multi_armed_bandit.ipynb

{"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"name":"python","version":"3.7.6","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"markdown","source":"This script is a simple approach to building multi armed bandit. The problem was inspired by the 2020 Christmas Kaggle competition where two teams of elfs would have to collect as many candy canes as possible from vending machines. The team with the most candy win.","metadata":{}},{"cell_type":"markdown","source":"### Prerequisites and Imports","metadata":{"_uuid":"d629ff2d2480ee46fbb7e2d37f6b5fab8052498a","_cell_guid":"79c7e3d0-c299-4dcb-8224-4455121ee9b0"}},{"cell_type":"code","source":"# import the necessary libraries\nimport numpy as np\nimport matplotlib.pyplot as plt\n%matplotlib inline\n\n# define function to visualise agent/elf's interaction with the machines\ndef plot_history(history):\n    rewards = history['rewards']\n    avg_rewards = history['avg_rewards']\n    chosen_machines = history['machines']\n    \n    fig = plt.figure(figsize=[20,6])\n    \n    line = fig.add_subplot(1,2,1)\n    line.plot(avg_rewards, color='C3', label='avg rewards')\n    line.set_title('Average Rewards')\n    \n    bchart = fig.add_subplot(1,2,2)\n    bchart.bar([i for i in range(len(chosen_machines))], chosen_machines, color='C3', label='chosen machines')\n    bchart.set_title('Chosen Actions')","metadata":{"trusted":true},"execution_count":3,"outputs":[]},{"cell_type":"markdown","source":"### Create the environment","metadata":{}},{"cell_type":"code","source":"# create a class for the environment that contains the probability to get a reward and the actual rewards\nclass Env(object):\n    def __init__(self, prob_reward, rewards):\n        if len(prob_reward) != len(rewards): \n            raise Exception(f'size of reward probability: {len(prob_reward)} does not does match size of rewards: {len(rewards)}')\n        \n        # pass arguments to the environment\n        self.prob_reward = prob_reward\n        self.rewards = rewards\n        self.k_machines = len(rewards)\n        \n    # define function to specify the machine the elf is going to use \n    def choose_machine(self, machine):\n        if machine < 0 or machine > self.k_machines:\n            raise Exception(f'machine must be a value between 0 and {self.k_machines -1}') # -1 because 0 counts as a number\n        return self.rewards[machine] if np.random.random() < self.prob_reward[machine] else 0.0","metadata":{"trusted":true},"execution_count":4,"outputs":[]},{"cell_type":"code","source":"# create environment\nenvironment = Env(prob_reward=[0.01, 0.05, 0.20, 0.50, 0.65, 0.90], \n                  rewards=[1.0, 1.0, 1.0, 1.0, 1.0, 1.0])\n\n# print the reward probabilities\nprint(f'Reward Probabilities: {environment.prob_reward}')\nprint(f'Reward: {environment.rewards}')","metadata":{"trusted":true},"execution_count":5,"outputs":[{"name":"stdout","text":"Reward Probabilities: [0.01, 0.05, 0.2, 0.5, 0.65, 0.9]\nReward: [1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n","output_type":"stream"}]},{"cell_type":"code","source":"# use a machine\n[environment.choose_machine(0) for _ in range(10)]","metadata":{"trusted":true},"execution_count":6,"outputs":[{"execution_count":6,"output_type":"execute_result","data":{"text/plain":"[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]"},"metadata":{}}]},{"cell_type":"markdown","source":"### Create a base line agent","metadata":{}},{"cell_type":"code","source":"# create random agent\nclass RandomAgent(object):\n    def __init__(self, env, max_iterations=2000):\n        self.env = env \n        self.iterations = max_iterations \n        \n    # let the agent take actions in the environment\n    def action(self):\n        # keep track of the rewards the agent generates and which machine it is using\n        machine_counts = np.zeros(self.env.k_machines)\n        \n        # store the reward the agent is generating\n        rewards= []\n        # store reward the agent