2, -14, -10)\n(0, 1, -16, -8)\n(0, 2, -18, -11)\n(0, 3, -20, -15)\n(0, 2, -23, -12)\n"
     ]
    }
   ],
   "source": [
    "env.reset()\n",
    "\n",
    "done = False\n",
    "while not done:\n",
    "   #env.render()\n",
    "   obs, rew, done, info = env.step(env.action_space.sample())\n",
    "   #print(discretize_bins(obs))\n",
    "   print(discretize(obs))\n",
    "env.close()"
   ]
  },
  {
   "source": [
    "## Q-Table Structure"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = {}\n",
    "actions = (0,1)\n",
    "\n",
    "def qvalues(state):\n",
    "    return [Q.get((state,a),0) for a in actions]"
   ]
  },
  {
   "source": [
    "## Let's Start Q-Learning!"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# hyperparameters\n",
    "alpha = 0.3\n",
    "gamma = 0.9\n",
    "epsilon = 0.90"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "0: 108.0, alpha=0.3, epsilon=0.9\n"
     ]
    }
   ],
   "source": [
    "def probs(v,eps=1e-4):\n",
    "    v = v-v.min()+eps\n",
    "    v = v/v.sum()\n",
    "    return v\n",
    "\n",
    "Qmax = 0\n",
    "cum_rewards = []\n",
    "rewards = []\n",
    "for epoch in range(100000):\n",
    "    obs = env.reset()\n",
    "    done = False\n",
    "    cum_reward=0\n",
    "    # == do the simulation ==\n",
    "    while not done:\n",
    "        s = discretize(obs)\n",
    "        if random.random()<epsilon:\n",
    "            # exploitation - chose the action according to Q-Table probabilities\n",
    "            v = probs(np.array(qvalues(s)))\n",
    "            a = random.choices(actions,weights=v)[0]\n",
    "        else:\n",
    "            # exploration - randomly chose the action\n",
    "            a = np.random.randint(env.action_space.n)\n",
    "\n",
    "        obs, rew, done, info = env.step(a)\n",
    "        cum_reward+=rew\n",
    "        ns = discretize(obs)\n",
    "        Q[(s,a)] = (1 - alpha) * Q.get((s,a),0) + alpha * (rew + gamma * max(qvalues(ns)))\n",
    "    cum_rewards.append(cum_reward)\n",
    "    rewards.append(cum_reward)\n",
    "    # == Periodically print results and calculate average reward ==\n",
    "    if epoch%5000==0:\n",
    "        print(f\"{epoch}: {np.average(cum_rewards)}, alpha={alpha}, epsilon={epsilon}\")\n",
    "        if np.average(cum_rewards) > Qmax:\n",
    "            Qmax = np.average(cum_rewards)\n",
    "            Qbest = Q\n",
    "        cum_rewards=[]"
   ]
  },
  {
   "source": [
    "## Plotting Training Progress"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
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121.611515 180.203814 \r\nL 121.614558 68.108914 \r\nL 121.635864 80.563902 \r\nL 121.745436 203.90847 \r\nL 121.644995 74.537295 \r\nL 121.751523 181.810909 \r\nL 121.763698 44.404257 \r\nL 121.842833 190.24816 \r\nL 121.861095 138.419335 \r\nL 121.903707 206.319113 \r\nL 121.918925 34.359911 \r\nL 121.955449 107.482749 \r\nL 121.958493 37.975876 \r\nL 121.991973 208.729756 \r\nL 122.061977 119.535965 \r\nL 122.098501 185.0251 \r\nL 122.138069 28.735078 \r\nL 122.171549 153.284967 \r\nL 122.275034 76.14439 \r\nL 122.177637 195.069446 \r\nL 122.281121 150.070776 \r\nL 122.372431 95.831308 \r\nL 122.293296 201.497827 \r\nL 122.393737 98.241951 \r\nL 122.463741 206.720887 \r\nL 122.427217 86.992284 \r\nL 122.503309 94.224213 \r\nL 122.515484 198.283636 \r\nL 122.57027 44.002483 \r\nL 122.615925 167.748825 \r\nL 122.701147 69.314235 \r\nL 122.722453 194.667672 \r\nL 122.731584 77.751486 \r\nL 122.768108 199.890732 \r\nL 122.780283 54.448603 \r\nL 122.847243 161.722217 \r\nL 122.880724 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128.423241 194.265898 \r\nL 128.514551 142.035299 \r\nL 128.56325 208.729756 \r\nL 128.566293 51.234412 \r\nL 128.624123 150.47255 \r\nL 128.730651 46.011353 \r\nL 128.715433 208.327982 \r\nL 128.736739 103.465011 \r\nL 128.751957 172.971885 \r\nL 128.74587 80.162129 \r\nL 128.803699 140.428204 \r\nL 