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ML-For-Beginners/8-Reinforcement/2-Gym/solution/notebook.ipynb

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{
"metadata": {
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"cells": [
{
"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": [
"Requirement already satisfied: gym in /Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages (0.18.3)\n",
"Requirement 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",
"Requirement 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",
"Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages (from gym) (1.6.0)\n",
"Requirement already satisfied: pyglet<=1.5.15,>=1.4.0 in /Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages (from gym) (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)\n0\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": [
"[ 0.03044442 -0.19543914 -0.04496216 0.28125618] -> 1.0\n",
"[ 0.02653564 -0.38989186 -0.03933704 0.55942606] -> 1.0\n",
"[ 0.0187378 -0.19424049 -0.02814852 0.25461393] -> 1.0\n",
"[ 0.01485299 -0.38894946 -0.02305624 0.53828712] -> 1.0\n",
"[ 0.007074 -0.19351108 -0.0122905 0.23842953] -> 1.0\n",
"[ 0.00320378 0.00178427 -0.00752191 -0.05810469] -> 1.0\n",
"[ 0.00323946 0.19701326 -0.008684 -0.35315131] -> 1.0\n",
"[ 0.00717973 0.00201587 -0.01574703 -0.06321931] -> 1.0\n",
"[ 0.00722005 0.19736001 -0.01701141 -0.36082863] -> 1.0\n",
"[ 0.01116725 0.39271958 -0.02422798 -0.65882671] -> 1.0\n",
"[ 0.01902164 0.19794307 -0.03740452 -0.37387001] -> 1.0\n",
"[ 0.0229805 0.39357584 -0.04488192 -0.67810827] -> 1.0\n",
"[ 0.03085202 0.58929164 -0.05844408 -0.98457719] -> 1.0\n",
"[ 0.04263785 0.78514572 -0.07813563 -1.2950295 ] -> 1.0\n",
"[ 0.05834076 0.98116859 -0.10403622 -1.61111521] -> 1.0\n",
"[ 0.07796413 0.78741784 -0.13625852 -1.35259196] -> 1.0\n",
"[ 0.09371249 0.98396202 -0.16331036 -1.68461179] -> 1.0\n",
"[ 0.11339173 0.79106371 -0.1970026 -1.44691436] -> 1.0\n",
"[ 0.12921301 0.59883361 -0.22594088 -1.22169133] -> 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, 2, -4, -9)\n(0, 3, -6, -12)\n(0, 2, -8, -9)\n(0, 3, -10, -13)\n(0, 4, -13, -16)\n(0, 4, -16, -19)\n(0, 4, -20, -17)\n(0, 4, -24, -20)\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": {},
"outputs": [
{
"output_type": "execute_result",
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117.974333 86.188736 \r\nL 117.977377 193.864124 \r\nL 117.989551 17.083636 \r\nL 118.086949 163.329313 \r\nL 118.120429 21.904922 \r\nL 118.175215 197.078315 \r\nL 118.190433 188.641064 \r\nL 118.233045 205.515565 \r\nL 118.223914 34.359911 \r\nL 118.284787 130.785632 \r\nL 118.318267 78.956807 \r\nL 118.324355 190.649933 \r\nL 118.394359 100.25082 \r\nL 118.497844 200.292506 \r\nL 118.415665 99.447273 \r\nL 118.503931 107.482749 \r\nL 118.506975 108.688071 \r\nL 118.531324 211.943947 \r\nL 118.589154 34.761685 \r\nL 118.616547 100.25082 \r\nL 118.680464 197.078315 \r\nL 118.665245 21.503149 \r\nL 118.726119 141.231752 \r\nL 118.796123 64.091175 \r\nL 118.805254 195.47122 \r\nL 118.835691 132.392727 \r\nL 118.939175 163.731086 \r\nL 118.89352 80.965676 \r\nL 118.945263 149.267228 \r\nL 118.966568 21.503149 \r\nL 119.033529 212.747494 \r\nL 119.051791 169.35592 \r\nL 119.143101 203.90847 \r\nL 119.127883 45.609579 \r\nL 119.155276 163.329313 \r\nL 119.252673 17.083636 \r\nL 119.161363 209.13153 \r\nL 119.270935 82.170998 \r\nL 119.307459 194.265898 \r\nL 119.334852 74.537295 \r\nL 119.383551 133.196275 \r\nL 119.392682 31.949268 \r\nL 119.435293 190.649933 \r\nL 119.487035 123.553703 \r\nL 119.59052 200.292506 \r\nL 119.55704 75.340843 \r\nL 119.596607 134.80337 \r\nL 119.630088 189.444612 \r\nL 119.605738 93.822439 \r\nL 119.703136 122.750155 \r\nL 119.706179 122.348381 \r\nL 119.71531 133.999823 \r\nL 119.748791 201.096053 \r\nL 119.727485 67.70714 \r\nL 119.824882 143.642395 \r\nL 119.919236 106.277428 \r\nL 119.858363 203.104922 \r\nL 119.934454 146.856585 \r\nL 120.034895 204.310244 \r\nL 119.958804 84.179867 \r\nL 120.037939 125.160798 \r\nL 120.089681 86.59051 \r\nL 120.044026 207.524435 \r\nL 120.114031 119.937738 \r\nL 120.153598 202.703149 \r\nL 120.168817 61.278758 \r\nL 120.226646 196.676541 \r\nL 120.275345 72.9302 \r\nL 120.342306 81.36745 \r\nL 120.418397 196.274767 \r\nL 120.448834 46.8149 \r\nL 120.457965 178.194945 \r\nL 120.467096 21.904922 \r\nL 120.552319 211.140399 \r\nL 120.567537 168.954146 \r\nL 120.631454 46.8149 \r\nL 120.658847 173.775432 \r\nL 120.683196 105.072106 \r\nL 120.692327 194.265898 \r\nL 120.737982 17.083636 \r\nL 120.792768 151.276098 \r\nL 120.893209 76.546164 \r\nL 120.862773 205.515565 \r\nL 120.90234 154.088514 \r\nL 120.941908 189.042838 \r\nL 120.984519 49.225543 \r\nL 120.999738 105.47388 \r\nL 121.002781 60.475211 \r\nL 121.097135 191.051707 \r\nL 121.103222 