Q_Reinforcement_Learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Q-Learning\n",
    "In the following two exercises, we will be using Q-Learning to solve two simple reinforcement learning problems. Each exercise has sections with ##TO DO## comments that you will have to change to make the code run."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# N-Armed Bandit Problem\n",
    "Imagine you are sitting infront of a slot machine with 10 buttons. When you press each button, you get a random reward that is generated from an unknown probability distribution. Each button has a different probability distribution with different means and variances. This means that given enough time, selecting the button with the highest mean will maximize your reward. However, you don't know which button this is. Below, you will implement an $\\epsilon$-greedy approach to maximize your reward at this slot machine.\n",
    "## $\\epsilon$ (epsilon)-greedy algorithm\n",
    "\"One very famous approach to solving reinforcement learning problems is the $\\epsilon$ (epsilon)-greedy algorithm, such that, with a probability $\\epsilon$, you will choose an action a at random (exploration), and the rest of the time (probability 1−$\\epsilon$) you will select the best lever based on what you currently know from past plays (exploitation). So most of the time you play greedy, but sometimes you take some risks and choose a random lever and see what happens.\"\n",
    "\n",
    "Experiment inspired by https://www.datacamp.com/community/tutorials/introduction-reinforcement-learning#implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import necessary packages\n",
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "np.random.seed(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#calculate the reward from the choice, mean and variance in the Q_values table\n",
    "def Reward(choice, buttons_mean, buttons_variance):\n",
    "    current_reward = np.random.normal(buttons_mean[choice],buttons_variance[choice])\n",
    "    return current_reward\n",
    "\n",
    "#Trial creates a new Q table to enact the Policy over \"it\" number of iterations\n",
    "def Trial(eps,num_buttons,buttons_mean,buttons_variance,it=1000):\n",
    "    Q_values = np.zeros(num_buttons) #initialize Q_values table\n",
    "    Q_tracker = np.zeros(num_buttons) #initialze tracking table\n",
    "    all_rewards = []\n",
    "    for i in range(it):\n",
    "        choice = Policy(eps,num_buttons,Q_values) #make choice\n",
    "        current_reward = Reward(choice,buttons_mean,buttons_variance) #get reward\n",
    "        all_rewards.append(current_reward) #store reward\n",
    "        Q_values,Q_tracker = UpdateQTable(choice,current_reward,Q_values,Q_tracker) #calculate new mean in Q_values table\n",
    "    return all_rewards #return rewards from the trials\n",
    "\n",
    "#Experiment now takes a list of epsilons to determine how different choices of greedy epsilons affect convergence of the Policy\n",
    "def Experiment(eps_list,num_buttons):\n",
    "    eps_rewards = []\n",
    "    for eps in eps_list: #iterate over different values of epsilon and run a trial for each\n",
    "        eps_rewards.append(Trial(eps,num_buttons,buttons_mean,buttons_variance))        \n",
    "    return eps_rewards #return all rewards for each epsilon value and trial\n",
    "    \n",
    "\n",
    "'''TO DO SECTION'''\n",
    "    \n",
    "#create an epsilon-greedy policy function that will allow our n-armed bandit to choose which button to press\n",
    "def Policy(eps,num_buttons,Q_values):\n",
    "    #initialize a random greedy probability\n",
    "    greedy_prob =  np.random.uniform(0, 1, 1)\n",
    "    if greedy_prob <= eps:\n",
    "        choice = np.random.randint(num_buttons)\n",
    "    else:\n",
    "        choice = np.argmax(Q_values,axis = 0)\n",
    "    return choice\n",
    "\n",
    "#write a function to figure out how to update the Q_values table\n",
    "#UpdateQTable updates both Q_values with a new current mean and also updates Q_tracker, tracking the number of times\n",
    "#Q_tracker[choice] has been chosen\n",
    "#return Q_value, Q_tracker as a tuple\n",
    "def UpdateQTable(choice,current_reward,Q_values,Q_tracker):\n",
    "    Q_tracker[choice] += 1\n",