128.858485 33.958137 \r\nL 128.864573 204.712018 \r\nL 128.913271 151.276098 \r\nL 128.919359 192.658803 \r\nL 128.998494 63.287627 \r\nL 129.016756 110.295166 \r\nL 129.077629 60.876984 \r\nL 129.025887 186.230421 \r\nL 129.114153 117.928869 \r\nL 129.117197 166.945277 \r\nL 129.175027 50.832639 \r\nL 129.223725 161.320443 \r\nL 129.321123 63.287627 \r\nL 129.308948 199.890732 \r\nL 129.333297 84.983415 \r\nL 129.357647 198.283636 \r\nL 129.409389 53.243282 \r\nL 129.442869 145.24949 \r\nL 129.518961 20.297827 \r\nL 129.491568 197.078315 \r\nL 129.549398 161.722217 \r\nL 129.640708 202.301375 \r\nL 129.610271 33.556364 \r\nL 129.655926 179.80204 \r\nL 129.716799 19.092506 \r\nL 129.668101 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132.498711 84.179867 \r\nL 132.568715 196.274767 \r\nL 132.516973 70.519557 \r\nL 132.61437 176.186075 \r\nL 132.626545 80.162129 \r\nL 132.653938 203.506696 \r\nL 132.733073 105.875654 \r\nL 132.775685 207.926208 \r\nL 132.800034 66.903592 \r\nL 132.842645 109.089845 \r\nL 132.882213 194.265898 \r\nL 132.906562 74.939069 \r\nL 132.943086 139.222882 \r\nL 132.955261 48.020222 \r\nL 133.013091 185.426874 \r\nL 133.052658 84.581641 \r\nL 133.156143 212.747494 \r\nL 133.089182 34.359911 \r\nL 133.165274 159.311574 \r\nL 133.174405 85.786962 \r\nL 133.250497 191.855255 \r\nL 133.268759 170.159468 \r\nL 133.271802 211.943947 \r\nL 133.350938 54.046829 \r\nL 133.375287 117.125322 \r\nL 133.472684 45.609579 \r\nL 133.387462 212.345721 \r\nL 133.484859 105.875654 \r\nL 133.490946 188.23929 \r\nL 133.548776 17.083636 \r\nL 133.594431 131.58918 \r\nL 133.679654 19.092506 \r\nL 133.664435 192.658803 \r\nL 133.700959 170.963016 \r\nL 133.704003 201.497827 \r\nL 133.761833 56.859246 \r\nL 133.810531 173.775432 \r\nL 133.868361 52.439734 \r\nL 133.898798 185.0251 \r\nL 133.920103 89.402927 \r\nL 133.971846 204.712018 \r\nL 133.993151 76.546164 \r\nL 134.032719 195.872993 \r\nL 134.111854 32.351042 \r\nL 134.148378 114.312905 \r\nL 134.157509 60.475211 \r\nL 134.203164 184.221552 \r\nL 134.242732 97.840177 \r\nL 134.321867 203.104922 \r\nL 134.267081 54.046829 \r\nL 134.352304 198.283636 \r\nL 134.382741 17.887184 \r\nL 134.46492 135.205144 \r\nL 134.53188 31.145721 \r\nL 134.486225 194.667672 \r\nL 134.574492 113.911131 \r\nL 134.592754 199.488958 \r\nL 134.662758 33.15459 \r\nL 134.68102 115.92 \r\nL 134.684064 25.922661 \r\nL 134.735806 184.623326 \r\nL 134.787548 82.974545 \r\nL 134.790592 204.310244 \r\nL 134.842334 65.698271 \r\nL 134.89712 125.964346 \r\nL 134.95495 43.60071 \r\nL 134.991474 203.104922 \r\nL 135.009736 79.760355 \r\nL 135.098002 203.506696 \r\nL 135.085828 50.029091 \r\nL 135.119308 113.107583 \r\nL 135.204531 46.011353 \r\nL 135.201487 158.9098 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168.764001 39.984745 \r\nL 168.861398 144.044169 \r\nL 168.940533 35.163459 \r\nL 168.964883 184.221552 \r\nL 168.97097 88.599379 \r\nL 169.037931 199.087184 \r\nL 169.010538 41.190067 \r\nL 169.083586 150.874324 \r\nL 169.092717 48.421996 \r\nL 169.174896 193.46235 \r\nL 169.199245 86.59051 \r\nL 169.284468 196.676541 \r\nL 169.2449 56.055698 \r\nL 169.308817 91.81357 \r\nL 169.366647 63.689401 \r\nL 169.397083 197.881863 \r\nL 169.409258 78.153259 \r\nL 169.506655 191.855255 \r\nL 169.439695 23.913792 \r\nL 169.521874 136.008692 \r\nL 169.534048 30.743947 \r\nL 169.57666 207.524435 \r\nL 169.634489 36.36878 \r\nL 169.710581 194.265898 \r\nL 169.646664 17.083636 \r\nL 169.747105 191.051707 \r\nL 169.847546 27.529756 \r\nL 169.862764 50.430865 \r\nL 169.877983 195.47122 \r\nL 169.957118 17.083636 \r\nL 169.972336 129.982084 \r\nL 170.027122 17.083636 \r\nL 170.036253 193.864124 \r\nL 170.084952 73.331973 \r\nL 170.151913 207.926208 \r\nL 170.121476 17.083636 \r\nL 170.194524 141.231752 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126.767894 \r\nL 171.515476 194.667672 \r\nL 171.491126 32.752816 \r\nL 171.536781 186.632195 \r\nL 171.573305 37.975876 \r\nL 