127.973215 \r\nL 121.164096 208.729756 \r\nL 121.133659 91.411796 \r\nL 121.212794 144.847716 \r\nL 121.252362 66.501818 \r\nL 121.270624 196.676541 \r\nL 121.32541 104.268559 \r\nL 121.401502 193.060576 \r\nL 121.407589 61.680532 \r\nL 121.422807 111.500488 \r\nL 121.495855 64.894723 \r\nL 121.462375 187.435743 \r\nL 121.526292 104.670333 \r\nL 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 50.430865 \r\nL 122.853331 187.837517 \r\nL 122.956815 72.528426 \r\nL 122.962903 205.917339 \r\nL 123.02682 64.492949 \r\nL 123.069431 175.784302 \r\nL 123.121173 73.733747 \r\nL 123.154654 209.935078 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124.630832 176.186075 \r\nL 124.661269 65.698271 \r\nL 124.728229 198.283636 \r\nL 124.743448 95.831308 \r\nL 124.828671 205.515565 \r\nL 124.801278 62.885854 \r\nL 124.856064 127.169667 \r\nL 124.8865 70.117783 \r\nL 124.929112 198.68541 \r\nL 124.962592 141.231752 \r\nL 125.041727 203.506696 \r\nL 124.983898 74.939069 \r\nL 125.06912 117.125322 \r\nL 125.133037 66.501818 \r\nL 125.12695 197.480089 \r\nL 125.181736 97.438404 \r\nL 125.206085 201.899601 \r\nL 125.230435 78.153259 \r\nL 125.294352 142.437073 \r\nL 125.300439 201.497827 \r\nL 125.306526 82.170998 \r\nL 125.406967 181.409135 \r\nL 125.449579 20.297827 \r\nL 125.510452 204.712018 \r\nL 125.519583 121.946608 \r\nL 125.595675 199.087184 \r\nL 125.601762 81.769224 \r\nL 125.629155 129.982084 \r\nL 125.64133 17.083636 \r\nL 125.656548 212.345721 \r\nL 125.738727 132.392727 \r\nL 125.811775 195.872993 \r\nL 125.805688 47.216674 \r\nL 125.817862 130.383858 \r\nL 125.820906 33.958137 \r\nL 125.924391 194.667672 \r\nL 125.991351 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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 187.033969 \r\nL 129.765498 82.974545 \r\nL 129.786804 205.917339 \r\nL 129.811153 61.278758 \r\nL 129.878114 181.409135 \r\nL 129.890288 42.797162 \r\nL 129.957249 202.703149 \r\nL 129.990729 58.064568 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131.430384 158.508027 \r\nL 131.512563 93.822439 \r\nL 131.451689 196.676541 \r\nL 131.536912 97.840177 \r\nL 131.558218 195.47122 \r\nL 131.582567 62.48408 \r\nL 131.649528 157.704479 \r\nL 131.722576 17.083636 \r\nL 131.658659 197.881863 \r\nL 131.762143 79.358581 \r\nL 131.783449 198.68541 \r\nL 131.768231 17.083636 \r\nL 131.871715 150.874324 \r\nL 131.874759 31.145721 \r\nL 131.969113 200.694279 \r\nL 131.981287 168.552373 \r\nL 132.029986 17.083636 \r\nL 132.090859 193.46235 \r\nL 132.093903 92.617118 \r\nL 132.15782 54.850377 \r\nL 132.203475 199.488958 \r\nL 132.28261 66.100044 \r\nL 132.279567 207.926208 \r\nL 132.313047 154.088514 \r\nL 132.36479 206.720887 \r\nL 132.370877 113.911131 \r\nL 132.389139 175.382528 \r\nL 132.43175 21.904922 \r\nL 132.428707 207.524435 \r\nL 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 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17.887184 \r\nL 135.460199 196.274767 \r\nL 135.533247 37.172328 \r\nL 135.551509 211.542173 \r\nL 135.584989 26.726208 \r\nL 135.645862 183.016231 \r\nL 135.654993 56.457472 \r\nL 135.755434 201.899601 \r\nL 135.804133 39.984745 \r\nL 135.861963 212.345721 \r\nL 135.865006 188.23929 \r\nL 135.86805 209.533304 \r\nL 135.898487 61.680532 \r\nL 135.965447 116.723548 \r\nL 136.035452 199.087184 \r\nL 135.998928 20.297827 \r\nL 136.05067 85.385188 \r\nL 136.132849 17.083636 \r\nL 136.08415 191.453481 \r\nL 136.157198 71.323104 \r\nL 136.227203 207.926208 \r\nL 136.184591 38.37765 \r\nL 136.26677 125.562572 \r\nL 136.272858 195.47122 \r\nL 136.379386 33.556364 \r\nL 136.409823 210.336851 \r\nL 136.394604 17.083636 \r\nL 136.492002 89.402927 \r\nL 136.543744 193.864124 \r\nL 136.574181 32.351042 \r\nL 136.601574 148.061907 \r\nL 136.616792 17.083636 \r\nL 136.653316 211.140399 \r\nL 136.711146 138.017561 \r\nL 136.772019 188.641064 \r\nL 136.74767 64.492949 \r\nL 136.817674 136.008692 \r\nL 136.90594 69.716009 \r\nL 136.881591 182.212683 \r\nL 136.924202 111.500488 \r\nL 136.978988 195.47122 \r\nL 137.009425 56.055698 \r\nL 137.033774 76.546164 \r\nL 137.097691 51.234412 \r\nL 137.106822 195.47122 \r\nL 137.152477 17.083636 \r\nL 137.219438 93.822439 \r\nL 137.2377 206.319113 \r\nL 137.286399 22.306696 \r\nL 137.325966 68.912461 \r\nL 137.395971 17.887184 \r\nL 137.347272 191.453481 \r\nL 137.435538 42.797162 \r\nL 137.459888 193.060576 \r\nL 137.548154 87.795831 \r\nL 137.599896 66.903592 \r\nL 137.581634 211.542173 \r\nL 137.621202 141.633525 \r\nL 137.721643 209.935078 \r\nL 137.691206 17.083636 \r\nL 137.72773 114.312905 \r\nL 137.809909 193.46235 \r\nL 137.840346 66.501818 \r\nL 137.898176 205.515565 \r\nL 137.952962 166.141729 \r\nL 138.004704 29.940399 \r\nL 137.974267 202.301375 \r\nL 138.065577 105.072106 \r\nL 138.141669 199.488958 \r\nL 138.102101 73.733747 \r\nL 138.147756 113.911131 \r\nL 138.196455 17.083636 \r\nL 138.214717 207.926208 \r\nL 138.257328 56.055698 \r\nL 138.327333 200.694279 \r\nL 138.269503 17.083636 \r\nL 138.3669 191.855255 \r\nL 138.369944 71.724878 \r\nL 138.439948 197.480089 \r\nL 138.479516 107.884523 \r\nL 138.48256 190.649933 \r\nL 138.500822 45.609579 \r\nL 138.592132 148.865455 \r\nL 138.598219 22.306696 \r\nL 138.601263 210.738625 \r\nL 138.704747 119.535965 \r\nL 138.723009 210.336851 \r\nL 138.786926 91.81357 \r\nL 138.814319 165.739956 \r\nL 138.875193 80.162129 \r\nL 138.844756 194.265898 \r\nL 138.923891 154.892062 \r\nL 138.987808 213.149268 \r\nL 138.993896 75.742616 \r\nL 139.036507 191.453481 \r\nL 139.060856 71.323104 \r\nL 139.146079 183.418004 \r\nL 139.173472 67.305366 \r\nL 139.152166 196.274767 \r\nL 139.276957 143.642395 \r\nL 139.359136 195.069446 \r\nL 139.286088 25.520887 \r\nL 139.383485 125.562572 \r\nL 139.416965 66.100044 \r\nL 139.39566 206.720887 \r\nL 139.477839 72.528426 \r\nL 139.569149 17.083636 \r\nL 139.590454 204.310244 \r\nL 139.593498 206.319113 \r\nL 139.596542 164.13286 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140.847489 76.14439 \r\nL 140.874882 188.23929 \r\nL 140.887057 55.252151 \r\nL 140.963148 203.90847 \r\nL 140.987498 135.205144 \r\nL 141.087939 206.720887 \r\nL 141.002716 22.70847 \r\nL 141.09707 189.042838 \r\nL 141.197511 62.885854 \r\nL 141.194467 194.265898 \r\nL 141.206642 74.537295 \r\nL 141.218816 183.819778 \r\nL 141.319257 136.812239 \r\nL 141.352738 17.083636 \r\nL 141.419698 199.087184 \r\nL 141.498834 17.083636 \r\nL 141.489703 211.140399 \r\nL 141.532314 80.965676 \r\nL 141.608406 199.890732 \r\nL 141.611449 17.887184 \r\nL 141.641886 78.956807 \r\nL 141.675366 210.336851 \r\nL 141.672323 17.083636 \r\nL 141.751458 115.92 \r\nL 141.787982 17.083636 \r\nL 141.839724 205.917339 \r\nL 141.864074 99.849047 \r\nL 141.964515 189.846386 \r\nL 141.897554 48.020222 \r\nL 141.973646 169.757694 \r\nL 141.98582 37.574102 \r\nL 142.064956 184.221552 \r\nL 142.089305 38.779424 \r\nL 142.159309 194.265898 \r\nL 142.119742 31.949268 \r\nL 142.201921 134.80337 \r\nL 142.241488 46.413126 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170.526284 90.206475 \r\nL 170.54759 202.301375 \r\nL 170.605419 58.466341 \r\nL 170.635856 79.760355 \r\nL 170.648031 202.301375 \r\nL 170.708904 59.269889 \r\nL 170.748472 168.552373 \r\nL 170.791083 41.59184 \r\nL 170.845869 201.497827 \r\nL 170.861087 82.572772 \r\nL 170.864131 84.179867 \r\nL 170.867175 192.257029 \r\nL 170.876306 29.136851 \r\nL 170.973703 76.546164 \r\nL 170.97979 148.865455 \r\nL 170.985878 60.876984 \r\nL 171.00414 112.304035 \r\nL 171.022402 210.336851 \r\nL 171.049795 44.404257 \r\nL 171.113712 104.670333 \r\nL 171.183716 17.083636 \r\nL 171.125886 194.667672 \r\nL 171.214153 69.716009 \r\nL 171.217196 203.506696 \r\nL 171.27807 49.627317 \r\nL 171.323725 178.194945 \r\nL 171.34503 31.145721 \r\nL 171.338943 200.292506 \r\nL 171.433297 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 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172.976436 211.943947 \r\nL 172.985567 17.083636 \r\nL 173.061658 97.840177 \r\nL 173.119488 17.083636 \r\nL 173.143837 192.257029 \r\nL 173.168187 101.857916 \r\nL 173.219929 203.90847 \r\nL 173.259497 17.083636 \r\nL 173.277759 136.410466 \r\nL 173.323414 45.207805 \r\nL 173.28689 198.283636 \r\nL 173.387331 123.955477 \r\nL 173.46951 43.198936 \r\nL 173.399505 203.90847 \r\nL 173.496903 72.528426 \r\nL 173.600387 199.087184 \r\nL 173.530383 27.93153 \r\nL 173.609518 168.954146 \r\nL 173.713003 193.46235 \r\nL 173.71909 17.083636 \r\nL 173.728221 195.47122 \r\nL 173.831706 114.714678 \r\nL 173.846924 17.083636 \r\nL 173.929103 197.480089 \r\nL 173.944322 72.528426 \r\nL 174.041719 189.444612 \r\nL 173.983889 17.083636 \r\nL 174.069112 156.499157 \r\nL 174.072156 17.083636 \r\nL 174.148247 207.122661 \r\nL 174.178684 195.872993 \r\nL 174.23347 40.788293 \r\nL 174.19999 200.694279 \r\nL 174.303474 55.653925 \r\nL 174.306518 208.729756 \r\nL 174.364348 17.083636 \r\nL 174.413046 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178.403294 17.48541 \r\nL 178.476342 150.47255 \r\nL 178.488516 17.083636 \r\nL 178.485473 183.819778 \r\nL 178.585914 36.36878 \r\nL 178.643743 198.68541 \r\nL 178.649831 29.940399 \r\nL 178.698529 155.293836 \r\nL 178.701573 17.083636 \r\nL 178.762446 193.060576 \r\nL 178.808101 192.257029 \r\nL 178.811145 195.069446 \r\nL 178.89028 17.083636 \r\nL 178.859844 204.310244 \r\nL 178.923761 58.466341 \r\nL 178.957241 180.203814 \r\nL 179.015071 17.083636 \r\nL 179.042464 121.946608 \r\nL 179.0729 210.738625 \r\nL 179.145948 50.029091 \r\nL 179.148992 201.096053 \r\nL 179.25552 119.134191 \r\nL 179.264651 41.190067 \r\nL 179.267695 200.292506 \r\nL 179.359005 44.806031 \r\nL 179.459446 194.265898 \r\nL 179.468577 99.849047 \r\nL 179.483795 17.083636 \r\nL 179.538581 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 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184.037121 203.104922 \r\nL 184.085819 60.475211 \r\nL 184.164955 200.694279 \r\nL 184.101038 36.36878 \r\nL 184.201479 117.928869 \r\nL 184.280614 17.083636 \r\nL 184.228872 206.720887 \r\nL 184.311051 76.14439 \r\nL 184.317138 207.122661 \r\nL 184.420623 165.338182 \r\nL 184.432797 31.547494 \r\nL 184.469321 196.676541 \r\nL 184.530195 190.24816 \r\nL 184.591068 200.694279 \r\nL 184.645854 17.083636 \r\nL 184.648898 203.506696 \r\nL 184.75847 184.221552 \r\nL 184.852823 17.083636 \r\nL 184.770644 207.122661 \r\nL 184.868042 201.899601 \r\nL 184.983701 17.083636 \r\nL 184.931959 210.336851 \r\nL 184.986745 82.572772 \r\nL 185.050662 17.083636 \r\nL 185.093273 197.881863 \r\nL 185.096317 30.743947 \r\nL 185.202845 96.233082 \r\nL 185.260675 17.083636 \r\nL 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 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292.507318 31.547494 \r\nL 292.519493 191.855255 \r\nL 292.61689 62.48408 \r\nL 292.647327 190.24816 \r\nL 292.668633 21.503149 \r\nL 292.726462 103.866785 \r\nL 292.814729 17.083636 \r\nL 292.76603 192.658803 \r\nL 292.832991 79.358581 \r\nL 292.939519 198.68541 \r\nL 292.878646 17.083636 \r\nL 292.942563 54.448603 \r\nL 292.951694 199.087184 \r\nL 293.046047 17.083636 \r\nL 293.055178 174.177206 \r\nL 293.103877 17.083636 \r\nL 293.134314 212.345721 \r\nL 293.167794 115.518226 \r\nL 293.210405 21.904922 \r\nL 293.176925 201.497827 \r\nL 293.277366 78.555033 \r\nL 293.28041 78.153259 \r\nL 293.283453 89.402927 \r\nL 293.350414 34.761685 \r\nL 293.383894 176.186075 \r\nL 293.389982 137.214013 \r\nL 293.472161 36.36878 \r\nL 293.493466 193.46235 \r\nL 293.578689 17.083636 \r\nL 293.511728 202.703149 \r\nL 293.606082 40.788293 \r\nL 293.642606 181.810909 \r\nL 293.660868 17.083636 \r\nL 293.709567 133.196275 \r\nL 293.80392 17.083636 \r\nL 293.758265 203.90847 \r\nL 293.819139 144.044169 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},
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}
}
],
"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",
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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 121.875903 103.393066 \r\nL 121.927697 96.394677 \r\nL 122.098311 109.756337 \r\nL 122.101357 109.006294 \r\nL 122.128778 114.044892 \r\nL 122.192758 113.833186 \r\nL 122.198851 113.772698 \r\nL 122.235412 124.902375 \r\nL 122.308532 128.676786 \r\nL 122.275018 122.972827 \r\nL 122.342045 124.20677 \r\nL 122.345092 124.370086 \r\nL 122.375559 120.093629 \r\nL 122.6132 91.797637 \r\nL 122.625387 94.332057 \r\nL 122.716787 90.382232 \r\nL 122.728974 88.113956 \r\nL 122.786861 94.301814 \r\nL 122.808188 93.932841 \r\nL 122.908729 98.808123 \r\nL 122.829515 93.690891 \r\nL 122.927009 97.580229 \r\nL 122.930055 96.104337 \r\nL 123.024502 103.08458 \r\nL 123.027549 102.334537 \r\nL 123.13723 109.732142 \r\nL 123.16465 108.933709 \r\nL 123.167697 107.439671 \r\nL 123.26519 112.677877 \r\nL 123.310891 116.754726 \r\nL 123.353544 111.510471 \r\nL 123.371824 111.939931 \r\nL 123.393151 114.304987 \r\nL 123.426665 107.385232 \r\nL 123.438851 107.385232 \r\nL 123.582045 96.672919 \r\nL 123.447991 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 \r\nL 124.761112 111.298765 \r\nL 124.764158 112.091149 \r\nL 124.846419 107.125136 \r\nL 124.858606 107.802595 \r\nL 124.925633 111.292716 \r\nL 124.9561 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126.211333 116.821262 \r\nL 126.244846 114.395718 \r\nL 126.247893 115.980487 \r\nL 126.302733 111.583056 \r\nL 126.348434 111.788713 \r\nL 126.458114 108.806685 \r\nL 126.363667 114.383621 \r\nL 126.464208 110.016433 \r\nL 126.485534 112.435927 \r\nL 126.528188 107.917521 \r\nL 126.558655 108.25625 \r\nL 126.595215 106.810602 \r\nL 126.653102 109.98014 \r\nL 126.656149 110.089017 \r\nL 126.665289 107.421524 \r\nL 126.753643 104.288279 \r\nL 126.704896 109.326877 \r\nL 126.778016 105.455685 \r\nL 126.905977 110.476137 \r\nL 126.787156 103.677356 \r\nL 126.918163 109.278487 \r\nL 127.009564 102.401073 \r\nL 127.040031 105.280272 \r\nL 127.058311 106.756163 \r\nL 127.122291 103.253945 \r\nL 127.216738 93.878402 \r\nL 127.247205 96.037801 \r\nL 127.311186 101.493762 \r\nL 127.362979 98.354468 \r\nL 127.381259 96.122484 \r\nL 127.451333 99.310168 \r\nL 127.466566 98.82022 \r\nL 127.51836 100.49572 \r\nL 127.54578 92.626314 \r\nL 127.624994 87.466741 \r\nL 127.658507 90.388281 \r\nL 127.661554 90.400378 \r\nL 127.734674 80.19011 \r\nL 127.780375 82.68219 \r\nL 127.816935 80.359475 \r\nL 127.844355 85.494853 \r\nL 127.896149 80.885715 \r\nL 127.920522 79.385628 \r\nL 127.993643 84.037107 \r\nL 128.13379 98.215347 \r\nL 128.310498 89.414434 \r\nL 128.209957 