Agent_Architecture1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cab-Driver Agent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "# Importing libraries\n",
    "import numpy as np\n",
    "import random\n",
    "import math\n",
    "from collections import deque\n",
    "import collections\n",
    "import pickle\n",
    "import time\n",
    "\n",
    "# for building DQN model\n",
    "from keras import layers\n",
    "from keras import Sequential\n",
    "from keras.layers import Dense, Activation, Flatten\n",
    "from keras.optimizers import Adam\n",
    "\n",
    "# for plotting graphs\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Import the environment\n",
    "from Env import CabDriver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Load the Time Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loading the time matrix provided\n",
    "Time_matrix = np.load(\"TM.npy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Check what the max, min and mean time values are. This will help us in defining the 'next_step' function in the Environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n",
      "11.0\n",
      "0.0\n",
      "3.0542857142857143\n",
      "7.93705306122449\n"
     ]
    }
   ],
   "source": [
    "print(type(Time_matrix))\n",
    "print(Time_matrix.max())\n",
    "print(Time_matrix.min())\n",
    "print(Time_matrix.mean())\n",
    "print(Time_matrix.var())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Since the max time is 11 hours between any 2 points, the next state of the cab driver may increase at most by  1 day."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Agent Class\n",
    "\n",
    "If you are using this framework, you need to fill the following to complete the following code block:\n",
    "1. State and Action Size\n",
    "2. Hyperparameters\n",
    "3. Create a neural-network model in function 'build_model()'\n",
    "4. Define epsilon-greedy strategy in function 'get_action()'\n",
    "5. Complete the function 'append_sample()'. This function appends the recent experience tuple <state, action, reward, new-state> to the memory\n",
    "6. Complete the 'train_model()' function with following logic:\n",
    "   - If the memory size is greater than mini-batch size, you randomly sample experiences from memory as per the mini-batch size and do the following:\n",
    "      - Initialise your input and output batch for training the model\n",
    "      - Calculate the target Q value for each sample: reward + gamma*max(Q(s'a,))\n",
    "      - Get Q(s', a) values from the last trained model\n",
    "      - Update the input batch as your encoded state and output batch as your Q-values\n",
    "      - Then fit your DQN model using the updated input and output batch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class DQNAgent:\n",
    "    def __init__(self, state_size, action_size):\n",
    "        # Define size of state and action\n",
    "        self.state_size = state_size\n",
    "        self.action_size = action_size\n",
    "\n",
    "        # Write here: Specify you hyper parameters for the DQN\n",
    "        self.discount_factor = 0.95\n",
    "        self.learning_rate = 0.01\n",
    "        self.epsilon = 1\n",
    "        self.epsilon_max = 1\n",
    "        self.epsilon_decay = -0.0005 #for 15k\n",
    "        #self.epsilon_decay = -0.00015 #for 20k\n",
    "        self.epsilon_min = 0.00001\n",
    "        \n",
    "        self.batch_size = 32\n",
    "\n",
    "        # create replay memory using deque\n",
    "        self.memory = deque(maxlen=2000)\n",
    "\n",
    "        # Initialize the value of the states tracked\n",
    "        self.states_tracked = []\n",
    "        \n",
    "        # We are going to track state [0,0,0] and action (0,2) at index 2 in the action space.\n",
    "        self.track_state = np.array(env.state_encod_arch1([0,0,0])).reshape(1, 36)\n",
    "\n",
    "        # create main model and target model\n",
    "        self.model = self.build_model()\n",
    "\n",
    "    # approximate Q function using Neural Network\n",
    "    def build_model(self):\n",
    "        \"\"\"\n",
    "        Function that takes in the agent and constructs the network\n",
    "        to train it\n",
    "        @return model\n",
    "        @params agent\n",
    "        \"\"\"\n",
    "        input_shape = self.state_size\n",
    "        model = Sequential()\n",
    "        # Write your code here: Add layers to your neural nets       \n",
    "        model.add(Dense(32, input_dim=self.state_size, activation='relu', kernel_initializer='he_uniform'))\n",
    "        model.add(Dense(32, activation='relu', kernel_initializer='he_uniform'))\n",
    "        # the output layer: output is of size num_actions\n",
    "        model.add(Dense(self.action_size, activation='relu', kernel_initializer='he_uniform'))\n",
    "        model.compile(loss='mse', optimizer=Adam(lr=self.learning_rate))\n",
    "        model.summary\n",
    "        return model\n",
    "\n",
    "    def get_action(self, state, possible_actions_index, actions):\n",
    "        \"\"\"\n",
    "        get action in a state according to an epsilon-greedy approach\n",
    "        possible_actions_index, actions are the 'ride requests' that teh driver got.\n",
    "        \"\"\"        \n",
    "        # get action from model using epsilon-greedy policy\n",
    "        # Decay in ε after each episode       \n",
    "        if np.random.rand() <= self.epsilon:\n",
    "            # explore: choose a random action from the ride requests\n",
    "            return random.choice(possible_actions_index)\n",
    "        else:\n",
    "            # choose the action with the highest q(s, a)\n",
    "            # the first index corresponds to the batch size, so\n",
    "            # reshape state to (1, state_size) so that the first index corresponds to the batch size\n",
    "            state = np.array(env.state_encod_arch1(state)).reshape(1, 36)\n",
    "\n",
    "            # Use the model to predict the Q_values.\n",
    "            q_value = self.model.predict(state)\n",
    "\n",
    "            # truncate the array to only those actions that are part of the ride  requests.\n",
    "            q_vals_possible = [q_value[0][i] for i in possible_actions_index]\n",
    "\n",
    "            return possible_actions_index[np.argmax(q_vals_possible)]\n",
    "\n",
    "    def append_sample(self, state, action_index, reward, next_state, done):\n",