171.555043 193.060576 \r\nL 171.649397 112.304035 \r\nL 171.743751 203.104922 \r\nL 171.737663 28.333304 \r\nL 171.752882 82.572772 \r\nL 171.755925 17.083636 \r\nL 171.853323 197.480089 \r\nL 171.862454 87.394058 \r\nL 171.956807 17.083636 \r\nL 171.938545 182.614457 \r\nL 171.962895 144.445942 \r\nL 171.981157 197.078315 \r\nL 172.038986 17.083636 \r\nL 172.063336 39.984745 \r\nL 172.069423 83.778093 \r\nL 172.072467 17.083636 \r\nL 172.084641 205.917339 \r\nL 172.185082 127.169667 \r\nL 172.197257 34.359911 \r\nL 172.248999 193.060576 \r\nL 172.294654 109.089845 \r\nL 172.297698 200.694279 \r\nL 172.328135 17.083636 \r\nL 172.401183 174.57898 \r\nL 172.504667 17.083636 \r\nL 172.462056 197.881863 \r\nL 172.513798 84.983415 \r\nL 172.516842 83.376319 \r\nL 172.599021 191.051707 \r\nL 172.58989 17.083636 \r\nL 172.62337 127.973215 \r\nL 172.644676 17.083636 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196.676541 \r\nL 176.921028 98.241951 \r\nL 177.009294 208.327982 \r\nL 176.933202 17.083636 \r\nL 177.027556 137.214013 \r\nL 177.033643 17.083636 \r\nL 177.036687 208.327982 \r\nL 177.137128 99.447273 \r\nL 177.191914 212.747494 \r\nL 177.167565 34.761685 \r\nL 177.249744 183.819778 \r\nL 177.350185 17.083636 \r\nL 177.316704 199.890732 \r\nL 177.362359 86.59051 \r\nL 177.417145 207.122661 \r\nL 177.411058 37.975876 \r\nL 177.444538 119.134191 \r\nL 177.535848 17.083636 \r\nL 177.481062 203.506696 \r\nL 177.55411 83.778093 \r\nL 177.602809 201.096053 \r\nL 177.566285 17.083636 \r\nL 177.663682 152.883193 \r\nL 177.691075 26.324435 \r\nL 177.748905 201.899601 \r\nL 177.776298 133.999823 \r\nL 177.79456 61.278758 \r\nL 177.800647 201.096053 \r\nL 177.873695 125.160798 \r\nL 177.876739 209.13153 \r\nL 177.971093 41.59184 \r\nL 177.986311 184.623326 \r\nL 178.065447 17.083636 \r\nL 178.016748 205.113792 \r\nL 178.095883 83.376319 \r\nL 178.114145 192.257029 \r\nL 178.168931 17.083636 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205.515565 \r\nL 179.581193 41.190067 \r\nL 179.599455 197.078315 \r\nL 179.608586 37.172328 \r\nL 179.693808 189.444612 \r\nL 179.699896 17.083636 \r\nL 179.775987 205.113792 \r\nL 179.80338 92.617118 \r\nL 179.903821 207.122661 \r\nL 179.845992 17.083636 \r\nL 179.912952 198.283636 \r\nL 179.992088 33.15459 \r\nL 179.943389 202.703149 \r\nL 180.022524 42.395388 \r\nL 180.083398 202.301375 \r\nL 180.049917 17.083636 \r\nL 180.13514 99.045499 \r\nL 180.211232 193.060576 \r\nL 180.162533 21.904922 \r\nL 180.22645 189.042838 \r\nL 180.28428 17.083636 \r\nL 180.244712 193.864124 \r\nL 180.339066 94.224213 \r\nL 180.418201 178.194945 \r\nL 180.402983 17.083636 \r\nL 180.451681 123.553703 \r\nL 180.527773 197.480089 \r\nL 180.53386 37.975876 \r\nL 180.576472 17.083636 \r\nL 180.564297 196.676541 \r\nL 180.628214 73.331973 \r\nL 180.661694 201.096053 \r\nL 180.734742 19.494279 \r\nL 180.74083 191.855255 \r\nL 180.819965 39.984745 \r\nL 180.853445 113.107583 \r\nL 180.862576 190.24816 \r\nL 180.868664 19.494279 \r\nL 180.953886 105.072106 \r\nL 181.039109 17.083636 \r\nL 180.999541 191.855255 \r\nL 181.063458 70.92133 \r\nL 181.130419 188.641064 \r\nL 181.090851 17.083636 \r\nL 181.17303 70.117783 \r\nL 181.218685 17.083636 \r\nL 181.206511 199.087184 \r\nL 181.276515 149.267228 \r\nL 181.309995 37.975876 \r\nL 181.376956 199.087184 \r\nL 181.486528 17.083636 \r\nL 181.404349 199.488958 \r\nL 181.489572 28.735078 \r\nL 181.556532 199.488958 \r\nL 181.498703 17.083636 \r\nL 181.602187 153.284967 \r\nL 181.638711 24.315565 \r\nL 181.635668 213.551042 \r\nL 181.708716 78.555033 \r\nL 181.769589 199.890732 \r\nL 181.733065 41.190067 \r\nL 181.821331 163.731086 \r\nL 181.912641 17.083636 \r\nL 181.833506 211.542173 \r\nL 181.933947 89.804701 \r\nL 181.958296 37.574102 \r\nL 181.949165 168.954146 \r\nL 181.970471 52.03796 \r\nL 182.061781 196.676541 \r\nL 182.064825 17.083636 \r\nL 182.080043 97.438404 \r\nL 182.128742 17.083636 \r\nL 182.168309 197.480089 \r\nL 182.186571 