101.614737 \r\nL 128.313544 90.00721 \r\nL 128.429318 82.331363 \r\nL 128.328778 91.386322 \r\nL 128.490252 86.190457 \r\nL 128.514625 83.057212 \r\nL 128.615166 92.686801 \r\nL 128.6761 84.472616 \r\nL 128.73094 89.105949 \r\nL 128.773593 92.838019 \r\nL 128.746173 88.089761 \r\nL 128.852807 91.144373 \r\nL 128.855854 90.049552 \r\nL 128.941161 98.541978 \r\nL 128.944208 98.917 \r\nL 128.996001 91.658516 \r\nL 129.075215 85.658168 \r\nL 129.096542 91.918611 \r\nL 129.102635 91.864173 \r\nL 129.163569 94.156644 \r\nL 129.111775 89.632189 \r\nL 129.194036 90.013259 \r\nL 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 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168.922783 73.578841 \r\nL 168.901456 79.095289 \r\nL 168.938016 75.169658 \r\nL 168.947156 77.202034 \r\nL 169.03551 71.274272 \r\nL 169.038557 72.296508 \r\nL 169.09035 66.102602 \r\nL 169.151284 71.661391 \r\nL 169.264011 64.723489 \r\nL 169.230498 73.113088 \r\nL 169.285338 65.261827 \r\nL 169.404158 75.121268 \r\nL 169.416345 69.483846 \r\nL 169.526026 58.747337 \r\nL 169.431579 71.322662 \r\nL 169.580866 64.185152 \r\nL 169.590006 65.987676 \r\nL 169.644846 58.154561 \r\nL 169.6875 62.461262 \r\nL 169.70578 61.318051 \r\nL 169.754527 66.719573 \r\nL 169.76976 73.379232 \r\nL 169.848974 64.820269 \r\nL 169.870301 71.237979 \r\nL 169.882488 69.731844 \r\nL 169.952561 74.595028 \r\nL 169.964748 73.463915 \r\nL 169.998262 78.998509 \r\nL 170.068335 71.461783 \r\nL 170.074429 69.550382 \r\nL 170.153643 77.032669 \r\nL 170.165829 75.901556 \r\nL 170.29379 93.079969 \r\nL 170.181063 75.877361 \r\nL 170.299883 92.674703 \r\nL 170.30293 91.646418 \r\nL 170.37605 104.288279 \r\nL 170.449171 107.87518 \r\nL 170.488778 107.433622 \r\nL 170.662439 82.627751 \r\nL 170.671579 83.825401 \r\nL 170.808679 77.704079 \r\nL 170.738606 85.609779 \r\nL 170.814773 78.302904 \r\nL 170.930547 81.944244 \r\nL 170.87266 75.381364 \r\nL 170.939687 81.750684 \r\nL 171.034134 75.042635 \r\nL 170.948827 82.240632 \r\nL 171.052414 79.56709 \r\nL 171.073741 82.216437 \r\nL 171.122488 76.675794 \r\nL 171.149908 78.08515 \r\nL 171.174281 82.77897 \r\nL 171.244355 77.788762 \r\nL 171.262635 78.956168 \r\nL 171.372316 67.941418 \r\nL 171.396689 69.090678 \r\nL 171.427156 73.542548 \r\nL 171.491136 66.036065 \r\nL 171.503323 68.044246 \r\nL 171.576443 61.596292 \r\nL 171.509416 68.141026 \r\nL 171.649564 63.634717 \r\nL 171.673937 64.705343 \r\nL 171.734871 56.7694 \r\nL 171.756198 54.670488 \r\nL 171.801898 63.749643 \r\nL 171.844552 56.714962 \r\nL 171.850645 57.259348 \r\nL 171.865878 54.694683 \r\nL 171.920719 45.476408 \r\nL 171.881112 55.051559 \r\nL 171.999932 49.92223 \r\nL 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2RSJUUQNMRFNnx3VXAMvfLq2vmVNty2nZP2WQDaBdlGOrSSlDNXn7j+OdXz0mJPXRwvHDmptr7hE1tIvnoWRUkWnBpgN4Zq41+7b8nXFiWtebV1BiZR5pywHjlAdHDQLZjLhueEdH+9nFiu9PJoCZRBQPz8PhMyHE90S0CcAnRPQkgDUAZkj9ZwB4n4jy4dHoLwvCuJl6iMvBpF4Kj57CjkOl2FfirzEfL3eWJ/3Vn5zZXZXeGYDH5FFRXYN4xQPOivBRImu61wzr6Gekj1Q9qpmUH753uya6faxE18pU1wg8Omujo7eitTZz3euR1sBYXOq9zew+bOx91ad9uuF2tzAV9kKI9QD6a7TvgMd+r24vB3CJK6NjogorZhw91HZXZaTq6Bd+QnWtwMCsZv47OpSFTic2m6uKYFTXCnR/aB7OPK2pt00vmZgVIkGzt4a7I3t/2S5NW74V1u62J+yzmjf0VpRSYpbBVK94ydnPGXsCZSu+G8GEI2iZkBHIBNYuxY/vVGUNXltSp3nLppKaCNRyZW1Pr1C3HY6drLKl2RYdc/5QCRR54nXFTnfs2E4FPQD8bjOZml49XrM6uQePOxtjqBzTWdgzISOQGBKl//oJHdOMlmdHuMW/m7VVNxYdw3u/+04SGj3fLvivvepNbmImGJduCzyKN1jojd0sqZ3Te223hKNTWNgzIcOJfVkIgQWbDvjYQ4+d0hb2WrbZUCv7ZRXVPuMwE3p6ZE2b7edi+MrifNw6uovlYwSiDQfKGoXppEDDw+qKGctDORxbqEs/ymjlt1GiDnjL23/c0kR/qBzGQpucgYlpnMi9GUt34snZmzFU4XJ47os/W95/9e7QRine9fk6n3Ut3+zz+xj7yiv91pVFU37NP+xXNtHtZ9nbV2fbLgiixU6FgB/1/E946fL+OHSiAteGyPMkGHyrk4ZZDy0XUk1Y2DPRhmyzlwXUF6sKMbxLC7Q2yC//5GxPJkK7Hiwyf/0w8CyZgaBVg9aozi3g67depkoE5nISTT9G92gVlOPeLvnmbztYig6q9MKRhtIcGIr8NWzGYaIOWdjLybnu/nxdRL/Ou4GWZm9nolrd1T/rpfvCKJjeIR+v2I1/zrPmW+8WRoF1fTVcQ5XC/sUfjdNx6GHnIREqMw4Le8YV9L7cQghvoJGydJ1snlDmG49GtD4WI+28TJUnXy3MQ6FpntFW3ze+PmKU0fLu8d392pR1g79Y5Z8iwwr/WWg9QV+o8kSysGcCZs6GInR6YI5m6t73ft+FSS8txW/5h/Dh8rqMk3IIuhJ19Gm0onYRnbOhCFnTZuO6mSv9hItSTt00srPfHMRelc9+kt1K4xo8MLEnLh/YPuDjuMnoHi2Dclx1MRjA15/eaaUxW8Le0Rnsw8KeCZj7vlwPAPhcQwvK2++pCrXzcJmpa5q60He0otbW5XmFHzcfRO5e3wee0uX0tSXbsXiLb8Ku3YoH7PIHxmDj4+NxaXZggjopIQ4jutpPTtiiUbJ5J4cESyAmJ/gLe6UHlds1hLXQ8y5zGxb2TMDILmk/aFSRypVqdC7bcSTkbpCRipFZQZ2Qy+wzi1MYfFulpSAxPk63Lm2wCaY1wqkLqxmZGs4BynkRvYLnbtKicfAekkpY2DOuoZViYIOkqS42KPWmh7KIRTRhJOzV+ffNkqZZqVyVZrH8nbKEoLqwuRXcKkqjRbA07OYabyNK000gZSz1yGru643EZhwmIjlUWoGsabPx3bp9OF5ehSe/3+Td1qJRku5+aSkJttMl9Htcv6B1faZWCNTUCgx5ZqFfmcRyVU1X2fU0EBIs2vHH9apzuxwaAamUlVRVh+5txWmJQquo8+4EWrrRKizsGVtskbT36XPz8MycPLy1tK56U28DL47z+7aJWjPOZzcOsdW/tLwaldW1KDpW7p3vkLFSaMMuWsLkvDNa+7UpTUiRVkk0GLni9dIvh8JOr4Rz4zARyQGpCtDeklPe/N1yHdbzemfins/XadaF/WHj/rDZkoON3QIpLy3K934Wai2y3IWShWkpviYYLcVeK9mX+s2rbXqDgMcSyXRt1UizPdiafbhgYc/oIoTw8xzZXHTcuyxPmsn/5