    "        \"\"\"appends the new agent run output to replay buffer\"\"\"\n",
    "        self.memory.append((state, action_index, reward, next_state, done))\n",
    "        \n",
    "    # pick samples randomly from replay memory (with batch_size) and train the network\n",
    "    def train_model(self):\n",
    "        \"\"\" \n",
    "        Function to train the model on eacg step run.\n",
    "        Picks the random memory events according to batch size and \n",
    "        runs it through the network to train it.\n",
    "        \"\"\"\n",
    "        if len(self.memory) > self.batch_size:\n",
    "            # Sample batch from the memory\n",
    "            mini_batch = random.sample(self.memory, self.batch_size)\n",
    "            # initialise two matrices - update_input and update_output\n",
    "            update_input = np.zeros((self.batch_size, self.state_size))\n",
    "            update_output = np.zeros((self.batch_size, self.state_size))\n",
    "            actions, rewards, done = [], [], []\n",
    "\n",
    "            # populate update_input and update_output and the lists rewards, actions, done\n",
    "            for i in range(self.batch_size):\n",
    "                state, action, reward, next_state, done_boolean = mini_batch[i]\n",
    "                update_input[i] = env.state_encod_arch1(state)     \n",
    "                actions.append(action)\n",
    "                rewards.append(reward)\n",
    "                update_output[i] = env.state_encod_arch1(next_state)\n",
    "                done.append(done_boolean)\n",
    "\n",
    "            # predict the target q-values from states s\n",
    "            target = self.model.predict(update_input)\n",
    "            # target for q-network\n",
    "            target_qval = self.model.predict(update_output)\n",
    "\n",
    "\n",
    "            # update the target values\n",
    "            for i in range(self.batch_size):\n",
    "                if done[i]:\n",
    "                    target[i][actions[i]] = rewards[i]\n",
    "                else: # non-terminal state\n",
    "                    target[i][actions[i]] = rewards[i] + self.discount_factor * np.max(target_qval[i])\n",
    "            # model fit\n",
    "            self.model.fit(update_input, target, batch_size=self.batch_size, epochs=1, verbose=0)\n",
    "            \n",
    "    def save_tracking_states(self):\n",
    "        # Use the model to predict the q_value of the state we are tacking.\n",
    "        q_value = self.model.predict(self.track_state)\n",
    "        \n",
    "        # Grab the q_value of the action index that we are tracking.\n",
    "        self.states_tracked.append(q_value[0][2])\n",
    "        \n",
    "    def save_test_states(self):\n",
    "        # Use the model to predict the q_value of the state we are tacking.\n",
    "        q_value = self.model.predict(self.track_state)\n",
    "        \n",
    "        # Grab the q_value of the action index that we are tracking.\n",
    "        self.states_test.append(q_value[0][2])\n",
    "\n",
    "    def save(self, name):\n",
    "        with open(name, 'wb') as file:  \n",
    "            pickle.dump(self.model, file,pickle.HIGHEST_PROTOCOL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. DQN block"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for episode in range(Episodes):\n",
    "\n",
    "    # Write code here\n",
    "    # Call the environment\n",
    "    # Call all the initialised variables of the environment\n",
    "    \n",
    "\n",
    "    #Call the DQN agent\n",
    "    \n",
    "    \n",
    "    while !terminal_state:\n",
    "        \n",
    "        # Write your code here\n",
    "        # 1. Pick epsilon-greedy action from possible actions for the current state\n",
    "        # 2. Evaluate your reward and next state\n",
    "        # 3. Append the experience to the memory\n",
    "        # 4. Train the model by calling function agent.train_model\n",
    "        # 5. Keep a track of rewards, Q-values, loss\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "episode_time = 24*30 #30 days before which car has to be recharged\n",
    "n_episodes = 15000\n",
    "m = 5\n",
    "t = 24\n",
    "d = 7\n",
    "\n",
    "# Invoke Env class\n",
    "env = CabDriver()\n",
    "action_space, state_space, state = env.reset()\n",
    "\n",
    "# Set up state and action sizes.\n",
    "state_size = m+t+d\n",
    "action_size = len(action_space)\n",
    "\n",
    "# Invoke agent class\n",
    "agent = DQNAgent(action_size=action_size, state_size=state_size)\n",
    "\n",
    "# to store rewards in each episode\n",
    "rewards_per_episode, episodes = [], []\n",
    "# Rewards for state [0,0,0] being tracked.\n",
    "rewards_init_state = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Run the episodes, build up replay buffer and train the model.\n",
    "### Note:\n",
    "#### The moment total episode time exceeds 720 (30 days), we ignore the most recent ride and do NOT save that experience in the replay memory\n",
    "#### The init state is randomly picked from the state space for each episode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving Model 0\n",
      "episode 9, reward 122.0, memory_length 1353, epsilon 0.9955001547284723 total_time 730.0\n",
      "episode 19, reward -376.0, memory_length 2000, epsilon 0.9905350769930761 total_time 725.0\n",
      "episode 29, reward -193.0, memory_length 2000, epsilon 0.9855947626861951 total_time 726.0\n",
      "episode 39, reward -270.0, memory_length 2000, epsilon 0.9806790882997144 total_time 721.0\n",
      "episode 49, reward -247.0, memory_length 2000, epsilon 0.9757879309415182 total_time 727.0\n",
      "episode 59, reward -186.0, memory_length 2000, epsilon 0.9709211683324178 total_time 722.0\n",
      "episode 69, reward -580.0, memory_length 2000, epsilon 0.9660786788030947 total_time 729.0\n",
      "episode 79, reward -79.0, memory_length 2000, epsilon 0.9612603412910584 total_time 727.0\n",
      "episode 89, reward -296.0, memory_length 2000, epsilon 0.9564660353376199 total_time 722.0\n",
      "episode 99, reward -94.0, memory_length 2000, epsilon 0.9516956410848808 total_time 725.0\n",
      "episode 109, reward -250.0, memory_length 2000, epsilon 0.9469490392727365 total_time 726.0\n",
      "episode 119, reward 69.0, memory_length 2000, epsilon 0.9422261112358942 total_time 730.0\n",
      "episode 129, reward 30.0, memory_length 2000, epsilon 0.9375267389009072 total_time 722.0\n",
      "episode 139, reward -12.0, memory_length 2000, epsilon 0.9328508047832221 total_time 725.0\n",