149.267228 \r\nL 182.26875 196.274767 \r\nL 182.238314 17.083636 \r\nL 182.271794 119.937738 \r\nL 182.366148 192.658803 \r\nL 182.378322 17.083636 \r\nL 182.411803 205.515565 \r\nL 182.487894 172.971885 \r\nL 182.515287 17.083636 \r\nL 182.497025 211.140399 \r\nL 182.60051 90.206475 \r\nL 182.688776 191.855255 \r\nL 182.703995 28.333304 \r\nL 182.707038 88.599379 \r\nL 182.798348 193.060576 \r\nL 182.810523 17.083636 \r\nL 182.850091 203.506696 \r\nL 182.920095 83.778093 \r\nL 182.938357 179.400266 \r\nL 183.026623 17.083636 \r\nL 183.124021 192.257029 \r\nL 183.136195 162.123991 \r\nL 183.163588 19.896053 \r\nL 183.236636 194.667672 \r\nL 183.245767 31.547494 \r\nL 183.27316 19.494279 \r\nL 183.358383 198.68541 \r\nL 183.431431 17.083636 \r\nL 183.467955 173.775432 \r\nL 183.541003 195.47122 \r\nL 183.489261 19.494279 \r\nL 183.556221 179.80204 \r\nL 183.632313 17.083636 \r\nL 183.589702 203.90847 \r\nL 183.668837 103.465011 \r\nL 183.723623 212.747494 \r\nL 183.738841 21.904922 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185.315461 191.453481 \r\nL 185.382421 198.283636 \r\nL 185.428076 17.083636 \r\nL 185.528518 201.497827 \r\nL 185.540692 155.293836 \r\nL 185.558954 193.060576 \r\nL 185.647221 17.083636 \r\nL 185.732443 211.943947 \r\nL 185.759836 119.937738 \r\nL 185.814622 195.47122 \r\nL 185.848103 17.083636 \r\nL 185.869408 127.571441 \r\nL 185.930282 17.083636 \r\nL 185.884627 179.400266 \r\nL 185.969849 52.841508 \r\nL 185.972893 196.274767 \r\nL 185.97898 17.083636 \r\nL 186.079421 141.633525 \r\nL 186.182906 17.083636 \r\nL 186.170731 196.676541 \r\nL 186.192037 31.547494 \r\nL 186.246823 197.480089 \r\nL 186.204212 17.083636 \r\nL 186.304653 138.821109 \r\nL 186.362482 213.149268 \r\nL 186.417268 17.083636 \r\nL 186.469011 202.703149 \r\nL 186.52684 50.430865 \r\nL 186.545102 199.087184 \r\nL 186.566408 21.503149 \r\nL 186.657718 171.364789 \r\nL 186.752072 17.083636 \r\nL 186.666849 206.319113 \r\nL 186.76729 95.027761 \r\nL 186.855556 183.819778 \r\nL 186.797727 17.083636 \r\nL 186.873818 80.965676 \r\nL 186.980347 17.083636 \r\nL 186.965128 209.533304 \r\nL 186.98339 25.119113 \r\nL 187.089919 196.676541 \r\nL 187.050351 17.083636 \r\nL 187.092962 156.900931 \r\nL 187.129486 17.083636 \r\nL 187.19036 194.667672 \r\nL 187.202534 74.939069 \r\nL 187.254277 205.917339 \r\nL 187.211665 17.083636 \r\nL 187.31515 120.339512 \r\nL 187.327325 211.943947 \r\nL 187.333412 17.083636 \r\nL 187.424722 178.596718 \r\nL 187.500814 17.083636 \r\nL 187.433853 209.935078 \r\nL 187.540381 42.395388 \r\nL 187.613429 198.68541 \r\nL 187.607342 17.083636 \r\nL 187.656041 172.971885 \r\nL 187.662128 17.083636 \r\nL 187.710827 188.23929 \r\nL 187.768656 73.331973 \r\nL 187.7717 189.846386 \r\nL 187.853879 17.083636 \r\nL 187.878228 57.26102 \r\nL 187.957364 17.083636 \r\nL 187.936058 203.90847 \r\nL 187.978669 93.420665 \r\nL 188.039543 199.087184 \r\nL 188.009106 17.083636 \r\nL 188.091285 166.945277 \r\nL 188.133896 195.872993 \r\nL 188.118678 17.083636 \r\nL 188.152158 78.956807 \r\nL 188.155202 17.083636 \r\nL 188.200857 196.676541 \r\nL 188.255643 188.641064 \r\nL 188.368259 17.083636 \r\nL 188.301298 209.935078 \r\nL 188.380433 20.297827 \r\nL 188.471743 189.444612 \r\nL 188.413914 17.083636 \r\nL 188.490005 88.599379 \r\nL 188.584359 17.083636 \r\nL 188.496093 198.283636 \r\nL 188.59349 167.347051 \r\nL 188.602621 189.444612 \r\nL 188.611752 103.465011 \r\nL 188.614796 17.083636 \r\nL 188.715237 199.890732 \r\nL 188.721324 58.868115 \r\nL 188.785241 192.658803 \r\nL 188.782197 42.797162 \r\nL 188.830896 120.339512 \r\nL 188.83394 25.119113 \r\nL 188.910031 194.265898 \r\nL 188.937424 188.641064 \r\nL 188.943512 190.24816 \r\nL 188.949599 153.686741 \r\nL 189.007429 74.135521 \r\nL 189.034822 198.283636 \r\nL 189.05004 124.759024 \r\nL 189.08352 197.881863 \r\nL 189.120044 17.083636 \r\nL 189.159612 155.293836 \r\nL 189.171787 17.083636 \r\nL 189.202223 193.060576 \r\nL 189.269184 156.900931 \r\nL 189.272228 192.257029 \r\nL 189.360494 49.627317 \r\nL 189.372669 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235.131155 35.967007 \r\nL 235.064195 195.069446 \r\nL 235.14333 149.267228 \r\nL 235.213334 208.327982 \r\nL 235.222465 31.547494 \r\nL 235.237684 138.821109 \r\nL 235.319863 17.083636 \r\nL 235.246815 196.274767 \r\nL 235.350299 63.287627 \r\nL 235.374649 211.140399 \r\nL 235.389867 17.083636 \r\nL 235.462915 177.793171 \r\nL 235.5664 17.083636 \r\nL 235.548138 200.292506 \r\nL 235.575531 138.419335 \r\nL 235.679015 196.676541 \r\nL 235.645535 17.083636 \r\nL 235.682059 154.490288 \r\nL 235.706408 193.060576 \r\nL 235.791631 17.083636 \r\nL 235.889028 204.712018 \r\nL 235.904247 121.14306 \r\nL 235.922509 193.864124 \r\nL 235.934683 62.082306 \r\nL 236.010775 124.759024 \r\nL 236.095998 30.743947 \r\nL 236.08991 210.336851 \r\nL 236.117303 83.376319 \r\nL 236.162958 192.658803 \r\nL 236.141653 40.386519 \r\nL 236.229919 189.444612 \r\nL 236.23905 17.083636 \r\nL 236.321229 200.292506 \r\nL 236.342535 74.537295 \r\nL 236.403408 197.078315 \r\nL 236.439932 50.430865 \r\nL 236.452107 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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(rewards)"
   ]
  },
  {
   "source": [
    "From this graph, it is not possible to tell anything, because due to the nature of stochastic training process the length of training sessions varies greatly. To make more sense of this graph, we can calculate **running average** over series of experiments, let's say 100. This can be done conveniently using `np.convolve`:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2814cc63488>]"
      ]
     },
     "metadata": {},
     "execution_count": 22
    },
    {
     "output_type": "display_data",
     "data": {
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110.421698 \r\nL 116.97379 100.967522 \r\nL 116.979883 101.257861 \r\nL 117.092611 107.246111 \r\nL 117.120031 106.3388 \r\nL 117.135264 104.941542 \r\nL 117.184011 116.434143 \r\nL 117.187058 116.440191 \r\nL 117.260178 117.625744 \r\nL 117.244945 114.298938 \r\nL 117.287598 115.678051 \r\nL 117.336345 105.95773 \r\nL 117.403372 110.669696 \r\nL 117.406419 110.669696 \r\nL 117.500866 98.608515 \r\nL 117.421652 111.812908 \r\nL 117.58008 100.30821 \r\nL 117.613593 105.570611 \r\nL 117.66234 97.441108 \r\nL 117.677574 97.586278 \r\nL 117.756787 86.80138 \r\nL 117.829908 93.442893 \r\nL 117.988335 105.752073 \r\nL 117.991382 103.889062 \r\nL 118.076689 113.905771 \r\nL 118.088876 110.488234 \r\nL 118.119343 112.61739 \r\nL 118.161996 108.54659 \r\nL 118.180276 108.570784 \r\nL 118.183323 108.334884 \r\nL 118.229023 113.137581 \r\nL 118.253397 115.901854 \r\nL 118.28691 109.919653 \r\nL 118.326517 111.982272 \r\nL 118.442291 101.83854 \r\nL 118.366124 113.542846 \r\nL 118.460571 103.495894 \r\nL 118.463618 103.876965 \r\nL 118.524552 97.997592 \r\nL 118.673839 87.884104 \r\nL 118.536738 98.348419 \r\nL 118.698213 90.708864 \r\nL 118.85664 106.768261 \r\nL 118.859687 106.683579 \r\nL 118.899294 103.949549 \r\nL 118.932807 110.960036 \r\nL 118.966321 120.595674 \r\nL 119.051628 113.433969 \r\nL 119.094281 114.480401 \r\nL 119.139982 110.814866 \r\nL 119.152168 111.65564 \r\nL 119.267942 95.953119 \r\nL 119.207009 113.349287 \r\nL 119.286222 100.290063 \r\nL 119.465977 111.050767 \r\nL 119.469023 109.998286 \r\nL 119.511677 108.117129 \r\nL 119.548237 112.677877 \r\nL 119.660964 116.845457 \r\nL 119.612217 110.578965 \r\nL 119.673151 115.974439 \r\nL 119.761505 114.2445 \r\nL 119.694478 118.496762 \r\nL 119.779785 116.101462 \r\nL 119.804158 118.285056 \r\nL 119.880326 114.861471 \r\nL 119.990006 111.776615 \r\nL 119.926026 119.198415 \r\nL 120.00524 112.865388 \r\nL 120.03266 113.343238 \r\nL 120.063127 109.217999 \r\nL 120.081407 109.804727 \r\nL 120.224601 96.805991 \r\nL 120.300768 90.636279 \r\nL 120.346468 94.773615 \r\nL 120.349515 95.160734 \r\nL 120.407402 88.482929 \r\nL 120.413495 