    "    Q_values[choice] += current_reward / Q_tracker[choice]\n",
    "    return Q_values, Q_tracker"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps_list = [0.1, 0.5, 0.7] ###TO DO### choose 3 values of epsilon\n",
    "\n",
    "num_buttons = 10 #number of buttons or arms our machine has\n",
    "\n",
    "buttons_mean = [np.random.normal(100,10) for x in range(num_buttons)] #initialize mean of each button\n",
    "buttons_variance = [np.random.normal(5,2) for x in range(num_buttons)] #initialize variance of each button\n",
    "\n",
    "# run the experiment\n",
    "final_exp = Experiment(eps_list, num_buttons)\n",
    "\n",
    "#compute running average of reward\n",
    "for i in range(len(final_exp)):\n",
    "    for j in range(len(final_exp[0])):\n",
    "        final_exp[i][j] = np.mean(final_exp[i][:j+1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1080x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the convergence of the reward's running average for various epsilon values\n",
    "#if you use more or less than 3 epsilons you will need to change the code below\n",
    "plt.figure(figsize=(15,12))\n",
    "plt.plot(final_exp[0],'b',label = 'First Epsilon')#blue\n",
    "plt.plot(final_exp[1],'r',label = 'Second Epsilon')#red\n",
    "plt.plot(final_exp[2],'k',label = 'Third Epsilon')#black\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The self-driving taxi problem\n",
    "In this exercise, we are going to use Q-Learning to teach a self-driving taxi how to most efficiently pick up and drop off passengers. Imagine that the parking lot pictured below is our environment and the taxi is our agent: \n",
    "\n",
    "![alt text](https://storage.googleapis.com/lds-media/images/Reinforcement_Learning_Taxi_Env.width-1200.png \"Taxi Example\")\n",
    "\n",
    "In this environment, there are 5 rows and 5 columns that the taxi can move between. Additionally, there are four cells labelled R, G, Y, B that represent the locations passengers can be picked up and dropped off at. Additionally, there are some barriers that the taxi cannot drive through. In the above example, the passenger is located in pickup location Y and would like to be dropped off at location R. \n",
    "\n",
    "There are a variety of states that our environment can be in at a given timestep. There are 5 rows the taxi can be located in, 5 columns the taxi can be located in, five locations the passenger can be located (the four locations plus the taxi), and four locations the passenger can be dropped off. This gives the environment a state space of size 500 (5 * 5 * 5 * 4). The action space of the environment is much simpler, with only 6 options:\n",
    "\n",
    "1. Move south (0)\n",
    "2. Move north (1)\n",
    "3. Move east (2)\n",
    "4. Move west (3)\n",
    "5. Pickup passenger (4)\n",
    "6. Dropoff passenger (5)\n",
    "\n",
    "The 'rules' for the environment are as follows: \n",
    "- Every timestep, the agent gets -1 point.\n",
    "- The agent gets +20 points if it successfully drops off a passenger in the correct location.\n",
    "- The agent gets -10 points if it tries to pick up a passenger in an incorrect cell.\n",
    "- The agent gets -10 points if it tries to drop off a passenger at the incorrect cell. \n",
    "\n",
    "Using this information, we will use reinforcement Q-learning to teach our agent how to most efficiently pick up and drop off passengers.\n",
    "\n",
    "You will have to change all of the ##TO DO## comments to make the code run properly.\n",
    "\n",
    "This exercise borrows some of the code and examples from this [blog post](https://www.learndatasci.com/tutorials/reinforcement-q-learning-scratch-python-openai-gym/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we will define a classes to help us keep track of the environment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from collections import namedtuple\n",
    "\n",
    "# Will be used to keep track of the environment's state\n",
    "State = namedtuple('State', ['row', 'col', 'passenger', 'destination'])\n",
    "\n",
    "# Class to display and update environment state. Keeps track of points and whether or not problem is solved.\n",
    "class Environment(object):\n",
    "    \n",
    "    def __init__(self):\n",
    "        \n",