      "episode 149, reward -31.0, memory_length 2000, epsilon 0.9281981919842428 total_time 721.0\n",
      "episode 159, reward -145.0, memory_length 2000, epsilon 0.9235687841884068 total_time 727.0\n",
      "episode 169, reward 261.0, memory_length 2000, epsilon 0.918962465660278 total_time 724.0\n",
      "episode 179, reward 81.0, memory_length 2000, epsilon 0.9143791212416534 total_time 721.0\n",
      "episode 189, reward 110.0, memory_length 2000, epsilon 0.9098186363486838 total_time 722.0\n",
      "episode 199, reward 126.0, memory_length 2000, epsilon 0.9052808969690094 total_time 721.0\n",
      "episode 209, reward -90.0, memory_length 2000, epsilon 0.9007657896589091 total_time 721.0\n",
      "episode 219, reward -36.0, memory_length 2000, epsilon 0.8962732015404654 total_time 732.0\n",
      "episode 229, reward -133.0, memory_length 2000, epsilon 0.891803020298741 total_time 730.0\n",
      "episode 239, reward 293.0, memory_length 2000, epsilon 0.8873551341789723 total_time 723.0\n",
      "episode 249, reward -72.0, memory_length 2000, epsilon 0.8829294319837746 total_time 726.0\n",
      "episode 259, reward -163.0, memory_length 2000, epsilon 0.8785258030703623 total_time 723.0\n",
      "episode 269, reward 351.0, memory_length 2000, epsilon 0.8741441373477834 total_time 722.0\n",
      "episode 279, reward 28.0, memory_length 2000, epsilon 0.8697843252741666 total_time 727.0\n",
      "episode 289, reward -153.0, memory_length 2000, epsilon 0.8654462578539829 total_time 725.0\n",
      "episode 299, reward -45.0, memory_length 2000, epsilon 0.8611298266353209 total_time 727.0\n",
      "episode 309, reward 7.0, memory_length 2000, epsilon 0.8568349237071754 total_time 729.0\n",
      "episode 319, reward -345.0, memory_length 2000, epsilon 0.8525614416967494 total_time 725.0\n",
      "episode 329, reward 413.0, memory_length 2000, epsilon 0.84830927376677 total_time 724.0\n",
      "episode 339, reward 356.0, memory_length 2000, epsilon 0.8440783136128177 total_time 727.0\n",
      "episode 349, reward -431.0, memory_length 2000, epsilon 0.8398684554606681 total_time 722.0\n",
      "episode 359, reward -216.0, memory_length 2000, epsilon 0.8356795940636483 total_time 721.0\n",
      "episode 369, reward -255.0, memory_length 2000, epsilon 0.8315116247000052 total_time 723.0\n",
      "episode 379, reward 47.0, memory_length 2000, epsilon 0.8273644431702872 total_time 733.0\n",
      "episode 389, reward -71.0, memory_length 2000, epsilon 0.8232379457947406 total_time 725.0\n",
      "episode 399, reward -172.0, memory_length 2000, epsilon 0.819132029410716 total_time 722.0\n",
      "episode 409, reward -106.0, memory_length 2000, epsilon 0.8150465913700896 total_time 722.0\n",
      "episode 419, reward 169.0, memory_length 2000, epsilon 0.8109815295366979 total_time 734.0\n",
      "episode 429, reward 117.0, memory_length 2000, epsilon 0.8069367422837833 total_time 722.0\n",
      "episode 439, reward 25.0, memory_length 2000, epsilon 0.8029121284914538 total_time 723.0\n",
      "episode 449, reward 153.0, memory_length 2000, epsilon 0.7989075875441549 total_time 726.0\n",
      "episode 459, reward -61.0, memory_length 2000, epsilon 0.7949230193281545 total_time 723.0\n",
      "episode 469, reward 133.0, memory_length 2000, epsilon 0.7909583242290396 total_time 731.0\n",
      "episode 479, reward -112.0, memory_length 2000, epsilon 0.7870134031292261 total_time 722.0\n",
      "episode 489, reward -43.0, memory_length 2000, epsilon 0.7830881574054811 total_time 722.0\n",
      "episode 499, reward 420.0, memory_length 2000, epsilon 0.7791824889264571 total_time 723.0\n",
      "episode 509, reward 208.0, memory_length 2000, epsilon 0.7752963000502389 total_time 721.0\n",
      "episode 519, reward -288.0, memory_length 2000, epsilon 0.7714294936219019 total_time 723.0\n",
      "episode 529, reward 32.0, memory_length 2000, epsilon 0.7675819729710842 total_time 724.0\n",
      "episode 539, reward 189.0, memory_length 2000, epsilon 0.763753641909569 total_time 725.0\n",
      "episode 549, reward 266.0, memory_length 2000, epsilon 0.7599444047288803 total_time 732.0\n",
      "episode 559, reward 429.0, memory_length 2000, epsilon 0.7561541661978903 total_time 723.0\n",
      "episode 569, reward 563.0, memory_length 2000, epsilon 0.7523828315604384 total_time 730.0\n",
      "episode 579, reward 213.0, memory_length 2000, epsilon 0.7486303065329623 total_time 725.0\n",
      "episode 589, reward 159.0, memory_length 2000, epsilon 0.7448964973021404 total_time 722.0\n",
      "episode 599, reward 662.0, memory_length 2000, epsilon 0.7411813105225479 total_time 724.0\n",
      "episode 609, reward 82.0, memory_length 2000, epsilon 0.7374846533143217 total_time 721.0\n",
      "episode 619, reward 357.0, memory_length 2000, epsilon 0.733806433260839 total_time 722.0\n",
      "episode 629, reward 221.0, memory_length 2000, epsilon 0.7301465584064071 total_time 723.0\n",
      "episode 639, reward 291.0, memory_length 2000, epsilon 0.7265049372539636 total_time 723.0\n",
      "episode 649, reward -153.0, memory_length 2000, epsilon 0.7228814787627905 total_time 730.0\n",
      "episode 659, reward -5.0, memory_length 2000, epsilon 0.7192760923462365 total_time 730.0\n",
      "episode 669, reward 80.0, memory_length 2000, epsilon 0.7156886878694535 total_time 722.0\n",
      "episode 679, reward 99.0, memory_length 2000, epsilon 0.7121191756471427 total_time 722.0\n",
      "episode 689, reward 136.0, memory_length 2000, epsilon 0.7085674664413126 total_time 728.0\n",
      "episode 699, reward 207.0, memory_length 2000, epsilon 0.7050334714590482 total_time 721.0\n",
      "episode 709, reward 128.0, memory_length 2000, epsilon 0.7015171023502909 total_time 722.0\n",
      "episode 719, reward -72.0, memory_length 2000, epsilon 0.6980182712056295 total_time 721.0\n",
      "episode 729, reward 275.0, memory_length 2000, epsilon 0.6945368905541035 total_time 721.0\n",
      "episode 739, reward 331.0, memory_length 2000, epsilon 0.6910728733610152 total_time 726.0\n",
      "episode 749, reward 127.0, memory_length 2000, epsilon 0.6876261330257543 total_time 722.0\n",
      "episode 759, reward 433.0, memory_length 2000, epsilon 0.684196583379633 total_time 722.0\n",
      "episode 769, reward 147.0, memory_length 2000, epsilon 0.6807841386837313 total_time 728.0\n",
      "episode 779, reward 433.0, memory_length 2000, epsilon 0.6773887136267543 total_time 723.0\n",