87.751031 \r\nL 120.462242 91.186714 \r\nL 120.486615 90.866131 \r\nL 120.489662 92.075878 \r\nL 120.510989 86.692503 \r\nL 120.599343 91.985147 \r\nL 120.718163 95.729316 \r\nL 120.64809 86.166262 \r\nL 120.727303 94.767566 \r\nL 120.840031 89.263216 \r\nL 120.858311 89.946723 \r\nL 120.995412 97.525791 \r\nL 120.904011 87.956689 \r\nL 121.001505 97.283841 \r\nL 121.022832 96.461213 \r\nL 121.031972 98.58432 \r\nL 121.175166 108.607077 \r\nL 121.178213 107.609035 \r\nL 121.303127 96.309994 \r\nL 121.312267 97.380621 \r\nL 121.315313 97.846374 \r\nL 121.379294 93.823964 \r\nL 121.40976 95.475269 \r\nL 121.525534 103.653161 \r\nL 121.458507 92.196853 \r\nL 121.586468 102.36478 \r\nL 121.592561 101.052204 \r\nL 121.662635 106.048461 \r\nL 121.693102 103.066434 \r\nL 121.711382 106.314606 \r\nL 121.790596 102.721656 \r\nL 121.796689 103.362822 \r\nL 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107.699766 \r\nL 123.639932 97.652814 \r\nL 123.655166 101.052204 \r\nL 123.7161 94.555861 \r\nL 123.74352 95.922875 \r\nL 123.75266 94.912736 \r\nL 123.82578 104.022134 \r\nL 123.83492 101.602639 \r\nL 123.920227 107.445719 \r\nL 123.947647 103.03619 \r\nL 123.950694 102.89102 \r\nL 123.972021 106.223874 \r\nL 123.975068 106.169436 \r\nL 124.051235 109.012342 \r\nL 123.999441 104.143109 \r\nL 124.084748 107.246111 \r\nL 124.124355 105.068566 \r\nL 124.103028 108.165519 \r\nL 124.194429 107.088844 \r\nL 124.200522 107.482012 \r\nL 124.206615 106.15129 \r\nL 124.212709 106.786407 \r\nL 124.310203 103.75599 \r\nL 124.255362 108.849026 \r\nL 124.328483 104.475789 \r\nL 124.343716 103.18136 \r\nL 124.39551 109.078878 \r\nL 124.401603 108.921611 \r\nL 124.407697 109.242194 \r\nL 124.41379 110.373308 \r\nL 124.48691 103.489845 \r\nL 124.489957 103.719697 \r\nL 124.648385 112.502464 \r\nL 124.50519 103.374919 \r\nL 124.654478 111.558861 \r\nL 124.718458 107.7784 \r\nL 124.748925 112.829095 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129.230596 86.450553 \r\nL 129.264109 92.577924 \r\nL 129.34637 97.979446 \r\nL 129.306763 91.229055 \r\nL 129.38293 95.426879 \r\nL 129.398163 89.015218 \r\nL 129.498704 93.043676 \r\nL 129.559638 87.914347 \r\nL 129.605338 92.432754 \r\nL 129.651038 89.67453 \r\nL 129.721112 95.838193 \r\nL 129.803372 85.779143 \r\nL 129.836886 92.813824 \r\nL 129.861259 93.442893 \r\nL 129.882586 86.093678 \r\nL 129.97094 76.657648 \r\nL 129.900866 88.755122 \r\nL 130.004453 77.673836 \r\nL 130.028827 76.331016 \r\nL 130.07148 87.206645 \r\nL 130.242095 120.027092 \r\nL 130.245141 118.883881 \r\nL 130.333495 129.826047 \r\nL 130.373102 121.980835 \r\nL 130.528483 98.935146 \r\nL 130.531529 99.298071 \r\nL 130.601603 94.682884 \r\nL 130.635117 88.277272 \r\nL 130.699097 99.419045 \r\nL 130.702144 99.11056 \r\nL 130.711284 102.945459 \r\nL 130.796591 94.440935 \r\nL 130.799638 95.106296 \r\nL 130.827058 91.356079 \r\nL 130.918458 91.725052 \r\nL 130.921505 92.825922 \r\nL 130.979392 87.593764 \r\nL 131.025092 91.537541 \r\nL 131.079932 89.015218 \r\nL 131.098213 93.563868 \r\nL 131.119539 93.430796 \r\nL 131.131726 94.99137 \r\nL 131.186566 88.343808 \r\nL 131.22008 91.622223 \r\nL 131.226173 90.835887 \r\nL 131.27492 95.106296 \r\nL 131.360227 98.560125 \r\nL 131.317574 93.104164 \r\nL 131.390694 96.406774 \r\nL 131.402881 94.31996 \r\nL 131.451628 100.205381 \r\nL 131.485141 99.122657 \r\nL 131.488188 99.709385 \r\nL 131.555215 93.787671 \r\nL 131.567402 94.07801 \r\nL 131.674036 80.359475 \r\nL 131.713643 81.000641 \r\nL 131.80809 90.212867 \r\nL 131.747156 79.506603 \r\nL 131.838557 85.767046 \r\nL 131.841603 85.724705 \r\nL 131.847697 86.65621 \r\nL 131.984797 98.475442 \r\nL 131.987844 96.727357 \r\nL 132.060964 107.391281 \r\nL 132.088385 102.388975 \r\nL 132.091431 102.31639 \r\nL 132.106665 104.318522 \r\nL 132.112758 102.739802 \r\nL 132.243765 122.204638 \r\nL 132.246812 120.341627 \r\nL 132.252905 118.02496 \r\nL 132.277279 123.831748 \r\nL 132.350399 123.620042 \r\nL 132.356493 