    "        # Initialize a random state\n",
    "        self.row, self.col, self.passenger, self.destination = self.reset()\n",
    "        self.state = State(self.row, self.col, self.passenger, self.destination) # Hint: Look at the namedtuple above to see what we want to store in our state.\n",
    "        \n",
    "        # Define walls and pickup/dropoff locations\n",
    "        self.walls = [(0, 1), (3, 0), (4, 0), (3, 2), (4, 2)]\n",
    "            \n",
    "        # Dictionary that will map the passenger's state to a location on the map\n",
    "        self.locs = [(0, 0), (0, 4), (4, 0), (4, 3), (-1, -1)]\n",
    "        self.loc_dict = dict(zip([0, 1, 2, 3, 4], self.locs))\n",
    "        \n",
    "        # Dictionary containing all possible states that will map a state to a row in the Q-table\n",
    "        self.state_space = self.populate_state_space()\n",
    "\n",
    "    \n",
    "    # Some inspiration from: https://github.com/openai/gym/blob/master/gym/envs/toy_text/taxi.py\n",
    "    def step(self, action):\n",
    "        \n",
    "        penalties = 0\n",
    "        points = -1\n",
    "        complete = False\n",
    "        col, row, passenger = self.col, self.row, self.passenger\n",
    "\n",
    "        if action == 0: # Step south\n",
    "            row = min(self.row + 1, 4)\n",
    "            \n",
    "        elif action == 1: # Step north\n",
    "            row = max(self.row - 1, 0)\n",
    "            \n",
    "        elif action == 2 and (self.row, self.col) not in self.walls: # Step east\n",
    "            col = min(self.col + 1, 4)\n",
    "            \n",
    "        elif action == 3 and (self.row, self.col - 1) not in self.walls: # Step west\n",
    "            col = max(self.col - 1, 0)\n",
    "            \n",
    "        elif action == 4: # Pickup passenger\n",
    "            if self.passenger != 4 and (self.row, self.col) == self.loc_dict[self.passenger]:\n",
    "                passenger = 4\n",
    "            else:\n",
    "                points += -10\n",
    "                penalties += 1\n",
    "                \n",
    "        elif action == 5: # Dropoff passenger\n",
    "            \n",
    "            # If holding the passenger and in the destination, the task is complete.\n",
    "            if self.passenger == 4 and (self.row, self.col) == self.loc_dict[self.destination]:\n",
    "                points += 20\n",
    "                complete = True\n",
    "            else:\n",
    "                points += -10\n",
    "                penalties += 1\n",
    "        \n",
    "        # Update location, points and state\n",
    "        self.row, self.col, self.passenger = row, col, passenger\n",
    "        self.points += points\n",
    "        self.penalties += penalties\n",
    "        self.complete = complete\n",
    "        self.state = State(self.row, self.col, self.passenger, self.destination)\n",
    "        \n",
    "        return self.state, points, complete\n",
    "        \n",
    "    def populate_state_space(self):\n",
    "        \n",
    "        space = []\n",
    "        \n",
    "        # Iterate through all possible state spaces to make dictionary that can be used as to create the Q-table\n",
    "        for row in range(5):    \n",
    "            for col in range(5):\n",
    "                for passenger in range(5):\n",
    "                    for destination in range(4):\n",
    "                        space.append(State(row=row, col=col, passenger=passenger, destination=destination))\n",
    "                        \n",
    "        return dict(zip(space, range(len(space))))\n",
    "        \n",
    "    \n",
    "    # Reset to initial random state\n",
    "    def reset(self):\n",
    "        row = np.random.randint(5)\n",
    "        col = np.random.randint(5)\n",
    "        # initialize this to 4 instead of 5 so passenger doesn't start in taxi\n",
    "        passenger = np.random.randint(4)\n",
    "        destination = np.random.randint(4)\n",
    "        \n",
    "        # Make sure passenger and destination aren't the same\n",
    "        while passenger == destination:\n",
    "            passenger = np.random.randint(4)\n",
    "            destination = np.random.randint(4)\n",