      "episode 789, reward 464.0, memory_length 2000, epsilon 0.6740102233228988 total_time 724.0\n",
      "episode 799, reward 250.0, memory_length 2000, epsilon 0.670648583309731 total_time 723.0\n",
      "episode 809, reward 551.0, memory_length 2000, epsilon 0.6673037095460755 total_time 728.0\n",
      "episode 819, reward 401.0, memory_length 2000, epsilon 0.6639755184099142 total_time 725.0\n",
      "episode 829, reward 154.0, memory_length 2000, epsilon 0.6606639266962953 total_time 723.0\n",
      "episode 839, reward 186.0, memory_length 2000, epsilon 0.6573688516152534 total_time 721.0\n",
      "episode 849, reward 334.0, memory_length 2000, epsilon 0.6540902107897397 total_time 721.0\n",
      "episode 859, reward 85.0, memory_length 2000, epsilon 0.6508279222535631 total_time 723.0\n",
      "episode 869, reward 684.0, memory_length 2000, epsilon 0.64758190444934 total_time 721.0\n",
      "episode 879, reward 603.0, memory_length 2000, epsilon 0.6443520762264566 total_time 722.0\n",
      "episode 889, reward 392.0, memory_length 2000, epsilon 0.6411383568390387 total_time 723.0\n",
      "episode 899, reward 181.0, memory_length 2000, epsilon 0.6379406659439346 total_time 721.0\n",
      "episode 909, reward 554.0, memory_length 2000, epsilon 0.6347589235987051 total_time 724.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 919, reward 631.0, memory_length 2000, epsilon 0.631593050259626 total_time 726.0\n",
      "episode 929, reward 327.0, memory_length 2000, epsilon 0.6284429667796988 total_time 721.0\n",
      "episode 939, reward 390.0, memory_length 2000, epsilon 0.6253085944066726 total_time 723.0\n",
      "episode 949, reward 281.0, memory_length 2000, epsilon 0.6221898547810748 total_time 722.0\n",
      "episode 959, reward 619.0, memory_length 2000, epsilon 0.6190866699342522 total_time 725.0\n",
      "episode 969, reward 172.0, memory_length 2000, epsilon 0.6159989622864221 total_time 721.0\n",
      "episode 979, reward 385.0, memory_length 2000, epsilon 0.6129266546447325 total_time 722.0\n",
      "episode 989, reward 224.0, memory_length 2000, epsilon 0.6098696702013323 total_time 724.0\n",
      "episode 999, reward 290.0, memory_length 2000, epsilon 0.6068279325314512 total_time 725.0\n",
      "Saving Model 1000\n",
      "episode 1009, reward 345.0, memory_length 2000, epsilon 0.6038013655914889 total_time 724.0\n",
      "episode 1019, reward 416.0, memory_length 2000, epsilon 0.6007898937171146 total_time 731.0\n",
      "episode 1029, reward 287.0, memory_length 2000, epsilon 0.5977934416213744 total_time 721.0\n",
      "episode 1039, reward 123.0, memory_length 2000, epsilon 0.5948119343928097 total_time 725.0\n",
      "episode 1049, reward 444.0, memory_length 2000, epsilon 0.5918452974935846 total_time 721.0\n",
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      "episode 1069, reward 605.0, memory_length 2000, epsilon 0.5859563383887504 total_time 722.0\n",
      "episode 1079, reward 573.0, memory_length 2000, epsilon 0.5830338689588568 total_time 725.0\n",
      "episode 1089, reward 302.0, memory_length 2000, epsilon 0.5801259754060536 total_time 723.0\n",
      "episode 1099, reward 129.0, memory_length 2000, epsilon 0.5772325850328504 total_time 722.0\n",
      "episode 1109, reward 475.0, memory_length 2000, epsilon 0.5743536255043372 total_time 726.0\n",
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      "episode 1129, reward 852.0, memory_length 2000, epsilon 0.5686387114438011 total_time 727.0\n",
      "episode 1139, reward 411.0, memory_length 2000, epsilon 0.5658026140386287 total_time 726.0\n",
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      "episode 1279, reward 383.0, memory_length 2000, epsilon 0.5275508606162479 total_time 730.0\n",
      "episode 1289, reward 824.0, memory_length 2000, epsilon 0.5249196897220061 total_time 723.0\n",
      "episode 1299, reward 500.0, memory_length 2000, epsilon 0.5223016418473468 total_time 725.0\n",
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      "episode 1319, reward 781.0, memory_length 2000, epsilon 0.5171046536778833 total_time 727.0\n",
      "episode 1329, reward 691.0, memory_length 2000, epsilon 0.514525583458104 total_time 728.0\n",
      "episode 1339, reward 249.0, memory_length 2000, epsilon 0.5119593764047093 total_time 733.0\n",
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      "episode 1379, reward 567.0, memory_length 2000, epsilon 0.50182190153885 total_time 721.0\n",
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     ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 1809, reward 919.0, memory_length 2000, epsilon 0.40474015917966877 total_time 721.0\n",
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      "Saving Model 2000\n",
      "episode 2009, reward 1113.0, memory_length 2000, epsilon 0.3662240406075948 total_time 737.0\n",
      "episode 2019, reward 1207.0, memory_length 2000, epsilon 0.3643974905849244 total_time 724.0\n",
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     ]
    },
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 2689, reward 1370.0, memory_length 2000, epsilon 0.26066740358669477 total_time 722.0\n",
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      "episode 2899, reward 1114.0, memory_length 2000, epsilon 0.23468525568799242 total_time 725.0\n",
      "episode 2909, reward 1090.0, memory_length 2000, epsilon 0.23351475809207786 total_time 726.0\n",
      "episode 2919, reward 1193.0, memory_length 2000, epsilon 0.2323500983772779 total_time 724.0\n",
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      "episode 2989, reward 1421.0, memory_length 2000, epsilon 0.22435851346107796 total_time 722.0\n",
      "episode 2999, reward 1261.0, memory_length 2000, epsilon 0.22323952070689196 total_time 729.0\n",
      "Saving Model 3000\n",
      "episode 3009, reward 1305.0, memory_length 2000, epsilon 0.22212610895235071 total_time 721.0\n",
      "episode 3019, reward 852.0, memory_length 2000, epsilon 0.22101825036210232 total_time 732.0\n",
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     ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 3569, reward 880.0, memory_length 2000, epsilon 0.16787930169900972 total_time 721.0\n",
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      "episode 3659, reward 1229.0, memory_length 2000, epsilon 0.16049218967615253 total_time 729.0\n",
      "episode 3669, reward 1865.0, memory_length 2000, epsilon 0.15969173154073077 total_time 726.0\n",
      "episode 3679, reward 1604.0, memory_length 2000, epsilon 0.15889526570691476 total_time 730.0\n",
      "episode 3689, reward 1501.0, memory_length 2000, epsilon 0.15810277226301725 total_time 723.0\n",
      "episode 3699, reward 1595.0, memory_length 2000, epsilon 0.15731423139666081 total_time 730.0\n",
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      "episode 3899, reward 1836.0, memory_length 2000, epsilon 0.1423438029572661 total_time 734.0\n",
      "episode 3909, reward 1412.0, memory_length 2000, epsilon 0.141633860278224 total_time 721.0\n",
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      "episode 3929, reward 1193.0, memory_length 2000, epsilon 0.14022457982170855 total_time 724.0\n",
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      "episode 3989, reward 1499.0, memory_length 2000, epsilon 0.13608031718169336 total_time 722.0\n",
      "episode 3999, reward 1457.0, memory_length 2000, epsilon 0.13540161376828327 total_time 721.0\n",
      "Saving Model 4000\n",
      "episode 4009, reward 1364.0, memory_length 2000, epsilon 0.13472629540226955 total_time 723.0\n",
      "episode 4019, reward 775.0, memory_length 2000, epsilon 0.1340543452006579 total_time 729.0\n",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 4449, reward 1402.0, memory_length 2000, epsilon 0.10812038464016717 total_time 721.0\n",
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      "episode 4879, reward 1788.0, memory_length 2000, epsilon 0.08720357074020693 total_time 723.0\n",
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      "episode 4909, reward 1787.0, memory_length 2000, epsilon 0.08590527871219816 total_time 728.0\n",
      "episode 4919, reward 1443.0, memory_length 2000, epsilon 0.08547682434716262 total_time 729.0\n",
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      "episode 4999, reward 1335.0, memory_length 2000, epsilon 0.08212523012503205 total_time 721.0\n",
      "Saving Model 5000\n",
      "episode 5009, reward 1922.0, memory_length 2000, epsilon 0.08171562883097767 total_time 721.0\n",
      "episode 5019, reward 1791.0, memory_length 2000, epsilon 0.08130807043190014 total_time 723.0\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 5329, reward 1756.0, memory_length 2000, epsilon 0.0696334655697859 total_time 721.0\n",
      "episode 5339, reward 1717.0, memory_length 2000, epsilon 0.06928616721137094 total_time 723.0\n",
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      "episode 5369, reward 1733.0, memory_length 2000, epsilon 0.06825463056925578 total_time 721.0\n",
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      "episode 5999, reward 1819.0, memory_length 2000, epsilon 0.049811470006787505 total_time 722.0\n",
      "Saving Model 6000\n",
      "episode 6009, reward 1481.0, memory_length 2000, epsilon 0.04956303426368557 total_time 722.0\n",
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    {
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     "text": [
      "episode 6199, reward 1509.0, memory_length 2000, epsilon 0.045071281909517265 total_time 724.0\n",
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      "episode 6859, reward 1679.0, memory_length 2000, epsilon 0.03240281426095298 total_time 725.0\n",
      "episode 6869, reward 1871.0, memory_length 2000, epsilon 0.03224120455061084 total_time 723.0\n",
      "episode 6879, reward 1872.0, memory_length 2000, epsilon 0.03208040087206167 total_time 726.0\n",
      "episode 6889, reward 1689.0, memory_length 2000, epsilon 0.03192039920520517 total_time 728.0\n",
      "episode 6899, reward 1980.0, memory_length 2000, epsilon 0.03176119554999133 total_time 727.0\n",
      "episode 6909, reward 1665.0, memory_length 2000, epsilon 0.031602785926320466 total_time 722.0\n",
      "episode 6919, reward 1494.0, memory_length 2000, epsilon 0.03144516637394371 total_time 721.0\n",
      "episode 6929, reward 1638.0, memory_length 2000, epsilon 0.03128833295236411 total_time 728.0\n",
      "episode 6939, reward 1347.0, memory_length 2000, epsilon 0.031132281740737917 total_time 721.0\n",
      "episode 6949, reward 1665.0, memory_length 2000, epsilon 0.030977008837776713 total_time 724.0\n",
      "episode 6959, reward 1522.0, memory_length 2000, epsilon 0.030822510361649826 total_time 724.0\n",
      "episode 6969, reward 1409.0, memory_length 2000, epsilon 0.030668782449887338 total_time 725.0\n",
      "episode 6979, reward 1801.0, memory_length 2000, epsilon 0.03051582125928343 total_time 724.0\n",
      "episode 6989, reward 1774.0, memory_length 2000, epsilon 0.030363622965800367 total_time 729.0\n",
      "episode 6999, reward 2061.0, memory_length 2000, epsilon 0.030212183764472877 total_time 721.0\n",
      "Saving Model 7000\n",
      "episode 7009, reward 1816.0, memory_length 2000, epsilon 0.030061499869313068 total_time 721.0\n",
      "episode 7019, reward 1598.0, memory_length 2000, epsilon 0.029911567513215692 total_time 723.0\n",
      "episode 7029, reward 1926.0, memory_length 2000, epsilon 0.029762382947864045 total_time 728.0\n",
      "episode 7039, reward 1404.0, memory_length 2000, epsilon 0.029613942443636205 total_time 726.0\n",
      "episode 7049, reward 1724.0, memory_length 2000, epsilon 0.029466242289511866 total_time 728.0\n",
      "episode 7059, reward 1454.0, memory_length 2000, epsilon 0.029319278792979464 total_time 725.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 7069, reward 1689.0, memory_length 2000, epsilon 0.029173048279943936 total_time 725.0\n",
      "episode 7079, reward 1836.0, memory_length 2000, epsilon 0.029027547094634832 total_time 722.0\n",
      "episode 7089, reward 1854.0, memory_length 2000, epsilon 0.02888277159951494 total_time 723.0\n",
      "episode 7099, reward 1549.0, memory_length 2000, epsilon 0.028738718175189356 total_time 721.0\n",
      "episode 7109, reward 1823.0, memory_length 2000, epsilon 0.028595383220314963 total_time 734.0\n",
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      "episode 7129, reward 1774.0, memory_length 2000, epsilon 0.028310854403266573 total_time 727.0\n",
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      "episode 7159, reward 1585.0, memory_length 2000, epsilon 0.027889360693021847 total_time 725.0\n",
      "episode 7169, reward 1936.0, memory_length 2000, epsilon 0.027750261926262603 total_time 724.0\n",
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      "episode 7359, reward 1890.0, memory_length 2000, epsilon 0.02523533712014747 total_time 727.0\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 7939, reward 1838.0, memory_length 2000, epsilon 0.018882683382569338 total_time 722.0\n",