is generating over time\n        avg_rewards = []\n        \n        for i in range(1, self.iterations+1):\n            machine = np.random.choice(self.env.k_machines)\n            reward = self.env.choose_machine(machine)\n            \n            # increasing the machine count to know how many time the machine has been used\n            machine_counts[machine] += 1 \n            \n            # append the results to the list rewards and avg_rewards\n            rewards.append(reward)\n            avg_rewards.append(sum(rewards)/len(rewards))\n            \n        # create a dictionary with the results to use our plotting function\n        return {'machines': machine_counts,\n                'rewards': rewards,\n                'avg_rewards': avg_rewards\n               }","metadata":{"trusted":true},"execution_count":7,"outputs":[]},{"cell_type":"code","source":"# create the instance\nrandom_agent = RandomAgent(env=environment, max_iterations=2000)\n\n# action the agent is taking\nra_history= random_agent.action()\n\n# print\nprint(f'total reward : {sum(ra_history[\"rewards\"])}')","metadata":{"trusted":true},"execution_count":8,"outputs":[{"name":"stdout","text":"total reward : 769.0\n","output_type":"stream"}]},{"cell_type":"code","source":"# plot the history\nplot_history(ra_history)","metadata":{"trusted":true},"execution_count":9,"outputs":[{"output_type":"display_data","data":{"text/plain":"<Figure size 1440x432 with 2 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kiRJ2qoAQyDjH0mSJEmSpLYKLwRyTiBJkiRJkqR2DIEkSZIkSZL6AEMgSZIkSZKkPqBLIVBEnBYRcyNiXkRcvY02x0XEzIiYHRGPdG+ZO8EwSJIkSZIkqUXJ9hpERDHwA+BkYDHwdERMSym9kNNmMHAjcFpK6bWIGN5TBW+X4Y8kSZIkSVI72w2BgCOAeSml+QARcSdwFvBCTpsLgd+mlF4DSCm90d2FdpUZkCRJUn7MmTwl3yXk1ZQX5+S7BEmSOtWV4WCjgEU5+4uzx3LtCwyJiIcj4pmIuLijC0XEpRExIyJmrFixYucq3i5TIEmSJEmSpLa6EgJFB8faJi0lwOHAO4FTgS9HxL7tTkrp5pTS1JTS1Orq6h0utkvsCiRJkiRJktROV4aDLQbG5OyPBpZ00GZlSmkTsCkiHgUOBl7qlip3hmGQJEmSJElSi670BHoamBQREyKiDDgfmNamze+BYyKiJCL6A0cC+RkUbfgjSZIkSZLUznZ7AqWUGiLiCmA6UAzcllKaHRGXZV+/KaU0JyLuB2YBTcCtKaXne7LwTgrOy9tKkiRJkiTtzroyHIyU0r3AvW2O3dRm/5vAN7uvtJ1kCCRJkiRJktROV4aD9SrJEEiSJEmSJKmdgguBWhgGSZIkSZIktejScLBexexHkiRJ6lPmTJ6S7xLyasqL+VmTR1LvU4A9gUyBJEmSJEmS2iq8EMhhYJIkSZIkSe0YAkmSJEmSJPUBhRcCNTMMkiRJkiRJalF4IZDhjyRJkiRJUjsFFwIlQyBJkiRJkqR2Ci4EcnEwSZIkSZKk9govBDIFkiRJkiRJaqcAQ6Ash4VJkiRJkiS1KLwQyPBHkiRJkiSpHUMgSZIkSZKkPsAQSJIkSZIkqQ8ouBDIJeIlSVJvFREVEfFURDwXEbMj4qvZ40Mj4oGIeDn755Ccc74QEfMiYm5EnJq/6iVJ0u6u4EKgZkZBkiSpF6oFTkgpHQwcApwWEUcBVwMPpZQmAQ9l94mI/YHzgQOA04AbI6I4L5VLkqTdXuGFQKY/kiSpl0oZG7O7pdmfBJwF3J49fjtwdnb7LODOlFJtSmkBMA84YheWLEmSepGSfBfQ7RwOJkmSerFsT55ngH2AH6SU/hYRI1JKSwFSSksjYni2+SjgyZzTF2ePtb3mpcClAGPHju3J8iWpT5kzeUq+S8irKS/OyXcJ2kGF1xPIrkCSJKkXSyk1ppQOAUYDR0TEgZ00j44u0cE1b04pTU0pTa2uru6uUiVJUi9TgCFQlj2CJElSL5ZSWgs8TGaun+URMRIg++cb2WaLgTE5p40GluzCMiVJUi9SeCGQ4Y8kSeqlIqI6IgZnt/sBJwEvAtOAD2WbfQj4fXZ7GnB+RJRHxARgEvDUrq1akiT1Fs4JJEmStPsYCdyenReoCLgrpXRPRPwVuCsi/gV4DXgfQEppdkTcBbwANACXp5Qa81S7JEnazRkCSZIk7SZSSrOAQzs4vgo4cRvnXAdc18OlSZKkAlBww8GSIZAkSZIkSVI7BRcCtTAMkiRJkiRJalF4IZDZjyRJkiRJUjuFFwKZAkmSJEmSJLVTeCGQw8AkSZIkSZLaMQSSJEmSJEnqAwovBGpmGCRJkiRJktSi8EIgwx9JkiRJkqR2Ci4ESoZAkiRJkiRJ7RRcCOTiYJIkSZIkSe0VYAhkCiRJkiRJktRWl0KgiDgtIuZGxLyIuLqD14+LiHURMTP785XuL3UHGQZJkiRJkiS1KNleg4goBn4AnAwsBp6OiGkppRfaNP1LSuldPVDjDjL8kSRJkiRJaqsrPYGOAOallOanlOqAO4GzerasN8EeQJIkSZIkSe10JQQaBSzK2V+cPdbW0RHxXETcFxEHdEt1O6M5BDIMkiRJkiRJarHd4WBAdHCsbcLyLDAupbQxIs4A/heY1O5CEZcClwKMHTt2B0uVJEmSJEnSzupKT6DFwJic/dHAktwGKaX1KaWN2e17gdKIGNb2Qimlm1NKU1NKU6urq99E2ZIkSZIkSdoRXQmBngYmRcSEiCgDzgem5TaIiD0jIrLbR2Svu6q7i5UkSZIkSdLO2e5wsJRSQ0RcAUwHioHbUkqzI+Ky7Os3AecCH4+IBqAGOD+l/EzKk6e3lSRJkiRJ2q11ZU6g5iFe97Y5dlPO9veB73dvaZIkSZIkSeouXRkOJkmSJEmSpF7OEEiSJEmSJKkPKLwQyCmBJEmSJEmS2im8EEiSJEmSJEntGAJJkiRJkiT1AYUXArlEvCRJkiRJUjuFFwJJkiRJkiSpHUMgSZIkSZKkPqCgQ6CUEjX/+Ee+y5AkSZIkScq7AgyBts4JtH7aNBa+7zzW3z89j/VIkiRJkiTlXwGGQFvVzl8AQN2C+XmuRJIkSZIkKb8KOgSiKIDMsDBJkiRJkqS+rKBDoIjs7TUZAkmSJEmSpL6t8EKg3F4/Rc0hUFN+apEkSZIkSdpNFF4IlGPl978PQEqGQJIkafcXEWMi4s8RMSciZkfEp7LHr42I1yNiZvbnjJxzvhAR8yJibkScmr/qJUnS7q4k3wXsEs4JJEmSeocG4DMppWcjogp4JiIeyL72nZTSf+c2joj9gfOBA4C9gAcjYt+UUuMurVqSJPUKBd0TqIVzAkmSpF4gpbQ0pfRsdnsDMAcY1ckpZwF3ppRqU0oLgHnAET1fqSRJ6o0KLwTqqNePw8EkSVIvExHjgUOBv2UPXRERsyLitogYkj02CliUc9piOgiNIuLSiJgRETNWrFjRg1VLkqTdWeGFQB1IjYZAkiSp94iISuA3wJUppfXAD4GJwCHAUuBbzU07OL3dN2IppZtTSlNTSlOrq6t7qGpJkrS76xMhkKuDSZKk3iIiSskEQL9IKf0WIKW0PKXUmDKrXdzC1iFfi4ExOaePBpbsynolSVLv0TdCICeGliRJvUBEBPBjYE5K6ds5x0fmNDsHeD67PQ04PyLKI2ICMAl4alfVK0mSepeCWx0sdRD4uES8JEnqJd4GXAT8IyJmZo99EbggIg4hM9RrIfAxgJTS7Ii4C3iBzMpil7symCRJ2paCC4E65OpgkiSpF0gpPUbH8/zc28k51wHX9VhRkiSpYPSN4WDOCSRJkiRJkvq4wguBOpz/x55AkiRJkiSpbyu8EKgDyZ5AkiRJkiSpj+sTIRCNhkCSJEmSJKlv6xMhkKuDSZIkSZKkvq7wQqCOpv+xJ5AkSZIkSerjCi8E6sC63/2O+iVL8l2GJEmSJElS3vSJEAig5h/P57sESZIkSZKkvOkzIdDrn/oUG/7053yXIUmSJEmSlBcFGAJ1NClQxvr779uFdUiSJEmSJO0+CjAE6kRDY74rkCRJkiRJyos+FQKlJlcJkyRJkiRJfVOfCoFobMh3BZIkSZIkSXnRpRAoIk6LiLkRMS8iru6k3T9FRGNEnNt9Je6gtO05gVKjPYEkSZIkSVLftN0QKCKKgR8ApwP7AxdExP7baHc9ML27i+wuyZ5AkiRJkiSpjyrpQpsjgHkppfkAEXEncBbwQpt2nwR+A/xTt1bYnewJJBWclBIRQe2CBSy79qtESQl7fPSjDDjqyHZta19+mVU/+Qk0NFJ54gkMOPJIGteupWzcuHZtm+rqqFu4kOKqKtbfdz9RWsrg895HUXn5LrgrSZIkSep+XQmBRgGLcvYXA61+u4qIUcA5wAl0EgJFxKXApQBjx47d0Vq7ptPhYPYEknaFutdeY+3dd5Pq6qh5bhYNK1cy4uqraNywkf6HH0ZRZSUlQ4du9zqpvh5KSogIAOqXLcucV1rKim99i1W3/rjD8zY9/jjlk/ah32GHs2X2bKK4mMrjjmXFDd9rabPu979v2S4dNYrB7zuXge86k4YVb7D+vvtY89Oftbvu8uuuo3jwYFJKDDnvfVSddBINK1dCUREDjjqKon79dvSjkiRJkqRdpishUHRwrG3S8l3gqpRSY/Mvax1JKd0M3AwwderUbac1PSTV1e/qt5TaWfub37D0mi8BUDRwIBN++xvKRo/Oc1XblxobWXv33Wz8y2MMOPpohlx4AVHUfkTp+gce4PVP/mu744uv+GSr/eFXXUXFlCmUVA+jbMwYKC1l06OPsvLGH1Lz3HOt2paOGkX96693Wl/078/Ir/0HZWPHsfauu1h7993Uvjyv5fWa556jqKqKqlNOpurEk9gw/X62vDgXmhqpfXkeK757Ayu+e0Ora1YccAAUFzPgyCMpmzCBlT/8IfWLMpn4qltuZdUtt7Zq3++wwxj2iU/Q75CDWX3bbQAM/fCHKa6q6rT2jjSuX09TzRY2P/UUVSccT9GAATt8DUmSJEnK1ZUQaDEwJmd/NLCkTZupwJ3ZAGgYcEZENKSU/rdbquwmTTWb812C+rja+QtaAiCApvXreeWkkymfPJnaF18EoGzcOEbf+APKJ07MV5kANK5bx7rfT2PLnDmk2lpqFy6g9oU5AGx86CGW/+d/MuwTn2DIhRdQMmwYjevWsfC891P36qsAjLjmGrbMfZGBJ2fub9Utt7Lpsccoqqpiy+zZvHH99V2upSUAKi4myspINTUM+eAHGXHNF+koeO73lgMZdsUVbJg+nX6HHkrZmNFs+PPDVJ18EsWVlQBUnXB8S/tUV8eaO3/FxocfpnHDBga/970Mfv957a49+D3nkBoboaiIjX9+mPX330eqryci2PLSS9Q8+yyLPvKRVuesvPGHAJTvP4Wq446ndOwYGpYtp+6116h59lmKBg6kdMRwqk46iU1P/JVNTz9Fw5Klra4R/fpRNno0FftPIcrKKRs/ns1PP83mZ5+lYt99GXjWu6k66SRKhgxp91mkhgbqly2nbPSoVsdqX5lP0YD+1C18lX5vOZDiQYO6/PchSZIkqXeK1MnwKYCIKAFeAk4EXgeeBi5MKc3eRvufAPeklH7d2XWnTp2aZsyYsTM1d2rDgw+263HQrGzCBCbed2+3v6cKy/r7p1P70lyGXXFFhz1dtiU1NVH70ks0rlvPgCOPaPXalrlzWXDW2S37Ex98kLLRo6iZOZOF51+wzWuW7DWSYR//OP0OOhhIlAwdyryTTqb/1KmM/t4NPdY7pGnzZhac856WQKdZlJYy6ns3sOHBB1n3m992eG7xsGHs/b+/o2TYsG1eP6XE2jvvZN0f7qFpwwZqX34ZgJLhw9nrG9dTMWVKq1CifulSKCqidMQImurqiAiitLQb7rR7Na5bx5o77mDDQ3+i/2GHUnXyybzx7e9Q8+yz2zynaOBAmtavb3e8fMoUiisr6X/EEWz66187vkZRETRtnessysooGT6c8sn7UVw1kNp589jyj38AULbPRPodcCBFAwey6a9PUDfvla2X6d+fQWefRVHVQIoHDaJxzRrKJu5N5THHUL9oEW/ccAM1z/6d/ocfzuD3nUvDG29QeeKJvaIHWz40bd4MJSUUlZV13zU3bWLjE09Q+/LLlI8fT+P69ZTsuScDjjqKKC/vMAzdHUTEMymlqfmuQ6311DMYwJzJU3rkur3FlBfn7PS5fnY7/9mBn5+f387zs3tz/Px23pv97DrT2TPYdnsCpZQaIuIKMqt+FQO3pZRmR8Rl2ddv6tZq36TOQq3SkXvuwkrUG62f/kdev/JKIPPf0vBPfSozQfCChVTst29Lu6aaGjb+5S+UjR3Lyh/9iMbVa9j8t7+1ulaUlTH+13fTuHoNr11yScvxPb/2Hy29Mvodcgj7PfsMGx9+mNIxYygZPpyaZ55h6Ze+TNPmzTQsWcqyL3+lXZ2bHn+cl446mhFf+hJD3n9el++veRLl5u2mTZtYc8cd9J86lf6HHgpA/fLlzDv2OADK99uP8okTqTjgAIqHDGHQOWcTEVQdfzwjr72WlTf9iDV33EHj6tUAjPz61xl8ztkdvnerzyaCIRdcwJALth2A5SodObJluzt/se5uxYMGMeyyyxh22WUtx8b/8hdAJhhYP/2Pmd4/VVUUV1Uy6KyzKKqspGnDBtY/8AAle+zBwDPOIIqLW123+pNXkBobqX35ZWpfnkeq3ULxHntQdfzxNG7cxOan/saaO+5k89NPU794MfWLF2+taehQ+h10EBsffrgl+ImKCiqPO46iAQMoqqqkftFi1vzyjnb3ExUVpLo6aGuzdcAAACAASURBVGqiaOBAap57jk1PPAHA8m98k8p3vIOKtxxI1XHHUbF/u0Uje73U1AQRkBKpvp6mDRtIdXVEeTkNK1ZQvs8+REkJKSU2/eUv1Mx8jtqXX2Ljw49QVJn5+y2bMIGifhU0rFhJVJRTPHgw5fvsQ9GAAWx86CHqly2ncc0a+h18EP2nTqV0r71oXLuWokGD2fKPWWx44AE2PvwI9UvadsDNUVxMv7e8hdKxY0j19RSVV9Dv0EMprqqk4sADKeupOfgkSZLU62y3J1BP6alvobY1HwlAv8MPZ/wvft7t76nCsGXOHBac8x4A+h9xBJufeqrV68XDhjHyP79Gw7JlLLv2qzt8/TE/uonKY4/tcvum2lo2Pvooa3/9azY98ijRrx+ppoY9/+OrlAwd2qrHW7/DDqP/4Yezfvp0Kt/xDoZ/9jMUVVQAmbBn6RevYd3vftfp+w3//OdJDQ2s+Pa3M/tXXcUeH75kh+9T+Ve//A3ql7xO6ahRlA4fDmT+O6ibP5+6V1+jfN99Ww0PA9gy9yUaVq6gdu5LpMYGisor2JztfVT9ySsonziRps2bWfub3xIV5dTOfYk1d94JDZkJ96OigsHnnkuqraWoqorSkSPpd9BbKB01ioZVq6jYb79d+yF0om7hQmqen836+++jbuFCyifsTfSrINXWUTJiOBv//HBmTqZ164BMD7hU335OuZIRIyjeYyh1L89r9XrVKaeQmhrZ+Kc/t+qptbPKJk6kYv/96f9PUxnw1rey5YUXKB44iIZVK6n5+0waV6+m5rnnWoZNRllZJrzLUdS/P2X77EP/Qw+l6tRTKN9335ahkampaYd6Pe4IewLtnuwJ1HPsCbTz7E3w5vj57Tw/uzfHz2/n5asnUJ8KgSoOOIAJv+l0lJr6qJQS8888k7p5rzDmllsYcOQRLLzwA2x5/vntnlt5wgn0P+xQiocMZfB730NTbS11r7xCw6rVvP7Zz9K0bh1jbr2Vyre/7c3V2NBA44YNLfO+1C5YwIrv3sCG6dPbtS0dNYqK/adQPHgwa+/u/L/5yhNOoH7Z0pb5fgBGfefbDDz99DdVrwpfw5o1bJk1i01P/o2NjzxC3YIF21yhsXjQIErHjaN80j6UjtyLLXPmUFw5gMrjj6f+9dcpqa5mwNFHU1JdDcDGxx9n9Y9vo3TUKPofcQSlo0bR79BDOh32lFJiw/Q/snnGDCgK6hYuJKKIwee/n1RTw8YnnqBk8GBW3f5TqK+H4mJK99yz3aTjJSNGUDpmNEX9+1NcWUnDqtWUjR9P8cAqUlMTqb6ekqFD2fzUU2x5cS5le0+g6sSTqDz2WEpH7UVReTmQ6VVX+9LLNG3aSOnoMaSazTSsWUP9osU0bamh30EHUb7ffhQPGEDtvHlsevJv1C9dQsmwahrXraN0zxEMPOOMVj3hOpMaG0kNDdDURM1zs2jaUkPtnDnULXyVhrVrqH9tEXULF0JKRFkZ/Q49lCgtpX7RIsbd8csurdi3owyBdk+GQD3HEGjn+Yvkm+Pnt/P87N4cP7+dt9sOB+vNoqKCvb5xPa//66cAaKrdkueKtLtJKbH69tt5478ykxSP+NKXqDzm7QCMv+OX1MyaRdmECRRXVbH+/vtZ8rnPQ0kJ437yP/Sf2vHvNUXl5S1DY/Z9/LHMZMbdMF9HlJS0mvi3fMIERn33O5nhP68vYe3dd9Pv0ENpXL2alTfe2OoX26pTT2Wvb36DKC2lbv58yiZMIDU0EEVFmeEsTU2s+tGP2DLnRfb65jdafomVOlMyZAiVxx5L5bHHMuKqz1M7fwFNGze0DF2rW/hqJtTYYxgb/vQQW2bNYsusWUCmtwolJaz7/bRW14yyMooHD6bhjTdajq29+24AiquHUVw1EIqCslGjKRleTfEeexBlZVQddxyrbr2V9ffe1/p6FRVsfOSRVscqTzqRqhNPYsBRR1I6cmTLMMnU1ETTxo0UDRjQbkheh3KG/XWkdMQISkeM2P51gH4HH0y/gw/uUtttieLilroHHHUkAFXHHdeqTcOaNWz888PUzJzJxocfpmnTJsqnTM7MS9UDIZAkSZJ2L4UXAuV8C135jncw8JRTaP5VONXWdXyO+pymzZtZ8N5zMz0Xskqqq1vNrxOlpfQ//PCW/UFnnsmgM8/cofeJkp79n1hEUDZmDGVjxrT80gdQdeop1C18lboFCxj6oYsp6tev5bXmVcciZ26dKCpi2Mc/3qO1qvCV7z2hZbt5jqlme37pGlJTE3Wvvkr960so3WskJUOHsv6++ygdMxZSE5ue+CtbXpxD/ZIlDL3kEqo/9a+k+no2PvIo9cuWsvHBh1omCW8b7Kz83v+FkhKqr7ySoRdfRNOmTRQNGkREsOGBB0j19VSdfjoNy5ZROmZMq2C2eTuKiigeOLAHP6H8KxkyhMHvOYfB7zkn36VIkiQpDwovBMqVDYT2efjPLL/+empmPJPngrQjUkMDr150MTV//zuD3/c+hl91FcWV3bMa1qLLPt4qANr73nspGz+ux+bF2NUq9ttvt5qDRYJMyFI+YQLlE7aGRbmTg1cec0z7k/r1Y9CZ7wJg2Ec/2uqlxo2baFi2lKLKSjZMn06/ww6n31sOBDJz4DQbeMYZLdtOkixJkqS+rDB+492O0j33pGRYNU21tfkupU/a8NBDzD/nPTSsWdPqeGpooH758swcFh1YP306NX//O5AZDvLS1KnMO/mUlglYm2pq2p2z9Ktf5ZXTTqd++RukxkbqFr9OU00NW+bMYfOzf2ftr3/Ngveey+annqJsn4mM/clPmPyPWZTvPaFgAiCpryiuHED5PvtQuueeDP3Qh1oCIEmSJEkdK+yeQGwdGlZUXkbasvvMCZRSYuUPbmTgGadTvvfe+S6nR7zx3e+y6qYftey/fPRbW7b3efjPLLn6C2x+8kmg/cpZK2++pWWVqj3/46us+fkvqH3pJeoXLeKV08+gadMmGtesYeC7z2Sv668nItj8zDOsveNOABZdeikDjjqS1bf/dJv1jfvZz1rNsSNJkiRJUiErvK4POQvT5K58FuUVpLo6Ujcs19sVda++2m6J3lzr/9+9rPz+93ntkg/vknp2hfqlS1lzxx2klNj4yCOtAqC25h13fEsABLDoY5ex6se3UTt/PhsefLAlABpxzTUMOe889p72eybPeYFB576X+sWLacz2Klo/7Q+8OGV/5kyewqsf+CAAQ//5n6mdO3ebAdDAd72Lff70kAGQJEmSJKlPKfCeQFtFRWa1o1RbS+RMktsTGjdu4pVTT2PQWe9mr+uvb/d6zXPPseSznwVotQJOW+vvu4+KAw7oNXNYrLz5ZtbecSe1815hzS9+AcCQD36QkhHDGXzuuay69Vaa1q+n/vUlbHriCQDG//rXbHrsMVZ897u88c1v8sY3v9lyvXG/+HmriZkjgj2/+EWipIQoKmLQ2Wez5PNXZZY8zqr+zKdb5g1Z87OfMebWW0n19Qx421uhvp6G1asp3XPPXfBpSJIkSZK0eynsECinV1BReQUATVu2tFopqSc0LF0CwLrfT+swBFr4/vNb7dctXkzZ6NGtjjVt3szr//ZpigYMYL9nZvRcsW9Sc6+f9ff8P9bfcw9ASwBUMnIkIz7/uZZVqEZ87nOZcxobWf71/6L/kUfQ78AD6HfgAZTvO4nFn7i85brDP/e5VgFQs6L+/Rl57bUt+3vf8wcaN2xgy/Oz6T/18Ja/2+Gf+yx7fPQjrXv7lJUZAEmSJEmS+qzCDoFy5PYE6klbXniBBe95b8t+SqnVUsS5k1MXDxlC45o1LL36Cww652wGv3freatuvTXTftMm5kyewsQHH6Rs9KgerX1nrL7tf1r13hn64Q+z+n/+h/L9p7D3b3/b4TlRXMyeX7qm1bGqE05g8guzoXmp5pzPrDNRUkLJkCFUHvP21scjHO4lSZIkSVKOApwTKHW4XVSR6QnU05ND5wZAkFnVqmbmTABqZs9m7sGHAFD96U8z6YnHAdg8YwZLr/lSq/mKVt74w1bXef1Tn8pc47nntrmaVj6sueOOlu0Bb3871f92JRN++xvG5xzvqigqIiK6HABJkiRJkqSu6zs9gZqHg3VzT6CmTZuIfv2IoqJWE1E3W/aVfweg4sADW5Y2Bxhw9FHtwo6a556j4oADmHvQwe2us2X2bOZMngLAkAsvZM+vfLk7b2OnrH/gAeoXL2bYJ6+g+vKtQ7kq9t8/j1VJkiRJkqSOFF5PoFytegJlh4N1Y0+gptpa5h4+lRXf+Q4AjWvXtrw2/LOfadV2y/PPUzt3bst+82TPY2+/neI99gDg1QsuZP0f7mlpM/j89zPlxTns9Y3W8wqtueuubruHjjTV1LD6Zz+naRurm6WUmDN5Cq9/8l8BGHjKKT1ajyRJfUVEjImIP0fEnIiYHRGfyh4fGhEPRMTL2T+H5JzzhYiYFxFzI+LU/FUvSZJ2dwUYAnU8HCwqMhMGN9V0Xwi07NqvArDqlsz8PQ3LlwMw6oYb2OMjH+n03OJBgwAYcOQR7Pv4Yy3Hl16zda6cEVddBUDl8ce3PrmhgWX/ed2bK74DTbW1vHrJh5l76GEsv+46Xj7qaBpWr27Xrm7+/Jbt8kmTKNtnn26vRZKkPqoB+ExKaQpwFHB5ROwPXA08lFKaBDyU3Sf72vnAAcBpwI0RUZyXyiVJ0m6vAEOgjhX17w9AU83mbrvmut/9rmW7fulS6pctA6B0zxFAZnUsgKLKyq0nlZSwz6OPtLvWqG9/q9X+5FnPtax0VVxVxcQ/Tmf8r+5kRHYY2Jqf/5wF572/2+6l7rXXmHvwIWx+8smWY02bN7dasQug7tVXmf/OdwGw9/+7h73/MM05fCRJ6iYppaUppWez2xuAOcAo4Czg9myz24Gzs9tnAXemlGpTSguAecARu7ZqSZLUWxR2CJQ7HGxANgTa3H0hUP+pU1u25x1/Amt++jMASkZkQqAxP7qJwe9/P/s8/GcmPvgA1Vdeyb5PPknp8OHtrjXwjDPY61v/DcCIa65pWVa9WdnYsfQ7+GCGXnghpeMyQ8m2zJrFnMlTWPG9/9tpnamujpeOOYY5k6cw54AD2fjoo8w/+xw2/e0pAOoWv84rp2ztPV42fjzDs8u518ycyZq776ZhzRpqX36ZV049raVd+cSJXfugJEnSDouI8cChwN+AESmlpZAJioDmh4lRwKKc0xZnj7W91qURMSMiZqxYsaIny5YkSbuxgg6BUs7QsJaeQN0YAqXGxlb7m554AoqKKBk2DICKffdl5FevpbiykrLRoxl22ccorhywzesNeuc7mfLiHIZe9MFO33fi/fcz9EMXt+yvvPFG1v7619tsX/P8bBpXrMzsNDay6NKPUfvii7x2ySWklNjwxz+2tB11ww1MvP8+9viXf2bfJ/8KwLIvf4WXj34r8898d0u7ybOe67RGSZK08yKiEvgNcGVKaX1nTTs41m6lipTSzSmlqSmlqdXV1d1VpiRJ6mUKLwTqYIUu2BoCpW4MgRpWraJ0VJsv25qaiJKeXXQtIhjxhS9QPHhwy7GlX/ryNlc+W/71r3d8oZTY9MQTbJ4xg9KxY5k85wUGnrp1kufiwYMZ8eUvtTqlaOBAprw4p11PJUmS1D0iopRMAPSLlNJvs4eXR8TI7OsjgTeyxxcDY3JOHw0s2VW1SpKk3qXwQqBcucPBsvPrdGdPoIaVK6k66USqP/Ppbrvmjhj3s58y5MILiWzAteGPD7Rr07huHVv+8Q8Aprw4h8kvzGbUDTcw7pe/pGTECBb9y0fY+Kc/Ub7vpA7n9hn6gQ8w8YE/MvqmH1Jx8EHsec0Xe/amJEnqwyLzj/GPgTkppW/nvDQN+FB2+0PA73OOnx8R5RExAZgEPLWr6pUkSb1LgYdAWzejtJQoK+u2EGj9Aw+QNm+maEAlwz76UQaeeWa3XHdHlE+axJ5f+TL7zXia0nFjWfmDH9DQZpx/zcyZAFRfeSUAUVTEwFNPof9hh7LHv/xLS7sh7z9/m+9TNmYMVccdx4Rf/YpBZ53VA3ciSZKy3gZcBJwQETOzP2cA/wWcHBEvAydn90kpzQbuAl4A7gcuTyk1dnxpSZLU1xV2CNRGUf/+NG3qnhBo6VVXA5neQACD33MOABN+99ttntNToqiIIeedR93Chbx8zDtIKZFSYuUtt7Du99OgpKTVHELNBr/vXADKxo2j8pi37+qyJUlSGymlx1JKkVI6KKV0SPbn3pTSqpTSiSmlSdk/V+ecc11KaWJKab+U0n35rF+SJO3eenbymnzInROozfxARf37d1tPoAHHHMOG6dPZ458/nNk/+mgmP/+PHp8PaFsGnXMOb3wzs7rYqx+8iJpnnml5reItb2kZDperqF8/Jj74AEUVFbusTkmSJEmSlB+F3ROoTQgU/ft135xAEZRNmEDZ+PFbD+UpAAIoGTqUCdMy0wPkBkBA+8mrc5SNHt2ympkkSZIkSSpchR0CtVHUf0CXQ6BUV8ecyVOYM3kKGx56qGV76Ze/DEDjypUU7zG0J8vdYRX77svwq69q2R9+9VWUjR+/3SXnJUmSJElS4Su84WC53sRwsMb161u2F19+Rcv22rt/zcivfY2G1aspnzSpe+rsRntccgmVb3sbjRs20P+ww9jjkkvyXZIkSZIkSdoNFFwIlFoFP+1DoPq1a7t0ncYNG7b52pa5L1E3fz4DjjpyZ0rscbtjOCVJkiRJkvKrjw0H29oTaONf/sLmZ5/dZtumTkKgBdll0utefa17C5QkSZIkSeohBdcTKFfqaDhYTSYEWvTRSwGY8uKcDs/trCdQs+JBA99khZIkSZIkSbtGYfcEap0BUdS/P2lT1+YE6qwnULM9/+NrO1OVJEmSJEnSLld4IVDa9kuZnkA1pKambbbZ8OCDvHjQwWz665MAjPreDR22Kx0zhuLKAW+qVEmSJEmSpF2loIeDtV8drB+kRMPSpa2ON9XW0rRpEyVDh7L4ik8CsPZXvwJgwFvfRtUpp9C4bh2V73gHg959JkWDBlFUVrZr7kGSJEmSJKkb9KkQKPr3B2DlTTe1HKudN48lX7yGLbNmtZ8fqKiIogH9Gb2N3kCSJEmSJEm9ReGFQGnb48GKsiFQatw6HGz+u85s2W6qrW19QlMTEdG99UmSJEmSJOVB4c0JlKvtcLABmTl8Un19h80b3nijx0uSJEmSJEnKhz4VAhVXVQGw6bHHOmxev3hxj5ckSZIkSZKUD10KgSLitIiYGxHzIuLqDl4/KyJmRcTMiJgREW/v/lLfvKLKTAjUuGZNh6/XLliQaZcNiyRJkiRJkgrFdkOgiCgGfgCcDuwPXBAR+7dp9hBwcErpEOCfgVu7u9CuSzlbbXsCVXZ65qbHnwCgdORIAIZcdFE31yZJkiRJkpQfXekJdAQwL6U0P6VUB9wJnJXbIKW0MaWWsVcDgG3Pzrwrtaliez18Nj70EAAD3vrWzJ9ve2uPlCVJkiRJkrSrdWV1sFHAopz9xcCRbRtFxDnA14HhwDu7pbpuVlTZeU+gZqV77cV+s56jqKyshyuSJEmSJEnaNbrSE6ijNdLb9fRJKf0upTQZOBv4WocXirg0O2fQjBUrVuxYpTuj7epgXQx1Ko8/zgBIkiRJkiQVlK6EQIuBMTn7o4El22qcUnoUmBgRwzp47eaU0tSU0tTq6uodLrZLUhdHohUVMemJxxl/911EeXmrl8rGjNnGSZIkSZIkSb1TV0Kgp4FJETEhIsqA84FpuQ0iYp+IiOz2YUAZsKq7i91hnQVCTU2UDB1Kv7e8hcnPzaR48OBdV5ckSZIkSdIutt05gVJKDRFxBTAdKAZuSynNjojLsq/fBLwXuDgi6oEa4P05E0Xnzw6UUDpuLI1r11L9qX/twYIkSZIkSZLyoysTQ5NSuhe4t82xm3K2rweu797Setbwz36m1f7o7/1fNky/32XhJUmSJElSQepSCNSr5PT+iX4V22y2x0c+0mq/dMRwhl58cY+VJUmSJEmSlE+FFwJlDTrrLKo/8+l2x8f97KfUL1ueh4okSZIkSZLyp2BDoGGXf4LS4cPbHe//T/+Uh2okSZIkSZLyqyurg/Uqu8N81JIkSZIkSbubgguBWmRWrJckSZIkSRKFHAJJkiRJkiSphSGQJEmSJElSH1B4IZBTAkmSJEmSJLVTeCFQM+cEkiRJkiRJalG4IZAkSZIkSZJaGAJJkiRJkiT1AYUXAiUnBZIkSb1TRNwWEW9ExPM5x66NiNcjYmb254yc174QEfMiYm5EnJqfqiVJUm9ReCFQC+cEkiRJvc5PgNM6OP6dlNIh2Z97ASJif+B84IDsOTdGRPEuq1SSJPU6BRwCSZIk9S4ppUeB1V1sfhZwZ0qpNqW0AJgHHNFjxUmSpF7PEEiSJGn3d0VEzMoOFxuSPTYKWJTTZnH2WDsRcWlEzIiIGStWrOjpWiVJ0m6q8EIg5wSSJEmF5YfAROAQYCnwrezxjsa+d/gglFK6OaU0NaU0tbq6umeqlCRJu73CC4GywimBJElSAUgpLU8pNaaUmoBb2DrkazEwJqfpaGDJrq5PkiT1HgUbAkmSJBWCiBiZs3sO0Lxy2DTg/Igoj4gJwCTgqV1dnyRJ6j1K8l2AJEmSMiLiDuA4YFhELAb+HTguIg4hM9RrIfAxgJTS7Ii4C3gBaAAuTyk15qNuSZLUOxRgCOScQJIkqXdKKV3QweEfd9L+OuC6nqtIkiQVksIdDuakQJIkSZIkSS0KNwSSJEmSJElSi8ILgVwiXpIkSZIkqZ3CC4GaORxMkiRJkiSpReGGQJIkSZIkSWphCCRJkiRJktQHFFwIlJwTSPr/7d1/rJ33XR/w9we76VhpB13dLIodYpA35E1QOivqFMHKOiBhKC6TihzxI9qKvEyNtmpCw90kYJuQgGnThFSIsjYiCNo004hqIUMadRv8AV3tQClJ21CThsZziE3L1iKmZk4/++M+9/bk/rDvvfb1uc9zXi/p6D7P93zP8efzPOec55yPn+/3AQAAgDUmVwRaYU4gAAAAgBXTLQIBAAAAsEIRCAAAAGABTK8IZE4gAAAAgDWmVwRaZk4gAAAAgBXTLQIBAAAAsEIRCAAAAGABTK8IZEogAAAAgDWmVwRaYU4gAAAAgGWbKgJV1R1V9XRVna2qE+vc/wNV9fHh9ttV9S3XPlQAAAAAtuuKRaCq2pPk3UnuTHI4yd1VdXhVt88k+bvd/c1J/l2SB651oJvmEvEAAAAAa2zmTKDbkpzt7me6+8UkDyc5Otuhu3+7u/9sWP1Ikv3XNsxtMBoMAAAAYMVmikA3J3luZv3c0LaRtyf59fXuqKrjVXWmqs5cvHhx81ECAAAAcFU2UwRa75yadcdcVdV3ZKkI9GPr3d/dD3T3ke4+sm/fvs1HCQAAAMBV2buJPueSHJhZ35/k/OpOVfXNSd6T5M7u/ty1CW87zAkEAAAAsNpmzgQ6neRQVR2sqhuSHEtycrZDVd2S5FeT/FB3/+G1D3PrqkwKBAAAALDsimcCdfelqrovyWNJ9iR5sLufqqp7h/vvT/LjSf5qkp8fii+XuvvIzoUNAAAAwFZsZjhYuvtUklOr2u6fWf6RJD9ybUMDAAAA4FrZzHCwcWlzAgEAAACsNr0i0DJzAgEAAACsmG4RCAAAAIAVikAAAAAAC2ByRaA2JxAAAADAGpMrAq0wJxAAAADAiukWgQAAAABYoQgEAAAAsACmVwQyJxAAAADAGtMrAi0zJxAAMDJV9WBVXaiqJ2faXltVj1fVp4e/Xzdz37uq6mxVPV1V3z2fqAGAsZhuEQgAYHx+Mckdq9pOJPlwdx9K8uFhPVV1OMmxJH9zeMzPV9We6xcqADA20ysCGQ0GAIxUd/9Wks+vaj6a5KFh+aEkb51pf7i7v9Tdn0lyNslt1yVQAGCUplcEWmY4GAAwDTd29/NJMvx9/dB+c5LnZvqdG9rWqKrjVXWmqs5cvHhxR4MFAHav6RaBAACmbb3/8Vr3nOjufqC7j3T3kX379u1wWADAbqUIBACwu71QVTclyfD3wtB+LsmBmX77k5y/zrEBACMyvSKQS8QDANNyMsk9w/I9ST44036sql5ZVQeTHEry0TnEBwCMxN55BwAAwJKqen+SNyd5XVWdS/ITSX46ySNV9fYkn03ytiTp7qeq6pEkn0hyKck7uvuluQQOAIyCIhAAwC7R3XdvcNdbNuj/U0l+auciAgCmZHrDwQAAAABYY3pFIHMCAQAAAKwxvSLQoGq9q6YCAAAALKbJFoEAAAAA+ApFIAAAAIAFMMEikDmBAAAAAFabYBFoYE4gAAAAgBXTLQIBAAAAsGJ6RSCXiAcAAABYY3pFoGWGgwEAAACsmG4RCAAAAIAVikAAAAAAC2ByRaA2JxAAAADAGpMrAq0wJxAAAADAiukWgQAAAABYoQgEAAAAsACmVwQyJRAAAADAGpsqAlXVHVX1dFWdraoT69z/TVX1O1X1par60Wsf5jaYEwgAAABgxd4rdaiqPUneneQ7k5xLcrqqTnb3J2a6fT7JP0vy1h2JEgAAAICrspkzgW5Lcra7n+nuF5M8nOTobIfuvtDdp5P8vx2IEQAAAICrtJki0M1JnptZPze0bVlVHa+qM1V15uLFi9t5iitrkwIBAAAArLaZItB6k+tsq9LS3Q9095HuPrJv377tPMUWmBMIAAAAYNlmikDnkhyYWd+f5PzOhAMAAADATthMEeh0kkNVdbCqbkhyLMnJnQ0LAAAAgGvpilcH6+5LVXVfkseS7EnyYHc/VVX3DvffX1V/LcmZJK9J8uWqemeSw939hR2MfaOAr/s/CQAAALDbXbEIlCTdfSrJqVVt988s/0mWhontGmVKIAAAAIAVmxkOBgAAAMDITbAIZDgYVol8AwAADABJREFUAAAAwGoTLAINjAcDAAAAWDHdIhAAAAAAKxSBAAAAABbA9IpALhEPAAAAsMb0ikDLzAkEAAAAsGLvvAMAAODKqurZJF9M8lKSS919pKpem+QDSW5N8myS7+/uP5tXjADA7jbdM4EAAKbnO7r7Dd19ZFg/keTD3X0oyYeHdQCAdU2uCNTmBAIAFsfRJA8Nyw8leescYwEAdrnJFYFWmBMIAJiWTvKhqnqiqo4PbTd29/NJMvx9/dyiAwB2PXMCAQCMw+3dfb6qXp/k8ar61GYfOBSNjifJLbfcslPxAQC73HTPBAIAmJDuPj/8vZDk0SS3JXmhqm5KkuHvhQ0e+0B3H+nuI/v27bteIQMAu8z0ikCmBAIAJqaqXlVVr15eTvJdSZ5McjLJPUO3e5J8cD4RAgBjMN3hYOYEAgCm48Ykj9bS95u9Sd7X3b9RVaeTPFJVb0/y2SRvm2OMAMAuN90iEADARHT3M0m+ZZ32zyV5y/WPCAAYo+kNBwMAAABgjekVgdqkQAAAAACrTa8ItMycQAAAAAArplsEAgAAAGDF9IpAhoMBAAAArDG9ItDAYDAAAACAr5hsEQgAAACAr1AEAgAAAFgAEywCmRMIAAAAYLUJFoEGLhEPAAAAsGK6RSAAAAAAVigCAQAAACyA6RWB2pxAAAAAAKtNrwi0zJxAAAAAACumWwQCAAAAYIUiEAAAAMACmFwRqM0JBAAAALDG5IpAK8wJBAAAALBiukUgAAAAAFZMrwhkOBgAAADAGpsqAlXVHVX1dFWdraoT69xfVfVzw/0fr6o3XvtQt8hwMAAAAIAVVywCVdWeJO9OcmeSw0nurqrDq7rdmeTQcDue5BeucZwAAAAAXIXNnAl0W5Kz3f1Md7+Y5OEkR1f1OZrkl3rJR5J8bVXddI1jBQAAAGCbNlMEujnJczPr54a2rfZJVR2vqjNVdebixYtbjXVTbjhwIK+6/fYdeW4AAACAsdpMEWi9yXVWz768mT7p7ge6+0h3H9m3b99m4tuyv3LXXbnlve9JfdX05rwGAAAA2K7NVErOJTkws74/yflt9AEAAABgTjZTBDqd5FBVHayqG5IcS3JyVZ+TSX54uErYm5L8n+5+/hrHCgAAAMA27b1Sh+6+VFX3JXksyZ4kD3b3U1V173D//UlOJfmeJGeT/EWSf7RzIQMAAACwVVcsAiVJd5/KUqFntu3+meVO8o5rGxoAAAAA14rZkwEAAAAWgCIQAAAAwAJQBAIAAABYAIpAAAAAAAtAEQgAAABgASgCAQCMWFXdUVVPV9XZqjox73gAgN1LEQgAYKSqak+Sdye5M8nhJHdX1eH5RgUA7FaKQAAA43VbkrPd/Ux3v5jk4SRH5xwTALBLKQIBAIzXzUmem1k/N7QBAKyxd17/8BNPPPGnVfXHO/T0r0vypzv03LuJPKdjEXJM5Dkli5BjIs+r9fU78Jy8XK3T1ms6VR1PcnxY/fOqenpHo5qf+b5na73dMRq23dWx/bbPtrs6tt