123.795456 \r\nL 132.359539 123.081705 \r\nL 132.40524 128.344106 \r\nL 132.49664 117.365648 \r\nL 132.499687 117.795108 \r\nL 132.56976 112.175832 \r\nL 132.825682 93.406601 \r\nL 132.575854 113.028704 \r\nL 132.831775 95.172832 \r\nL 132.837869 95.553902 \r\nL 132.840915 94.434886 \r\nL 132.871382 91.610126 \r\nL 132.947549 95.753511 \r\nL 132.996296 88.827707 \r\nL 133.06637 93.557819 \r\nL 133.300964 105.425441 \r\nL 133.087697 92.100073 \r\nL 133.319244 105.032273 \r\nL 133.361898 94.828054 \r\nL 133.441112 100.277966 \r\nL 133.450252 100.973571 \r\nL 133.456345 98.493589 \r\nL 133.462439 95.795852 \r\nL 133.520326 106.375093 \r\nL 133.553839 103.090629 \r\nL 133.556886 102.897069 \r\nL 133.575166 107.990106 \r\nL 133.578213 107.736059 \r\nL 133.715313 120.964647 \r\nL 133.733593 119.053246 \r\nL 133.767107 129.033662 \r\nL 133.840227 118.248764 \r\nL 133.855461 119.295195 \r\nL 133.879834 113.016606 \r\nL 133.882881 113.167825 \r\nL 134.071775 97.955251 \r\nL 134.093102 101.723614 \r\nL 134.105289 103.27814 \r\nL 134.190596 100.011822 \r\nL 134.196689 97.646765 \r\nL 134.294183 101.772004 \r\nL 134.29723 101.40908 \r\nL 134.464797 76.923792 \r\nL 134.571431 72.012218 \r\nL 134.540964 77.135498 \r\nL 134.583618 73.234063 \r\nL 134.623225 75.756386 \r\nL 134.601898 71.963828 \r\nL 134.690252 73.923619 \r\nL 134.699392 72.012218 \r\nL 134.778606 82.464435 \r\nL 134.888286 90.624182 \r\nL 134.827353 81.974488 \r\nL 134.900473 88.712781 \r\nL 135.037574 80.123574 \r\nL 135.04062 80.395767 \r\nL 135.071087 84.696419 \r\nL 135.110694 79.028753 \r\nL 135.165534 84.000815 \r\nL 135.189908 82.319266 \r\nL 135.226468 87.80547 \r\nL 135.272168 85.482755 \r\nL 135.290448 85.017002 \r\nL 135.305682 89.214826 \r\nL 135.360522 87.865957 \r\nL 135.366615 89.505165 \r\nL 135.439736 85.452511 \r\nL 135.467156 84.490762 \r\nL 135.494576 88.997071 \r\nL 135.531136 88.960779 \r\nL 135.66519 109.992238 \r\nL 135.668237 108.87927 \r\nL 135.683471 107.548548 \r\nL 135.747451 117.293063 \r\nL 135.765731 113.506554 \r\nL 135.768778 113.597285 \r\nL 135.780964 111.208034 \r\nL 135.927205 89.487019 \r\nL 136.055166 70.481887 \r\nL 136.070399 73.572792 \r\nL 136.149613 84.871833 \r\nL 136.186173 76.107213 \r\nL 136.19836 73.959911 \r\nL 136.274527 85.355732 \r\nL 136.518262 107.076746 \r\nL 136.283667 83.033017 \r\nL 136.530448 104.070524 \r\nL 136.637082 98.269785 \r\nL 136.652316 98.638758 \r\nL 136.676689 103.489845 \r\nL 136.731529 94.89459 \r\nL 136.835117 84.279056 \r\nL 136.874724 88.035322 \r\nL 136.87777 89.202728 \r\nL 136.956984 82.077316 \r\nL 136.969171 82.416045 \r\nL 136.984404 81.351468 \r\nL 137.042291 89.359996 \r\nL 137.109318 93.775574 \r\nL 137.084945 85.912215 \r\nL 137.158065 90.787497 \r\nL 137.267746 95.112344 \r\nL 137.182439 89.553555 \r\nL 137.298213 91.92466 \r\nL 137.404846 79.464262 \r\nL 137.423127 83.940327 \r\nL 137.46578 87.678447 \r\nL 137.490154 82.10756 \r\nL 137.535854 85.083538 \r\nL 137.593741 83.97662 \r\nL 137.566321 87.684495 \r\nL 137.599834 86.438456 \r\nL 137.694281 94.840151 \r\nL 137.627254 85.688412 \r\nL 137.721701 90.231014 \r\nL 137.724748 88.984974 \r\nL 137.797869 95.100247 \r\nL 137.825289 91.622223 \r\nL 137.931923 95.735364 \r\nL 137.916689 91.513346 \r\nL 137.941063 94.138498 \r\nL 138.069023 79.252556 \r\nL 137.956296 95.330099 \r\nL 138.093397 81.726489 \r\nL 138.227451 93.182797 \r\nL 138.291431 96.71526 \r\nL 138.239638 91.622223 \r\nL 138.340178 93.769525 \r\nL 138.343225 93.588063 \r\nL 138.361505 98.445199 \r\nL 138.373692 99.794067 \r\nL 138.449859 92.590021 \r\nL 138.492512 87.055427 \r\nL 138.556493 92.807776 \r\nL 138.775854 109.865214 \r\nL 138.788041 107.850985 \r\nL 138.794134 107.965911 \r\nL 138.797181 107.554597 \r\nL 139.083569 87.255035 \r\nL 139.098802 88.132102 \r\nL 139.202389 93.340065 \r\nL 139.129269 84.817394 \r\nL 139.22067 93.049725 \r\nL 139.24809 91.283494 \r\nL 139.269416 94.731274 \r\nL 139.403471 107.0586 \r\nL 139.290743 93.21909 \r\nL 139.412611 105.274223 \r\nL 139.504011 98.578271 \r\nL 139.531431 101.342544 \r\nL 139.537525 103.689454 \r\nL 139.583225 95.318002 \r\nL 139.635018 99.431143 \r\nL 139.708139 97.132623 \r\nL 139.671579 102.328488 \r\nL 139.732512 100.683231 \r\nL 139.897033 117.268868 \r\nL 139.915313 114.323133 \r\nL 139.988434 119.36778 \r\nL 140.006714 116.966432 \r\nL 140.061554 118.956466 \r\nL 140.0189 115.944195 \r\nL 140.070694 118.732663 \r\nL 140.092021 124.757205 \r\nL 140.165141 117.438233 \r\nL 140.186468 121.702593 \r\nL 140.414969 105.165345 \r\nL 140.192561 122.355856 \r\nL 140.454576 107.82679 \r\nL 140.472856 111.964126 \r\nL 140.49723 105.364954 \r\nL 140.56121 105.588757 \r\nL 140.667844 112.079052 \r\nL 140.680031 109.756337 \r\nL 140.740964 115.284883 \r\nL 140.789711 110.754379 \r\nL 140.838458 110.808817 \r\nL 140.908532 106.411385 \r\nL 140.911579 106.598896 \r\nL 140.954232 102.927313 \r\nL 140.963372 103.151116 \r\nL 141.088286 92.571875 \r\nL 141.09438 94.235278 \r\nL 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284.011235 86.958647 \r\nL 284.075215 81.266785 \r\nL 284.148335 78.520659 \r\nL 284.093495 83.522964 \r\nL 284.190989 79.379579 \r\nL 284.200129 80.359475 \r\nL 284.264109 73.082844 \r\nL 284.367697 66.241722 \r\nL 284.379883 69.804429 \r\nL 284.501751 75.091025 \r\nL 284.41949 67.130887 \r\nL 284.507844 74.782539 \r\nL 284.584011 73.536499 \r\nL 284.550498 77.788762 \r\nL 284.623618 74.340981 \r\nL 284.626665 74.328884 \r\nL 284.629711 74.764393 \r\nL 284.663225 78.145637 \r\nL 284.730252 73.137283 \r\nL 284.733299 73.282452 \r\nL 284.846026 64.711392 \r\nL 284.748532 74.939806 \r\nL 284.900866 67.45147 \r\nL 284.910006 70.493985 \r\nL 284.97094 60.326058 \r\nL 284.99836 63.501645 \r\nL 285.02578 59.775623 \r\nL 285.101947 64.142811 \r\nL 285.108041 63.28389 \r\nL 285.150694 66.907084 \r\nL 285.181161 61.312002 \r\nL 285.220768 64.118616 \r\nL 285.330448 74.4922 \r\nL 285.357869 72.604994 \r\nL 285.379195 70.058476 \r\nL 285.427942 79.313043 \r\nL 285.430989 78.986411 \r\nL 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "def running_average(x,window):\n",
    "    return np.convolve(x,np.ones(window)/window,mode='valid')\n",
    "\n",
    "plt.plot(running_average(rewards,100))"
   ]
  },
  {
   "source": [
    "## Varying Hyperparameters and Seeing the Result in Action\n",
    "\n",
    "Now it would be interesting to actually see how the trained model behaves. Let's run the simulation, and we will be following the same action selection strategy as during training: sampling according to the probability distribution in Q-Table: "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "obs = env.reset()\n",
    "done = False\n",
    "while not done:\n",
    "   s = discretize(obs)\n",
    "   env.render()\n",
    "   v = probs(np.array(qvalues(s)))\n",
    "   a = random.choices(actions,weights=v)[0]\n",
    "   obs,_,done,_ = env.step(a)\n",
    "env.close()"
   ]
  },
  {
   "source": [
    "\n",
    "## Saving result to an animated GIF\n",
    "\n",
    "If you want to impress your friends, you may want to send them the animated GIF picture of the balancing pole. To do this, we can invoke `env.render` to produce an image frame, and then save those to animated GIF using PIL library:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "360\n"
     ]
    }
   ],
   "source": [
    "from PIL import Image\n",
    "obs = env.reset()\n",
    "done = False\n",
    "i=0\n",
    "ims = []\n",
    "while not done:\n",
    "   s = discretize(obs)\n",
    "   img=env.render(mode='rgb_array')\n",
    "   ims.append(Image.fromarray(img))\n",
    "   v = probs(np.array([Qbest.get((s,a),0) for a in actions]))\n",
    "   a = random.choices(actions,weights=v)[0]\n",
    "   obs,_,done,_ = env.step(a)\n",
    "   i+=1\n",
    "env.close()\n",
    "ims[0].save('images/cartpole-balance.gif',save_all=True,append_images=ims[1::2],loop=0,duration=5)\n",
    "print(i)"
   ]
  }
 ]
}