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      "episode 7999, reward 1969.0, memory_length 2000, epsilon 0.018324615750025048 total_time 725.0\n",
      "Saving Model 8000\n",
      "episode 8009, reward 1873.0, memory_length 2000, epsilon 0.018233221347685697 total_time 722.0\n",
      "episode 8019, reward 2044.0, memory_length 2000, epsilon 0.018142282776829687 total_time 724.0\n",
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     ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 8809, reward 1928.0, memory_length 2000, epsilon 0.012222093773158674 total_time 727.0\n",
      "episode 8819, reward 1544.0, memory_length 2000, epsilon 0.012161135826156058 total_time 725.0\n",
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      "episode 8849, reward 1693.0, memory_length 2000, epsilon 0.011980080101480892 total_time 721.0\n",
      "episode 8859, reward 1620.0, memory_length 2000, epsilon 0.011920329202701425 total_time 731.0\n",
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      "episode 8879, reward 1532.0, memory_length 2000, epsilon 0.011801719945369903 total_time 722.0\n",
      "episode 8889, reward 1949.0, memory_length 2000, epsilon 0.011742858621580235 total_time 723.0\n",
      "episode 8899, reward 1895.0, memory_length 2000, epsilon 0.011684290869867704 total_time 725.0\n",
      "episode 8909, reward 1309.0, memory_length 2000, epsilon 0.011626015226035489 total_time 721.0\n",
      "episode 8919, reward 1817.0, memory_length 2000, epsilon 0.011568030233189445 total_time 724.0\n",
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      "episode 8959, reward 1782.0, memory_length 2000, epsilon 0.011338967887344734 total_time 726.0\n",
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      "episode 8979, reward 1997.0, memory_length 2000, epsilon 0.011226143271752802 total_time 724.0\n",
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      "episode 8999, reward 1608.0, memory_length 2000, epsilon 0.011114441279843205 total_time 723.0\n",
      "Saving Model 9000\n",
      "episode 9009, reward 1782.0, memory_length 2000, epsilon 0.011059007772698278 total_time 726.0\n",
      "episode 9019, reward 1503.0, memory_length 2000, epsilon 0.011003850741323658 total_time 727.0\n",
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      "episode 9249, reward 1982.0, memory_length 2000, epsilon 0.009808460003419995 total_time 727.0\n",
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     "text": [
      "episode 9679, reward 1509.0, memory_length 2000, epsilon 0.007910929457080072 total_time 728.0\n",
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      "episode 9999, reward 1774.0, memory_length 2000, epsilon 0.006741249401800625 total_time 724.0\n",
      "Saving Model 10000\n",
      "episode 10009, reward 1725.0, memory_length 2000, epsilon 0.006707627280141827 total_time 723.0\n",
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     ]
    },
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      "episode 10539, reward 1920.0, memory_length 2000, epsilon 0.005146131559545177 total_time 724.0\n",
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      "Saving Model 11000\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "episode 11389, reward 1925.0, memory_length 2000, epsilon 0.003364385323933774 total_time 722.0\n",
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      "Saving Model 12000\n",
      "episode 12009, reward 1883.0, memory_length 2000, epsilon 0.002467598175404897 total_time 727.0\n",
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    },
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     "text": [
      "episode 12239, reward 1586.0, memory_length 2000, epsilon 0.0021995334703221957 total_time 721.0\n",
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      "episode 12999, reward 1541.0, memory_length 2000, epsilon 0.0015041760586242804 total_time 726.0\n",
      "Saving Model 13000\n",
      "episode 13009, reward 2143.0, memory_length 2000, epsilon 0.0014966739492340226 total_time 724.0\n",
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      "episode 13079, reward 1305.0, memory_length 2000, epsilon 0.0014451964717519742 total_time 721.0\n"
     ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 13089, reward 1802.0, memory_length 2000, epsilon 0.0014379885242784493 total_time 721.0\n",
      "episode 13099, reward 1968.0, memory_length 2000, epsilon 0.0014308165265929267 total_time 723.0\n",
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      "episode 13119, reward 1429.0, memory_length 2000, epsilon 0.0014165796642788893 total_time 723.0\n",
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     ]
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    {
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     "output_type": "stream",
     "text": [
      "episode 13939, reward 1553.0, memory_length 2000, epsilon 0.0009401134485367081 total_time 723.0\n",
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      "Saving Model 14000\n",
      "episode 14009, reward 1427.0, memory_length 2000, epsilon 0.0009077786378036242 total_time 732.0\n",
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      "episode 14489, reward 1625.0, memory_length 2000, epsilon 0.0007140839681773742 total_time 729.0\n",
      "episode 14499, reward 1472.0, memory_length 2000, epsilon 0.0007105224595279177 total_time 726.0\n",
      "episode 14509, reward 1617.0, memory_length 2000, epsilon 0.0007069787139769558 total_time 727.0\n",
      "episode 14519, reward 1378.0, memory_length 2000, epsilon 0.0007034526429306651 total_time 725.0\n",
      "episode 14529, reward 1755.0, memory_length 2000, epsilon 0.0006999441582370858 total_time 731.0\n",
      "episode 14539, reward 1441.0, memory_length 2000, epsilon 0.0006964531721839179 total_time 726.0\n",
      "episode 14549, reward 1792.0, memory_length 2000, epsilon 0.0006929795974963283 total_time 721.0\n",
      "episode 14559, reward 1734.0, memory_length 2000, epsilon 0.0006895233473347682 total_time 722.0\n",
      "episode 14569, reward 1450.0, memory_length 2000, epsilon 0.0006860843352928048 total_time 732.0\n",
      "episode 14579, reward 1483.0, memory_length 2000, epsilon 0.0006826624753949572 total_time 722.0\n",
      "episode 14589, reward 1617.0, memory_length 2000, epsilon 0.0006792576820945501 total_time 723.0\n",
      "episode 14599, reward 1558.0, memory_length 2000, epsilon 0.0006758698702715732 total_time 726.0\n",
      "episode 14609, reward 1564.0, memory_length 2000, epsilon 0.0006724989552305546 total_time 721.0\n",