    "        \n",
    "        self.points = 0\n",
    "        self.penalties = 0\n",
    "        self.complete = False\n",
    "        self.row, self.col, self.passenger, self.destination = row, col, passenger, destination\n",
    "\n",
    "        return row, col, passenger, destination\n",
    "    \n",
    "    # Print out environment\n",
    "    def display(self, action=None):\n",
    "        loc_map = {self.loc_dict[self.passenger]: 'P',\n",
    "                   self.loc_dict[self.destination]: 'D',\n",
    "                   (self.row, self.col): 'T'}\n",
    "        \n",
    "        out = '+---------+\\n'\n",
    "        for row in range(5):\n",
    "            out += '|'\n",
    "            for col in range(5):\n",
    "\n",
    "                if (row, col) in loc_map:\n",
    "                    out += loc_map[(row, col)]\n",
    "                else: \n",
    "                    out += ' '\n",
    "                if (row, col) in self.walls or col == 4:\n",
    "                    out += '|'\n",
    "                else:\n",
    "                    out += ':'\n",
    "            out += '\\n'\n",
    "                \n",
    "        out += '+---------+\\n'\n",
    "        out += 'Points: {}\\n'.format(self.points)\n",
    "        \n",
    "        if action is not None:\n",
    "            \n",
    "            act_map = {0: 'Moved South',\n",
    "                       1: 'Moved North',\n",
    "                       2: 'Moved East',\n",
    "                       3: 'Moved West',\n",
    "                       4: 'Picked Up Passenger',\n",
    "                       5: 'Dropped Off Passenger'}\n",
    "            \n",
    "            out += 'Action: {}\\n'.format(act_map[action])\n",
    "            \n",
    "        return out\n",
    "    \n",
    "    def __repr__(self):\n",
    "        return(self.display())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, lets see how well we do by choosing random actions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 Epochs completed\n"
     ]
    }
   ],
   "source": [
    "from IPython.display import clear_output\n",
    "\n",
    "# Initialize environment\n",
    "env = Environment()\n",
    "\n",
    "# Lists to store points\n",
    "points = []\n",
    "eps = []\n",
    "errors = []\n",
    "\n",
    "for i in range(1, 1001):\n",
    "    \n",
    "    frames = []\n",
    "    epochs = 0\n",
    "    \n",
    "    # Repeat while the task is not complete\n",
    "    while not env.complete: ## TO DO ##: Hint: There is an attribute in the environment class that says whether or not the task is complete. \n",
    "        \n",
    "        # Take a random action\n",
    "        action = np.random.randint(6)\n",
    "        \n",
    "        env.step(action)## TO DO ## Replace with method in class that takes a step for us\n",
    "        frames.append(env.display(action) + 'Epochs: {}\\n'.format(epochs))\n",
    "\n",
    "        epochs += 1\n",
    "    \n",
    "    if i % 100 == 0:\n",
    "        clear_output(wait=True)\n",
    "        print('{} Epochs completed'.format(i))\n",
    "    points.append(env.points)\n",
    "    errors.append(env.penalties)\n",
    "    eps.append(epochs)\n",
    "    env.reset()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "| : | : : |\n",
      "| : : : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "|T| : | : |\n",
      "+---------+\n",
      "Points: -4128\n",
      "Action: Dropped Off Passenger\n",
      "Epochs: 977\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "%matplotlib inline\n",
    "from time import sleep\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# print out solution\n",
    "for frame in frames:\n",
    "    clear_output(wait=True)\n",
    "    print(frame)\n",
    "    sleep(.01)\n",
    "        \n",
    "plt.hist(points)\n",
    "plt.title('Distribution of Scores When Solving Problem Randomly')\n",
    "plt.show()\n",
    "\n",
    "plt.hist(eps)\n",
    "plt.title('Distribution of Timesteps Required to Solve Problem Randomly')\n",
    "plt.show()\n",
    "\n",
    "plt.hist(errors)\n",