/2TXnbbfgdbG5FoO7et1PPXVVnuvvITj3/biHP6ViEHBN5Tski5JjIk1E4l+TAzPr+JOdXd+ruB5I8cL2Cmhev5e2z7a6O7bd9tt3Vsf22b1G3neFgAADjdTrJoao6WFU3JDmW5OScYwIAdqm5nQkEAMDV6e5LVXVfkseS7EnyYHc/NeewAIBdaqpFoMmf7jyQ53QsQo6JPKdkEXJM5MkIdPepJKfmHccu4bW8fbbd1bH9ts+2uzq23/Yt5Lar7jVzBwIAAAAwMeYEAgAAAFgAkysCVdUdVfV0VZ2tqhPzjme7qupAVf33qvpkVT1VVf98aP/JqvpfVfWx4fY9M49515D301X13fOLfmuq6tmq+oMhnzND22ur6vGq+vTw9+tm+o8uz6r6GzP77GNV9YWqeufY92dVPVhVF6rqyZm2Le+7qvrbw2vgbFX9XNXuutbkBnn++6r6VFV9vKoeraqvHdpvrar/O7NP7595zBjz3PJrdDfnuUGOH5jJ79mq+tjQPuZ9udExZHLvT0im8/1vHtb7XGRzNvqsZXOq6i9V1Uer6veH7fdv5h3T2FTVnqr6var6tXnHMja1zm/QhdHdk7llaULEP0ryDUluSPL7SQ7PO65t5nJTkjcOy69O8odJDif5ySQ/uk7/w0O+r0xycNgOe+adxyZzfTbJ61a1/WySE8PyiSQ/M/Y8Z3Lbk+RPknz92Pdnkm9P8sYkT17Nvkvy0SR/J0kl+fUkd847t03k+V1J9g7LPzOT562z/VY9zxjz3PJrdDfnuV6Oq+7/D0l+fAL7cqNjyOTen25umdD3vzltv8t+Lrpddtut+1k777jGchuOK18zLL8iyf9M8qZ5xzWmW5J/keR9SX5t3rGM7ZZ1foMuym1qZwLdluRsdz/T3S8meTjJ0TnHtC3d/Xx3/+6w/MUkn0xy82UecjTJw939pe7+TJKzWdoeY3U0yUPD8kNJ3jrTPvY835Lkj7r7jy/TZxR5dvdvJfn8quYt7buquinJa7r7d3rpE/mXZh6zK6yXZ3d/qLsvDasfSbL/cs8x1jwvY5T783I5Dme4fH+S91/uOXZ7jslljyGTe39CJvT9bx62+NnPjG18X2dGL/nzYfUVw82EtZtUVfuT/IMk75l3LIzL1IpANyd5bmb9XCbwQVxVtyb51ixVx5PkvmEIyoMzp/KPOfdO8qGqeqKqjg9tN3b388nSATbJ64f2Mee57Fhe/iNzavtzq/vu5mF5dfuY/OMsnSGx7OBwau5vVtW3DW1jznMrr9Ex5/ltSV7o7k/PtI1+X646hizi+5PpG/Mxk4lY5/s6mzAMZ/pYkgtJHu9u22/z/lOSf5nky/MOZKTW+w26EKZWBFpvnoJRV5Or6muS/Nck7+zuLyT5hSTfmOQNSZ7P0tCFZNy5397db0xyZ5J3VNW3X6bvmPNMVd2Q5K4k/2VomuL+3MhGOY0616r610kuJfmVoen5JLd097dmOEW3ql6T8ea51dfoWPNMkrvz8gLt6PflOseQDbuu0zb2/cni8DplrrbwWcsq3f1Sd78hS2dU31ZVf2veMY1BVX1vkgvd/cS8YxmxrfwGnZSpFYHOJTkws74/yfk5xXLVquoVWTqg/Ep3/2qSdPcLw4fll5P853xliNBoc+/u88PfC0kezVJOLwzDEJaHXlwYuo82z8GdSX63u19Iprk/s/V9dy4vH0o1mlyr6p4k35vkB4ahMhmG03xuWH4iS/NU/PWMNM9tvEZHmWdV7U3yD5N8YLlt7PtyvWNIFuj9yUIZ8zGTkdvgs5Yt6u7/neR/JLljzqGMxe1J7qqqZ7M0BPbvVdUvzzekcdngN+hCmFoR6HSSQ1V1cDjj4liSk3OOaVuGuSnem+ST3f0fZ9pvmun2fUmWr+RwMsmxqnplVR1McihLk3nualX1qqp69fJylibbfTJL+dwzdLsnyQeH5VHmOeNlZxpMbX8OtrTvhiEpX6yqNw2v+x+eecyuVVV3JPmxJHd191/MtO+rqj3D8jdkKc9nRpznll6jY80zyd9P8qnuXhn6NOZ9udExJAvy/mThTOb7H+Nymc9aNmE4zi5fXfWrMxyL5xvVOHT3u7p7f3ffmqXPvP/W3T8457BG4zK/QRfC3nkHcC1196Wqui/JY1m6UsSD3f3UnMPartuT/FCSPxjGySbJv0pyd1W9IUunOT+b5J8kSXc/VVWPJPlEloamvKO7X7ruUW/djUkeXTqGZm+S93X3b1TV6SSPVNXbk3w2yduSUeeZqvrLSb4zwz4b/OyY92dVvT/Jm5O8rqrOJfmJJD+dre+7f5rkF5N8dZbm1pmdX2fuNsjzXVm6ktLjw+v3I919b5ausvJvq+pSkpeS3NvdyxNujjHPN2/jNbpr81wvx+5+b9bO1ZWMeF9m42PI5N6fMLHvf9fdZT4XubJ1P2u7+9QcYxqTm5I8NPyHy1cleaS7Xeqc62Hd36DzDen6qWEEAwAAAAATNrXhYAAAAACsQxEIAAAAYAEoAgEAAAAsAEUgAAAAgAWgCAQAAACwABSBAAAAABaAIhAAAADAAlAEAgAAAFgA/x/x8svrDjqKQQAAAABJRU5ErkJggg==\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","source":"### Create 'intelligent' agents","metadata":{}},{"cell_type":"code","source":"# create epsilon greedy agent\nclass EpsilonGreedyAgent(object):\n    def __init__(self, env, max_iterations=2000, epsilon=0.01):\n        self.env = env \n        self.iterations = max_iterations\n        self.epsilon = epsilon\n        \n    # let the agent take actions in the environment\n    def action(self):\n        # initialise the q_values\n        q_values = np.zeros(self.env.k_machines)\n        # keep track of total reward generated by each machine\n        machine_rewards = np.zeros(self.env.k_machines)\n        # keep track of the rewards the agent generates and which machine it is using\n        machine_counts = np.zeros(self.env.k_machines)\n        \n        # store the reward the agent is generating\n        rewards= []\n        # store reward the agent is generating over time\n        avg_rewards = []\n        \n        for i in range(1, self.iterations+1):\n            machine = np.random.choice(self.env.k_machines) if np.random.random() < self.epsilon else np.argmax(q_values)\n            \n            # store information\n            reward = self.env.choose_machine(machine)\n            machine_rewards[machine] += reward \n            machine_counts[machine] += 1\n            q_values[machine] = machine_rewards[machine]/machine_counts[machine]\n        \n            # append the results to the list rewards and avg_rewards\n            rewards.append(reward)\n            avg_rewards.append(sum(rewards)/len(rewards))\n            \n        # create a dictionary with the results to use our plotting function\n        return {'machines': machine_counts,\n                'rewards': rewards,\n                'avg_rewards': avg_rewards\n               }","metadata":{"trusted":true},"execution_count":10,"outputs":[]},{"cell_type":"code","source":"# create an instance of the epsilon greedy agent\negreedy_agent = EpsilonGreedyAgent(env=environment, max_iterations=2000, epsilon=0.1)\neg_history = egreedy_agent.action()\n\n# print\nprint(f'total reward : {sum(eg_history[\"rewards\"])}')","metadata":{"trusted":true},"execution_count":11,"outputs":[{"name":"stdout","text":"total reward : 1639.0\n","output_type":"stream"}]},{"cell_type":"code","source":"plot_history(eg_history)","metadata":{"trusted":true},"execution_count":12,"outputs":[{"output_type":"display_data","data":{"text/plain":"<Figure size 1440x432 with 2 Axes>","image/png":"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\n"},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","source":"# create epsilon greedy agent with decay\nclass EpsilonGreedyDecayAgent(object):\n    def __init__(self, env, max_iterations=2000, epsilon=0.01, decay=0.001, decay_interval=50):\n        self.env = env \n        self.iterations = max_iterations\n        self.epsilon = epsilon\n        self.decay = decay\n        self.decay_interval = decay_interval\n        \n    # let the agent take actions in the environment\n    def action(self):\n        # initialise the q_values\n        q_values = np.zeros(self.env.k_machines)\n        # keep track of total reward generated by each machine\n        machine_rewards = np.zeros(self.env.k_machines)\n        # keep track of the rewards the agent generates and which machine it is using\n        machine_counts = np.zeros(self.env.k_machines)\n        \n        # store the reward the agent is generating\n        rewards= []\n        # store reward the agent is generating over time\n        avg_rewards = []\n        \n        for i in range(1, self.iterations+1):\n            machine = np.random.choice(self.env.k_machines) if np.random.random() < self.epsilon else np.argmax(q_values)\n            \n            # store information\n            reward = self.env.choose_machine(machine)\n            machine_rewards[machine] += reward \n            machine_counts[machine] += 1\n            q_values[machine] = machine_rewards[machine]/machine_counts[machine]\n        \n            # append the results to the list rewards and avg_rewards\n            rewards.append(reward)\n            avg_rewards.append(sum(rewards)/len(rewards))\n            \n            # if statement for the decay of epsilon at interval step time\n            if i%self.decay_interval == 0:\n              self.epsilon = self.epsilon * self.decay\n              \n        # create a dictionary with the results to use our plotting function\n        return {'machines': machine_counts,\n                'rewards': rewards,\n                'avg_rewards': avg_rewards\n               }","metadata":{"trusted":true},"execution_count":19,"outputs":[]},{"cell_type":"code","source":"# create an instance of the epsilon greedy agent with decay\negreedyd_agent = EpsilonGreedyDecayAgent(env=environment, max_iterations=2000, epsilon=0.01, decay=0.001, decay_interval= 50)\negd_history = egreedyd_agent.action()\n\n# print total rewards and charts\nprint(f'total reward : {sum(egd_history[\"rewards\"])}')\nplot_history(egd_history)","metadata":{"trusted":true},"execution_count":16,"outputs":[{"name":"stdout","text":"total reward : 1781.0\n","output_type":"stream"},{"output_type":"display_data","data":{"text/plain":"<Figure size 1440x432 with 2 Axes>","image/png":"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\n"},"metadata":{"needs_background":"light"}}]}]}