      "episode 14619, reward 1055.0, memory_length 2000, epsilon 0.0006691448526984429 total_time 725.0\n",
      "episode 14629, reward 1903.0, memory_length 2000, epsilon 0.0006658074788224999 total_time 725.0\n",
      "episode 14639, reward 1967.0, memory_length 2000, epsilon 0.0006624867501682045 total_time 725.0\n",
      "episode 14649, reward 504.0, memory_length 2000, epsilon 0.0006591825837171684 total_time 731.0\n",
      "episode 14659, reward 1905.0, memory_length 2000, epsilon 0.0006558948968650576 total_time 721.0\n",
      "episode 14669, reward 2099.0, memory_length 2000, epsilon 0.0006526236074195298 total_time 727.0\n",
      "episode 14679, reward 1808.0, memory_length 2000, epsilon 0.0006493686335981781 total_time 724.0\n",
      "episode 14689, reward 1467.0, memory_length 2000, epsilon 0.0006461298940264879 total_time 723.0\n",
      "episode 14699, reward 1819.0, memory_length 2000, epsilon 0.0006429073077358008 total_time 724.0\n",
      "episode 14709, reward 1553.0, memory_length 2000, epsilon 0.000639700794161292 total_time 723.0\n",
      "episode 14719, reward 1829.0, memory_length 2000, epsilon 0.0006365102731399544 total_time 727.0\n",
      "episode 14729, reward 1887.0, memory_length 2000, epsilon 0.0006333356649085975 total_time 724.0\n",
      "episode 14739, reward 2077.0, memory_length 2000, epsilon 0.0006301768901018495 total_time 723.0\n",
      "episode 14749, reward 2055.0, memory_length 2000, epsilon 0.000627033869750176 total_time 726.0\n",
      "episode 14759, reward 1760.0, memory_length 2000, epsilon 0.0006239065252779041 total_time 726.0\n",
      "episode 14769, reward 1603.0, memory_length 2000, epsilon 0.0006207947785012593 total_time 725.0\n",
      "episode 14779, reward 1944.0, memory_length 2000, epsilon 0.0006176985516264101 total_time 722.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode 14789, reward 1777.0, memory_length 2000, epsilon 0.0006146177672475235 total_time 723.0\n",
      "episode 14799, reward 1779.0, memory_length 2000, epsilon 0.0006115523483448293 total_time 728.0\n",
      "episode 14809, reward 1633.0, memory_length 2000, epsilon 0.0006085022182826951 total_time 722.0\n",
      "episode 14819, reward 1934.0, memory_length 2000, epsilon 0.0006054673008077113 total_time 724.0\n",
      "episode 14829, reward 1687.0, memory_length 2000, epsilon 0.0006024475200467823 total_time 722.0\n",
      "episode 14839, reward 1587.0, memory_length 2000, epsilon 0.0005994428005052322 total_time 724.0\n",
      "episode 14849, reward 1634.0, memory_length 2000, epsilon 0.0005964530670649156 total_time 724.0\n",
      "episode 14859, reward 1596.0, memory_length 2000, epsilon 0.0005934782449823409 total_time 721.0\n",
      "episode 14869, reward 1701.0, memory_length 2000, epsilon 0.0005905182598868013 total_time 730.0\n",
      "episode 14879, reward 1866.0, memory_length 2000, epsilon 0.0005875730377785148 total_time 721.0\n",
      "episode 14889, reward 1467.0, memory_length 2000, epsilon 0.0005846425050267752 total_time 730.0\n",
      "episode 14899, reward 1602.0, memory_length 2000, epsilon 0.0005817265883681118 total_time 731.0\n",
      "episode 14909, reward 1686.0, memory_length 2000, epsilon 0.000578825214904456 total_time 725.0\n",
      "episode 14919, reward 1640.0, memory_length 2000, epsilon 0.00057593831210132 total_time 721.0\n",
      "episode 14929, reward 2048.0, memory_length 2000, epsilon 0.0005730658077859833 total_time 727.0\n",
      "episode 14939, reward 1527.0, memory_length 2000, epsilon 0.0005702076301456883 total_time 722.0\n",
      "episode 14949, reward 1644.0, memory_length 2000, epsilon 0.0005673637077258456 total_time 723.0\n",
      "episode 14959, reward 1913.0, memory_length 2000, epsilon 0.0005645339694282461 total_time 722.0\n",
      "episode 14969, reward 1872.0, memory_length 2000, epsilon 0.0005617183445092846 total_time 726.0\n",
      "episode 14979, reward 1979.0, memory_length 2000, epsilon 0.0005589167625781924 total_time 727.0\n",
      "episode 14989, reward 1764.0, memory_length 2000, epsilon 0.0005561291535952752 total_time 723.0\n",
      "episode 14999, reward 1193.0, memory_length 2000, epsilon 0.0005533554478701629 total_time 722.0\n",
      "8199.945088386536\n"
     ]
    }
   ],
   "source": [
    "start_time = time.time()\n",
    "score_tracked = []\n",
    "\n",
    "for episode in range(n_episodes):\n",
    "\n",
    "    done = False\n",
    "    score = 0\n",
    "    track_reward = False\n",
    "\n",
    "    # reset at the start of each episode\n",
    "    env = CabDriver()\n",
    "    action_space, state_space, state = env.reset()\n",
    "    # Save the initial state so that reward can be tracked if initial state is [0,0,0]\n",
    "    initial_state = env.state_init\n",
    "\n",
    "\n",
    "    total_time = 0  # Total time driver rode in this episode\n",
    "    while not done:\n",
    "        # 1. Get a list of the ride requests driver got.\n",
    "        possible_actions_indices, actions = env.requests(state)\n",
    "        # 2. Pick epsilon-greedy action from possible actions for the current state.\n",
    "        action = agent.get_action(state, possible_actions_indices, actions)\n",
    "\n",
    "        # 3. Evaluate your reward and next state\n",
    "        reward, next_state, step_time = env.step(state, env.action_space[action], Time_matrix)\n",
    "        # 4. Total time driver rode in this episode\n",
    "        total_time += step_time\n",
    "        if (total_time > episode_time):\n",
    "            # if ride does not complete in stipu;ated time skip\n",
    "            # it and move to next episode.\n",
    "            done = True\n",
    "        else:\n",
    "            # 5. Append the experience to the memory\n",
    "            agent.append_sample(state, action, reward, next_state, done)\n",
    "            # 6. Train the model by calling function agent.train_model\n",
    "            agent.train_model()\n",
    "            # 7. Keep a track of rewards, Q-values, loss\n",
    "            score += reward\n",
    "            state = next_state\n",
    "\n",
    "    # store total reward obtained in this episode\n",
    "    rewards_per_episode.append(score)\n",
    "    episodes.append(episode)\n",
    "    \n",
    "\n",
    "    # epsilon decay\n",
    "    agent.epsilon = (1 - 0.00001) * np.exp(agent.epsilon_decay * episode)\n",
    "\n",
    "    # every 10 episodes:\n",
    "    if ((episode + 1) % 10 == 0):\n",