+Xux+erCjXrwhYcPomhnVtonqf/4z/gjk/WaG6rDxxxULSi1yPzAfhPPBpVTDJiYu86TT1O9fDR0uzj4wjjT/eNllULuQYabolGhLgoWMDozTEEazJYD9bsmbDT+9EfcI6qJux36+oKM/+oKshcWmGcKEqtccocPVmFb2zmHXGbu8d1c7yvmxPJLR16ZijNLuoHtJawv/Ss9pg6vJNPmzrRl16qXz3s9jdjapDz6Dx/SV/N9mCbG9VzW2yzZ8JGaUU1sqbNRmlFtd9k0sET+vnU1bnLlfbnsT1bRrQZZ4jOW4cVurdu7No4lmwtNu+kgZHASIj33fbjnWdjcKfmGNixGWZMyfa2b1NFMyfpZH/Uw+lbiR7BNKe0SkvGsC6ee948Vd+xIBh8fP1g/H1snXLB3jhM2DjjH/N1tyl/fyO66gvI8qoa9Hh4nnd9cKfmPtkcI4U2kp91IIXJu7RshC9vHurWkByhHL16cjVBdW2dM+ps1crUCEoTHQAkxYfXLuM0VYEVFtw50rusNnsFkxFdW6Brq8b429iu3jZOl8BEPOkNPRqRlqDUCg5atsN9jwqnvHbFAKx8cKz3XSM+gB9cw6QEDOgQmjqiehjJq8Nllbhy8GnedaVwaZWmn3HULH97sLGS5O2/l/tVTLWE0qQYaHyAnYLh708d5F1u38wzAc6aPVNvsPK6LSBw48hOpv1CxYiuGchonOy1z8bZ+CXcf14Pv7Zwuyoanb/kZBUenNTT9jG3mAR0BZvINfoBtymKyDx0fi9Hx/j8xqF47YoBIXuzYGHP4EhZJY7rlPpzyk9b/CNmX9Dw0gkWPTPTDLfLNm55HsHOJNmNIzujkyLaNBIwG32lg0T46RpRtI0tRuO6QSA1i43o0lLb5RKw7hlz1zj/bJl2ad0kBRPOMC5k4yamwp6I2hPRYiLaTEQbiehvUvujRLSXiNZKfxMV+9xPRPlEtIWIxgfzApjAGfDEAvR59Afb+2nlapf52ydrfdZnLN2JvSXuFsD+6e5RutvMfrPqH7WVH/n401uhhzQZG2la51drjMvfNUryCOnbbJQ1/EPfNn5tTtIoOMXK/OzI7vYTtv2osNeridbAP8CaZl8N4C4hRE8AgwHcQkTye8uLQoh+0t8cAJC2XQbgdAATAPyPiOw57DJhxWjiVcncXP/EZ3ocOO5+3pQsA+3a6oSrnOjKimb/+pXZmHfH2dYGF2TsCt24OELB9Em2NNLxp3t895VvMWYxBdcN74ibRna2NTYtRvdoaclmn5aSiB1Pe/VM3DyqMz5Q2MXVPOTAnBUtmAp7IUSREGK1tHwCwGYAbQ12mQzgEyFEhRBiJ4B8AAPdGCzjLsdOVaGi2j88f3An37woe46c9EbORhp6KRrMZL0s2+VJSLtm02BUiLLD97cNd/2Y6jmVoV1a4Pf7R/t4rsjLKYnaouOh83uhUbI13U7P5XFsz1Z4++qz0L6ptfKFSpv39+v3GZp/AvG6knnnmrP82sxKTQLASw4nk93Cls2eiLIA9AcgV564lYjWE9HbRCTXMmsLYI9it0IYPxyYMNH3sR9w0f9+865nTZuNmb8V+PUb8exiDHp6YQhHZh09bwyt6M9hXeoeYuq6n+GeYLVLexfruA7q2AyAtsDKbNLAR0C2TW+AgumTsPyBsbqBaLLw7WpgGwf0I3RrpNw0vTVKBpqx58gpNG2o7zfvxl0epfE5vXlVXbyC3ptxqs2IZLexLOyJqBGALwHcIYQ4DuBVAJ0B9ANQBOAFuavG7n6PWiK6gYhyiCinuNhZIAnjnG2Sp8XGfb6+1f+YtTEcw3FMok7gT8Mk/4nEBIXLjSy/5PS/ekLg+hHBjeIMBKMso3aQg67s5P9q0iARt47u6tP2x/4enU42iZlNsOoVs1Gn4bBD4+QEpFp8s3CKlmKgDEB79A+na+53tgXtP5hYEvZElAiPoP9QCPEVAAghDgghaoQQtQDeRJ2pphCAslROOwB+sfBCiDeEENlCiOyMjPB+CLFIcWnwco87wUwL1EPrrXxsz5Z4WMMdTlkFSv7BJkuZD/Vs9r3bafvPy/t/fpO9jJdu4pYlSb72QLM9pjf0zCPEe4W9cX+9eRzZlVcvvYYR8fFkrNkH8Q1umuSSm9E4GZec2c5nW9v0Bq6nk7CLFW8cAjADwGYhxL8U7UqfoT8CyJWWZwG4jIiSiagjgK4AVrg3ZMYNjL54Rn7z/YMUPETkzJ6qtc9bU87yKxABAGWVdUFC8l7HpZJwejKgfVPjzI+h9E5R888/9XHlOHKErdF9//624XjtigGGx5Ft8LIZx+zhcUZbbfdYWaN/aFJPPGLRh13O0NmuaQOkN0zE+X0yNR/EWt/fyf38vY6ccOPZnbDj6YlIS0nEMxf19tlmN/VEMLAygmEArgQwWuVm+SwRbSCi9QDOAfB3ABBCbATwGYBNAOYBuEUIEfzaXowtWjXWj5w0ErqntzH2X7fCoxf0woWqH1gcEZo5yFGSoVP3VEuDG9WtpWK7578c6aun2evVVd15qMyvrbVBNGowOPO0puadLBAvmbeMhP0ZbZtY9gk/Q/qO9G9vPL42TbQfpLXSOFKTE3CtxehUeXK5b7t0EBFe/vMAnJXVzKdPzkNj0UfjTe2JC8+wdA4ziMj7oFMXjFGnrAgHVrxxlgohSAjRR+lmKYS4UgjRW2r/gxCiSLHPU0KIzkKI7kKIucG9BMYJRknJ9IT920t3ouRk4MFXU4ZmITXZ16ZeUV3ryMPFzmv5PEWNXHm/RtI4GupMniXreJ3IKGMH/jKog+WxuIHepdsVK3KQUdMAE4LJz4pBnZpj+QNjfNIua6FV/xUAaix+D/oqJnDJGySnzZJ7Ruk+uPXMRaMc+PDrYbVaWDAJ/wiYoCGEwKK8A5rBT0a/Jz0l5PHvN+H79UXaG21ARLhYZdOsrK7VtPEqPWiCid5Dw8yMfbKi7qX15lGB+5e7gd1H5l3juuH9qQP9NGG7KD25jHLuyOgJdavZLpVxFrKicEqnQLiTNMLPumQmA/yTzIUDFvZRRnVNLW7/eA027TuOV5dsx7Xv5uAJRZ1YGSNPCbVbYjDo38H3Fb9FoyTU1Aq/4tjn9vQtsBEIsouhFnoPuETJU2WgjiBUCqxQa29W71Oyib04MT4OI7oGrsUeVgVcDeroeVC/8mdtW79aB5FNHVZ81gHf5HVyLd+vdSKJzfLPTOrtb6IKdDJX77rDBQv7KGPHoTLMWrcPE1/6Bc/O2wIAmPn7LszLLUKZorjI+sJjeocIC/FxhFoh8CeVxq/8kVqN7NXjuhH6idi0BOel2e3RvFEyCqZPwmc6XjdWA4jcpGD6JM+CjixSm8OSwmRCaJqahILpkzCpT6amSadG9dok55dXpmA2QvnduELK6qlnSjMzmb94aT+seHCM3z5P/7G34wC2SX1Cl/fGCizsowy97/RNH6zGtK82eNeX79RPNzw3N3BTjV2ICEJ4XrevHprl0y5z7bCO+G3aaEfHv/+8HprauSwYSeOXcG4v/bcK2QunV6Z54I+ebdpNOiiCrNQvbZP7u+NtYkYPgyIu3Vt5Jm1lU9fAjs1QXeM70LvGdcODE3viAo2cPEr+fWk/AHXzLYDHx/+tq7LxmI6Pu555RyYpIQ4tVU4L8XGEPw/q4JPzvz7Dwj7KMHrz3H2kruqU0WTo6t0luttG92ipuy0QjpRVorSiGodKK5CSWKctKzWyuDhCG40i2B9ep58LRaZVWophGmOtj23fMf3EbfKErpXJxFJFXninWSO1JpCV9/rZi/Xty+eFKLOiUVKyW0d3wZc3D8V9E3rgzauy8f7UgX5BU8kJ8bj+7E5+DgK3j/EN3jq/TybuHtcN94yvy/NDRBjbq5WuKa2Rg8/9pMkDor7Bwj7qMJD2CsFkZQJN+xDByQkjuzJ+u3afz+u9cmJN71Vcfv0HgDeuPFP3HHYn6YwmCmWBVGthMvGEwnw2pJP2hLPaD1vtpy3nAFIH68go507BDLIAAB5KSURBVGDUIwpVJoi2Gg9imfg48rqKnturFZIT4i1PxGarXEwT4uNw6+iufh5dRlg1ZXXKqJv0VR5f+WCRuXxgB812La4ZlmWpXzBhYR9lGP2wjygKYzv10Q5iWVAvyrwvPpq9wcWdJgVR6b1yt0pLMfxstCbjurbUN0skeAOH7H0getegFkbqdXm/sxSTzMojpSrSQ6ifx6EoaD2sS3NcMeg0844K1MJezx1YmWbgkxsG2x8crJcenHVrnX1emcvmNI0gvWcu6o1bzrGWMtrouxQqWNhHGUZf6T1H6swSTos5Oy2IbQel0FAKLiOZNfOagbh9TFdN+/hzF/fBkM7NbQs9I/kgexPp+efroTeERJN6r17ThuLzUNqse2TWCZN+qijRUCj2fxrQznbFJav+9ACw4oEx+PLmoX4ZWa1iteyk8jNVmpMCVXL0ooVDSejKzjAhwaq72M/bIjf5nFJoLMqrq3hl5GqY1SIVd56rnYUxo7EnmMaugmv0WT5zUW9cMyzLtjlMT76ZuW2SV9YLRRvhg6mD8P6yAiQn1D10/tC3DVo1Tsalbyzz9gsWk/pkYvb6Ikdup2qFw+j+tkxLQcsAIpSdpOJQfm5OzZf5T52HgsMnDatjhQrW7KOI4+VVun7GMq8t2Q4AeOfXghCMKHDi4wj92ns0VacR57JA1hImsneIli+6kYxMSYzXDL03Q8scAAAX9PH1QFGfW09YDe/aAq9fme3XrpzIDmbuffnYTu6NOuulUVR3oITClKVFQnxcRAh6gDX7qMJKacHpc/NcqSQUKpQTl04LM8sapNbut47u6peq13u+IAiIjhrVtQZ0SEc7VcK1MT1bIS0lAcclTx5ZMFo1JyhTAARzmkWeS3fyWQWrxqwWgeamkYeqVaqxvsCaPeMKcnpbtyk8esorrALNJWXFnKFMtbxi5+HATqg5Bv+27q3T/K6tSYNEzL59hHf913zPWL5b55ctXJMmivsRTJlaG4Bm73TeyAlOFYVogoV9PWb5jsPImjYbBRoZGENF89QkbHlyQtBCw1ftOqpYc/aDlQWs2e99zcPn+nhjHCo1rrdqh/sm9ECvzDS0VmR6bCNNJv+hbxvNB5GWgDqh8Nm3SqVBYfhAkeW1k3kBdVCV1UnUYBMsxSXcsBkngjlwvBylFdW64ePfrPVoeb9uP2RYfDuYpCTGIzkh3kcMd2jW0CeAyy2cygLZVm8mkNRZH7cXlzo7oQY3j+rsnR8474zWmHBGa0zuV1etM2+/f6IsrdE6sWuv31NiOd+MXWQvIidmEqXb6gMTe0SMbXvtI+PCPYSgwMI+gpHrvnpzoahIkn5oVdXB09zMGCj5fSsF6ZmnNdUV9p0znD+UQq33bZVKN7rNq1f4B35pmVq0nk25e+1nT3QaQGeFJy48A+2aNsCo7vYjq5U2+xvOjux5pLQGHlHZKk07TXJ9gIV9PaZK0ozCWWJQjvRUCiYj7w+tdAdK1JWfOrZIDdjobJQmwYhQBsLIV9gzMw3T5c/Upcfb6J7BSXEBeIq7PDjJWjUpNS0b1x/BeU73lvjX//WNuORmdmCbfT1mzgZPwrJXFm8P2xjkPDZKsbS5SF8jNpuUO3bKtziK0uUwmP7iWgQrD5AW8gNySKfm6Bugq6kavaId4SZbSkx3ncVqVOGEiHDRgHY+8Qz1DRb29Ri5apS6xJ8dPphqnkTMCsrJxC0G5g8zd7uemZ5Iw2uHeQRAIAU1ZN95py8GoawbKrwTnYpGDWFvZ/Lwrauy8anD9AKhxEnAE2MfFvZRQEJ8nKWEXDJZ02Z7l4cHmCNexurP1UzwPj7Zk6L2ppGd0LRhok+6Y7s4qWmrxKzoh1WsJOHScmFs1rBu/PIEq53Sh2N7tcIgh+kFooV7xnc3TL0cS7Cwr8dcdlZ7AJ6MiP/7KT9o51ELXPm8SqxaWJSavVYmQNkdr2VaCtY8Mg7dFT9Uu5GgRcfKAQB7j+qnKjYiOdH5K/tfR3X2ZuDsoBM1q6QulqDug1SmIHj9yjPx0fWDcPc4a1kWGQ+3nNMF8+44O9zDiAh4grYekxAvuxQCz/+wNWjnaZPu682hLNwtY2RP3/T4eCzZUoybP1ztEwGqFU2qDqEH6kxEdmNwZBfQds2MJ4X1cKLZt01vgN5tm+DeCT0AeEwpfdqbF7/wPgT1iogTMLSzO29hkUboQqtiGxb2UUKz1CQcKXMvCEhJlSr4peRkFR6c2NNH6zZS7BsmJXiTWCknaLX20cqEKAfb2I24TEmMk87jzCbsRNj/qqqkNdag2pUdIiXgyE2i74oiG9NvMxG1J6LFRLSZiDYS0d+k9mZEtICItkn/m0rtREQvEVE+Ea0nosiquhtFyHKxvKomaIIe0M59f/3ZnXzyjJt5yshavFwrFAC+X+9f/vBsjcLX8gSeXWEve3uo3TmtEsoJWjPClcgrmLSV8gEp6xcwwcOKZl8N4C4hxGoiagxgFREtAHA1gIVCiOlENA3ANAD3ATgPQFfpbxCAV6X/jENOVlajYZL/rZJF39Nz8oJ6/gwL/tC5e40LmDeTik8r2bTPP0BIyzPj6Yt64+VF+bYLrjx6wem4emgWWjusAevWBK0bRGNul0m9M9HsuiQM6Rzbk8ihwvTbLIQoEkKslpZPANgMoC2AyQBmSt1mArhQWp4M4D3hYRmAdCKqv5EILiGEcJxqttcj83WOGciIrJNoISpJq/jGvRO64zmD2qhWldXOGY3w4qX9bGvaSQlx6NbKuSdGUnz99amuDxARhnZpEfL4iVjF1q+HiLIA9AewHEArIUQR4HkgAJAjUNoC2KPYrVBqUx/rBiLKIaKc4uLILaThFh3vn4O7PlsX8HFeX7IdP0gTpBVVdQWRz8pyVmbQCu2aNsDFOrVPZZR1YGW6t2qMS7L9PXdkjjtI6gUA/7msH2ZM8c/h7jaJCaETQt55BZ6tZIKEZWFPRI0AfAngDiGEUYIO7fxN6gYh3hBCZAshsjMygpOkKdL4yqSwiBHHpACqZ+bm4Yb3V/kdzzc7pDWmDDGvGdqjdWPExZGhhg5om1+ClcJ2cr+2GNPTnYlP7eN7gtQymzjz4nECK7dMsLEk7IkoER5B/6EQ4iup+YBsnpH+y/XjCgEo1bl2AKwl4Y5S7AQ86fHb9kM+6+8v2+V7DgensFLPU37FNnvV1hL2ai8eM+6T3BXDzX8u64+C6ZMcT+w6Qf74QlnQg4ktrHjjEIAZADYLIf6l2DQLwBRpeQqAbxXtV0leOYMBHJPNPbHKzsOB55tX1/h8+JvcgI95pgXTz+Yi/5c4rYhE2TWwqSKcv1xhZtIiSxVs9OeB1qNDo41mqZ5JcHWa5Wcu6o2+7cz99BnGDCveOMMAXAlgAxGtldoeADAdwGdENBXAbgCXSNvmAJgIIB/ASQDXuDriesjyHUcCPsb+4+V+2n2gNE4211wzNTxZtLR42TVQqZdWmKRevnNcd9z+8RrveiS5Ooaai/q3hRACF/b3nd66fGAHXB7DD0HGPUyFvRBiKfTjH8Zo9BcAbglwXFGFVlSomoMnypHRKNlrLlHb4P+7cBsOnnA3lXGDJHNvk/SG/vllxvVq7dcmW3mUJqvKamPNvqzCd4JWy6MnVoiLI8PJbIYJlNhVpUKIme03d+8xDHxqIT7PKfS2qQtnuCXo7SYH03IXvW10F782cqDZK/OZF0yf5GeqYhjGPfjXFQIqdDTcrGmzkTVtNj5cvhsAsKKgztwTjBzkfx/bDRdKpfCmnWdtMnScRri/VoBPqvSWoJxkNRP2IzSiZRmGCQ6cGycEmAm9j1d4hH2ipNl+tnIPdh1xPqk7Y0o2ps7M8WufOqIjGibG465x3ZCabH7rVz98LtIteqQkxMd5I2QfkiaP9R5yMpzHnGFCBwt7FymvqsHGfcf9wvorqqzViJWLNt/75fqAxqH0QR/ZLQNLtnqC1uLIo5VbEfRA4Pngza5blvWRlJaAYaIV/pW5yKOzNuJPr/6GXZKr5Wc5e5B/sNRUw5UJhqL77jVneZfdqmlqFbO5CiLCfRN6YNatw0M0IoaJXVizd5FNkk96yckqnNYcuPeL9UhOiMP1Izp5++wrOaVbdNvNHCEfXz8YLdOSfY7ptPC2Xc48rSlW7TqKszqalxS8eVTnEIyIYRgW9i6yvtCT+fFwWYU3VUBFda2PZp9g4F7oZhpbrUyCdo7fVueBZIUGUoUnKy6noeaFS/oikc1GTAzCwj4IrCw4iiGd6hKDKSdodxSXoWXjFM2UwMEOlQ+VEUf2l49EYf8nk4RuDBOtsIoTBI6dqsI9X9RluFSmDZCXH9JId/DubwX4dOVuW+d6aFJPy31DVQDjkQtOx9ndMnweeAzDhBfW7IPAR8t9BbZSs1+ytRiz1u7TzQh535cbbJ1rytAsPDl7s6W+ZgUwWqelYP9xT5FurefCm1dlW8rJ37FFKt67dqClMTEMExpY2IcApQviO78WAACSXIoWVdcm/UPfNo6PpXwWaAn7c12qp8owTOhhM04AlFVU47n5eag0CZoqq/Qv0lHpkj1bra2/eGk/x8dSeu6E2k2TYZjgwsI+AK6bmYNXFm/HN2uNi5L8ss3dbJVGaEWlWk0wdk4PZQFx14bEMEwEwMI+AH7fcRgAsGZ3ScjPTQTT6lEyP/x9JF68tK9pv39ccDoW3TUSDZPiMS1CCokwDOMObLN3gd0B5LExY94dIzDh37/4tV8x6DTLKXE7tkhFxxaputu/u3U45m/cj8T4OHTKaIRNj09wPF6GYSIT1uxdoE2TBkGrt9o8VTv75Ucr7LloGtG7XRPcPb67a8djGCbyYGHvAkO7NMftn6wx7+gAoarV3q99OoDgFfNmGCY6YWHvAmUVNZi9PjhldlMSfatJrd0T+vkBhmHqPyzsXeDRWRuDduyGiealA7+8eUjQzs8wTHTAwl6DaV+uxyWv/Wa5f3UQTSpWSvWVW8yXzzBM7MLeOBp8snKP4facgiO4+LXfvetxBITThB6MEoYMw0QXpmojEb1NRAeJKFfR9igR7SWitdLfRMW2+4kon4i2ENH4YA08nCgFPRCe8nqt0uoEfLdWjUJ+foZh6hdWNPt3AbwM4D1V+4tCiOeVDUTUC8BlAE4H0AbAj0TUTQhhrVRThPPIt7nomZnm1x7kzMSa3DWuzlXSzaInDMNEJ6bCXgjxMxFlWTzeZACfCCEqAOwkonwAAwH8brxbZLLrcBlOa14XjPTe77s0+wXTZq9HUUl5yM/JMEz9JZAJ2luJaL1k5pErbLcFoDR4F0ptfhDRDUSUQ0Q5xcXFAQwjeIx87iesL4xMV8fOLfUjYhmGYdQ4FfavAugMoB+AIgAvSO1a9gRNtVcI8YYQIlsIkZ2RkaHVJSLYfeSkX1v/Duk+6/dOCH30aeHRUz7rvds24XquDMPo4kjYCyEOCCFqhBC1AN6Ex1QDeDR5ZcKWdgD2BTbEyEOd+OyLnEJHx9kcQA6aU5W+0yDf3TYc93HyMoZhdHAk7IkoU7H6RwCyp84sAJcRUTIRdQTQFcCKwIYYXuS87ifKq3T77DjkLBFag6S6gKl5d4zwLmc09njaZDVvqLuv3IdhGMYKphO0RPQxgFEAWhBRIYB/ABhFRP3gMdEUALgRAIQQG4noMwCbAFQDuKW+e+I8Oz8Pk/pk4vI3l7l63LvHdfNZ79G6zstn5YNjTfcf2rm5q+NhGCa6seKNc7lG8wyD/k8BeCqQQUUSuw6fRL/Hf0DJSX3N3gm3ju7q1/bhdYOQf7DUrz37tKbI2XUUo3u0xKK8gwCAZAtpFBiGYWQ4XYIF3Bb0rdNSNNuHdWmBKUOz/Npfv/JMNE9Nwp3n1r0NWK0+xTAMA3C6BC+HSyuwcd9xnN0t+J5BN43s5F3u2z4dI7q0MOzfvFEyVj18rk9bYhw/pxmGsQ4Le4m/vLUceftPIPcxdzI8/HjnSGQ2ScGO4jJc8PJSn23tm9VNvH57yzBHx09MYGHPMIx1WGJIbDlwAgDw1OzNrhyvY4tUpCYnoHe7Jt422bumVxv/lAt2SWFhzzCMDVizB5C3/7g3v82+klPGnS2ilRxt0V2jcOxUFZqmJjk+7tpHzsX+4+WWUh8zDMPIsLAH8MmKugwPp6qC5ykaF0cBCXoASG+YhPSGgR2DYZjYI+aF/UPfbMAHy+qKd6/YeSSMo2EYhgkOMW8LUAp6hmGYaCXmhT3DMEwsENPCvromsNqt7107EL/ce45f+9y/jdDozTAMEz5i2mb/yKyNAe2vF4ClVc2KYRgmnMS0Zj9nQ5HjfXu3rfOfb8kZKBmGiXBiWrMPpHbsjKuzvctL7jkHOw6VYtJLS/GPC3r59f3qr0NRXROGQrUMwzASMS3sA6Fl47pkZg2S4nF6myYomD5Js++ADk012xmGYUJFTJtxGIZhYoWYFvbCoR1nbM+WLo+EYRgmuMS0sHfCiK4t8MaV2eYdGYZhIoiYFvZ6ev3401vp7pPVPBVxGknOGIZhIpmYFvYnyqs12+dvPKC7zxCu/cowTD0k5oR9Ta3A/mPleOTbXL9tZlWqLj6zHSb2zgzW0BiGYYJGzLle/nNeHt74eYfmtkbJxkW8OygqTDEMw9QnTDV7InqbiA4SUa6irRkRLSCibdL/plI7EdFLRJRPROuJaEAwB2+XlQVHdAU9ACSZFATp3yHd7SExDMOEBCtmnHcBTFC1TQOwUAjRFcBCaR0AzgPQVfq7AcCr7gzTHS557XfD7ftKyr3Lc24fgXeuPguXD+zgbRtuUhicYRgmUjEV9kKInwGoK3pMBjBTWp4J4EJF+3vCwzIA6URUb4zcKwrqLrNXmzSc06MlhnWpm5AlYi8chmHqJ04naFsJIYoAQPovRxm1BbBH0a9QavODiG4gohwiyikuLnY4DPdY8cAYzfZmXAKQYZgowG1vHC3VV9OdXQjxhhAiWwiRnZFh7AUTCL9tP4SPlu9GZbVx7vqWaSma7a2baLczDMPUJ5wK+wOyeUb6f1BqLwTQXtGvHYB9zocXOH9+czke+HoDKi0UKpHTFr91VV2EbAanL2YYJgpwKuxnAZgiLU8B8K2i/SrJK2cwgGOyuSfcHCmt1N3WOSMVABAvRcY2Ta0z3TROSQzuwBiGYUKAFdfLjwH8DqA7ERUS0VQA0wGcS0TbAJwrrQPAHAA7AOQDeBPAX4MyagekJOlfavfWjQEAXVs2AgA0aeAv4FulsYbPMEz9xTSoSghxuc4mvxlN4UkjeUuggwoGRsVD+rbz+M8/ceEZmNyvLbpIQl9GL089wzBMfSGq0yUcKq3wLg+dvki33/UjOgEAUhLjMbwr+9IzDBN9RLWwv+Kt5Zb6cRZLhmGinagW9nn7T4R7CAzDMBFBVAt7K2x8bHy4h8AwDBN0olbYV1vwq7+wXxukJsdc4k+GYWKQqBX2XR6ca9qndzvOYskwTGwQtcLeCuVVNeEeAsMwTEiIaWE/4YzW4R4CwzBMSIhpYS/046wYhmGiipgS9lufPM9nPS2FJ2cZhokNokra1dQKfLJyN/4vu71Pe3JCHH6+9xwkJcThgYk90CApAWN6tNRNa8wwDBNtRJWw/2LVHjz4dS5KTlZ52+4/rwduHNnZu37D2Z21dmUYholqosqMU1rh8a5Zs7sEAHDjyE4+gp5hGCZWiSphXyUFUv24+QAAYN2eknAOh2EYJmKIKmE/fW6ez3r+wbIwjYRhGCayiCphr0aZ4phhGCaWiWphzzAMw3iIamGf89DYcA+BYRgmIohqYd+iEdeNZRiGAaJY2PeQiogzDMMwUSzs371mYLiHwDAMEzEEFEFLRAUATgCoAVAthMgmomYAPgWQBaAAwP8JIY4GNkxz5HTF7Zs1wPSL+qB1E06FwDAMI+OGZn+OEKKfECJbWp8GYKEQoiuAhdJ60Bn+z0UAgPQGSRjWpUUoTskwDFNvCIYZZzKAmdLyTAAXBuEcfhwqrQQAbNh7LBSnYxiGqVcEKuwFgB+IaBUR3SC1tRJCFAGA9L9lgOewxcTeXJCEYRhGTaBZL4cJIfYRUUsAC4goz3QPCenhcAMAdOjQIcBh1PHipf1cOxbDMEy0EJBmL4TYJ/0/COBrAAMBHCCiTACQ/h/U2fcNIUS2ECI7IyMjkGEAAAZ08BQPT06ID/hYDMMw0YZjYU9EqUTUWF4GMA5ALoBZAKZI3aYA+DbQQVqhY4tGaM3FSBiGYTQJxIzTCsDXRCQf5yMhxDwiWgngMyKaCmA3gEsCH6YxczYU4cvVhcE+DcMwTL3FsbAXQuwA0Fej/TCAMYEMyi5//XB1KE/HMAxT74jaCFqGYRimDhb2DMMwMUC9F/alFdXhHgLDMEzEU++F/Wcr94R7CAzDMBFPvRf2S7YWe5ffuirboCfDMEzsEmgEbdhp3igJAPDtLcPQt316mEfDMAwTmdRrzf5kZTW+Wr0XANC+WcMwj4ZhGCZyqdfC/pFvN3qXGyXX+5cUhmGYoFGvhf1pCm0+KaFeXwrDMExQqdfq8G1juiI1OQF7S06FeygMwzARTb0W9gBw7fCO4R4CwzBMxMO2D4ZhmBiAhT3DMEwMwMKeYRgmBmBhzzAMEwOwsGcYhokBWNgzDMPEACzsGYZhYgAW9gzDMDEACSHCPQYQUTGAXQ53bwHgkIvDqQ/wNccGfM2xQSDXfJoQIsNKx4gQ9oFARDlCiJhKZM/XHBvwNccGobpmNuMwDMPEACzsGYZhYoBoEPZvhHsAYYCvOTbga44NQnLN9d5mzzAMw5gTDZo9wzAMYwILe4ZhmBigXgt7IppARFuIKJ+IpoV7PHYgovZEtJiINhPRRiL6m9TejIgWENE26X9TqZ2I6CXpWtcT0QDFsaZI/bcR0RRF+5lEtEHa5yUiotBfqT9EFE9Ea4joe2m9IxEtl8b/KRElSe3J0nq+tD1LcYz7pfYtRDRe0R5x3wkiSieiL4goT7rfQ6L9PhPR36XvdS4RfUxEKdF2n4nobSI6SES5irag31e9c5gihKiXfwDiAWwH0AlAEoB1AHqFe1w2xp8JYIC03BjAVgC9ADwLYJrUPg3AP6XliQDmAiAAgwEsl9qbAdgh/W8qLTeVtq0AMETaZy6A88J93dK47gTwEYDvpfXPAFwmLb8G4GZp+a8AXpOWLwPwqbTcS7rfyQA6St+D+Ej9TgCYCeA6aTkJQHo032cAbQHsBNBAcX+vjrb7DOBsAAMA5Cragn5f9c5hOt5w/xAC+KCHAJivWL8fwP3hHlcA1/MtgHMBbAGQKbVlAtgiLb8O4HJF/y3S9ssBvK5of11qywSQp2j36RfG62wHYCGA0QC+l77IhwAkqO8rgPkAhkjLCVI/Ut9ruV8kficApEmCj1TtUXuf4RH2eyQBliDd5/HReJ8BZMFX2Af9vuqdw+yvPptx5C+UTKHUVu+QXlv7A1gOoJUQoggApP8tpW5612vUXqjRHm7+DeBeALXSenMAJUKIamldOU7vtUnbj0n97X4W4aQTgGIA70imq7eIKBVRfJ+FEHsBPA9gN4AieO7bKkT3fZYJxX3VO4ch9VnYa9kl650fKRE1AvAlgDuEEMeNumq0CQftYYOIzgdwUAixStms0VWYbKs31wyPpjoAwKtCiP4AyuB59daj3l+zZEOeDI/ppQ2AVADnaXSNpvtsRtivsT4L+0IA7RXr7QDsC9NYHEFEifAI+g+FEF9JzQeIKFPangngoNSud71G7e002sPJMAB/IKICAJ/AY8r5N4B0IkqQ+ijH6b02aXsTAEdg/7MIJ4UACoUQy6X1L+AR/tF8n8cC2CmEKBZCVAH4CsBQRPd9lgnFfdU7hyH1WdivBNBVmuFPgmdiZ1aYx2QZaWZ9BoDNQoh/KTbNAiDPyE+Bx5Yvt18lzeoPBnBMeoWbD2AcETWVNKpx8NgziwCcIKLB0rmuUhwrLAgh7hdCtBNCZMFzvxYJIf4CYDGAi6Vu6muWP4uLpf5Car9M8uLoCKArPJNZEfedEELsB7CHiLpLTWMAbEIU32d4zDeDiaihNCb5mqP2PisIxX3VO4cx4ZzIcWFyZCI8XizbATwY7vHYHPtweF7L1gNYK/1NhMdWuRDANul/M6k/AXhFutYNALIVx7oWQL70d42iPRtArrTPy1BNEob5+kehzhunEzw/4nwAnwNIltpTpPV8aXsnxf4PSte1BQrvk0j8TgDoByBHutffwON1EdX3GcBjAPKkcb0Pj0dNVN1nAB/DMydRBY8mPjUU91XvHGZ/nC6BYRgmBqjPZhyGYRjGIizsGYZhYgAW9gzDMDEAC3uGYZgYgIU9wzBMDMDCnmEYJgZgYc8wDBMD/D9pwksMstgtRgAAAABJRU5ErkJggg==\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)"
]
}
]
}
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