    "        print(\"episode {0}, reward {1}, memory_length {2}, epsilon {3} total_time {4}\".format(episode,\n",
    "                                                                         score,\n",
    "                                                                         len(agent.memory),\n",
    "                                                                         agent.epsilon, total_time))\n",
    "    # Save the Q_value of the state, action pair we are tracking\n",
    "    if ((episode + 1) % 5 == 0):\n",
    "        agent.save_tracking_states()\n",
    "\n",
    "    # Total rewards per episode\n",
    "    score_tracked.append(score)\n",
    "\n",
    "    if(episode % 1000 == 0):\n",
    "        print(\"Saving Model {}\".format(episode))\n",
    "        agent.save(name=\"model_weights.pkl\")\n",
    "    \n",
    "elapsed_time = time.time() - start_time\n",
    "print(elapsed_time)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The 'total_time' above includes the 'last ride' time also in each episode. Although it exceeds 24*30 = 720, our code drops the last ride from the replay buffer. So the total ride time per episode is limited to < 720"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "agent.save(name=\"model_weights.pkl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tracking Convergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       " 602.08374,\n",
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       " 620.2181,\n",
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       " 636.56195,\n",
       " 636.2468,\n",
       " 632.32605,\n",
       " 646.10583,\n",
       " 606.54346,\n",
       " 616.9256,\n",
       " 599.3125,\n",
       " 606.47546,\n",
       " 643.4396,\n",
       " 607.65356,\n",
       " 620.7705,\n",
       " 624.19965,\n",
       " 601.80743,\n",
       " 624.0374,\n",
       " 578.3992,\n",
       " 576.6234,\n",
       " 629.2721,\n",
       " 637.4689,\n",
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       " 610.1699,\n",
       " 629.71704,\n",
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       " 603.8289,\n",
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       " 628.98157,\n",
       " 620.88873,\n",
       " 647.0967,\n",
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       " 592.138,\n",
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       " 596.9855,\n",
       " 618.2953,\n",
       " 588.31934,\n",
       " 625.28784,\n",
       " 605.56934,\n",
       " 647.191,\n",
       " 629.82623,\n",
       " 605.76587,\n",
       " 619.5135,\n",
       " 607.0701,\n",
       " 604.2787,\n",
       " 609.3356,\n",
       " 588.47595,\n",
       " 629.43066,\n",
       " 627.6762,\n",
       " 613.1858,\n",
       " 600.4866,\n",
       " 611.1347,\n",
       " 628.34045,\n",
       " 618.3073,\n",
       " 598.1847,\n",
       " 591.06256,\n",
       " 596.5237,\n",
       " 600.36475,\n",
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       " 591.7363,\n",
       " 590.7082,\n",
       " 586.9859,\n",
       " 566.2207,\n",
       " 577.5064,\n",
       " 579.1036,\n",
       " 574.1349,\n",
       " 572.65466,\n",
       " 579.36053,\n",
       " 598.3794,\n",
       " 585.3821,\n",
       " 562.38226,\n",
       " 554.0099,\n",
       " 545.8179,\n",
       " 568.15576,\n",
       " 618.62006,\n",
       " 605.7906,\n",
       " 616.06726,\n",
       " 601.76953,\n",
       " 624.51465,\n",
       " 599.0954,\n",
       " 590.87054,\n",
       " 579.94354,\n",
       " 611.86743,\n",
       " 605.5511,\n",
       " 609.5937,\n",
       " 594.9978,\n",
       " 648.31024,\n",
       " 642.0066,\n",
       " 648.4495,\n",
       " 571.54944,\n",
       " 597.4194,\n",
       " 628.0727,\n",
       " 622.26855,\n",
       " 608.5841,\n",
       " 620.8648,\n",
       " 588.6018,\n",
       " 599.1485,\n",
       " 571.1736,\n",
       " 596.49316,\n",
       " 566.33276,\n",
       " 569.13446,\n",
       " 572.6953,\n",
       " 566.2217,\n",
       " 600.7601,\n",
       " 594.5148,\n",
       " 590.31134,\n",
       " 612.7206,\n",
       " 604.2846,\n",
       " 623.7125,\n",
       " 639.63214,\n",
       " 610.0551,\n",
       " 614.7143,\n",
       " 606.3843,\n",
       " 594.12415,\n",
       " 631.96136,\n",
       " 579.05615,\n",
       " 587.87964,\n",
       " 608.82587,\n",
       " 609.74634,\n",
       " 648.4538,\n",
       " 641.24274,\n",
       " 601.5826,\n",
       " 607.1503,\n",
       " 603.7514,\n",
       " 593.0355,\n",
       " 610.79297,\n",
       " ...]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "agent.states_tracked"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "state_tracked_sample = [agent.states_tracked[i] for i in range(len(agent.states_tracked)) if agent.states_tracked[i] < 1000]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Plot the Q-Value convergence for state action pairs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(0, figsize=(16,7))\n",
    "plt.title('Q_value for state [0,0,0]  action (0,2)')\n",
    "xaxis = np.asarray(range(0, len(agent.states_tracked)))\n",
    "plt.semilogy(xaxis,np.asarray(agent.states_tracked))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### We are using log scale because the initial q_values are way to high compared to the steady state value (around 600)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. Track rewards per episode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "score_tracked_sample = [score_tracked[i] for i in range(len(score_tracked)) if (i % 4 == 0)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(0, figsize=(16,7))\n",
    "plt.title('Rewards per episode')\n",
    "xaxis = np.asarray(range(0, len(score_tracked_sample)))\n",
    "plt.plot(xaxis,np.asarray(score_tracked_sample))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### We can see from the above plot that the rewards converge at around 1500. Since the initial state is picked to be random for each episode, some initial states may be less rewarding than others inherently regardless of the model quality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Epsilon-decay sample function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "Try building a similar epsilon-decay function for your model.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "time = np.arange(0,15000)\n",
    "epsilon = []\n",
    "for i in range(0,15000):\n",
    "    epsilon.append((1 - 0.00001) * np.exp(-0.0005 * i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(time, epsilon)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}