    "plt.title('Distribution of Errors When Solving Problem Randomly')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, selecting actions at random isn't a good way to solve this problem. It can take up to 1000 epochs to find the passenger, pick them up, and drop them off at the correct location. Next, lets try implementing a Q-Learning function to see if it helps speed up the process. First, we will have to learn a Q function that maps state, action pairs to a reward. We can define this Q function as:\n",
    "\n",
    "$$\n",
    "Q(s, a) = (1-\\alpha)Q(s, a) + \\alpha(r + \\gamma \\max\\limits_{a} Q(s', a))\n",
    "$$\n",
    "\n",
    "where $a$ is the action we take, $s$ and $s'$ are the current and next state, respectively, r is the reward,  $\\alpha$ is the step size, and $\\gamma$ is the discount on future rewards. Recall that we also need an $\\epsilon$ hyperparameter that defines the probability with which we take a random action. This parameter will ensure that we both explore the entire state space and take actions that maximize reward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50000 Epochs completed\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "# Create an empty Q-table that is of size (state space by action space)\n",
    "q_table = np.zeros([500, 6])\n",
    "\n",
    "env = Environment()\n",
    "\n",
    "# Map each state to a unique id\n",
    "state_map = env.state_space\n",
    "\n",
    "# Hyperparameters\n",
    "alpha = 0.1\n",
    "gamma = 0.5\n",
    "epsilon = 0.1\n",
    "\n",
    "# For plotting metrics\n",
    "all_epochs = []\n",
    "all_penalties = []\n",
    "rewards = []\n",
    "\n",
    "for i in range(1, 50001):\n",
    "    \n",
    "    state = env.reset()\n",
    "    \n",
    "    epochs, penalties, points = 0, 0, 0\n",
    "    done = False\n",
    "    \n",
    "    while not env.complete:\n",
    "        \n",
    "        # Map the action to a location in the Q-table\n",
    "        state_num = state_map[state]\n",
    "        \n",
    "        # Take random action with probability epsilon\n",
    "        if np.random.uniform(0, 1) < epsilon:\n",
    "            action = np.random.randint(6)\n",
    "        \n",
    "        # Otherwise take the action that maximizes reward\n",
    "        else:\n",
    "            action = np.argmax(q_table[state_num]) \n",
    "\n",
    "        # Determine the state and reward given by an action\n",
    "        next_state, reward, _ = env.step(action) \n",
    "        \n",
    "        # Map the action to a location in the Q-table\n",
    "        next_num = state_map[next_state]\n",
    "        \n",
    "        # Look up the reward for the last time step\n",
    "        old_value = q_table[state_num, action]\n",
    "        \n",
    "        # Predict reward for the next timestep\n",
    "        next_max = np.max(q_table[next_num])\n",
    "        \n",
    "        # Update Q-Table with discounted future reward\n",
    "        new_value = (1 - alpha) * old_value + alpha * (reward + gamma * next_max)\n",
    "        q_table[state_num, action] = new_value\n",
    "        \n",
    "        state = next_state\n",
    "        epochs += 1\n",
    "    \n",
    "    rewards.append(env.points)\n",
    "    all_penalties.append(env.penalties)\n",
    "    all_epochs.append(epochs)\n",
    "    \n",
    "    if i % 100 == 0:\n",
    "        clear_output(wait=True)\n",
    "        print('{} Epochs completed'.format(i))\n",
    "\n",
    "plt.plot(range(50000), rewards)\n",
    "plt.title('Reward as model trains')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(range(50000), all_penalties)\n",
    "plt.title('Incorrect pickup/dropoff occurences')\n",
    "plt.show()\n",
    "\n",
    "plt.plot(range(50000), all_epochs)\n",
    "plt.title('Time required to solve problem')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "points = []\n",
    "eps = []\n",
    "errors = []\n",
    "\n",
    "all_frames = []\n",
    "\n",
    "for _ in range(1000):\n",
    "    \n",
    "    state = env.reset() ## TODO ## Reinitialize the environment\n",
    "    epochs, penalties, reward = 0, 0, 0\n",
    "    \n",
    "    frames = []\n",
    "    while not env.complete:\n",
    "        \n",
    "        state_num = state_map[state]\n",
    "\n",
    "        # Always take the action that maximizes reward\n",
    "        action = np.argmax(q_table[state_num])\n",
    "            \n",
    "        state, reward, _ = env.step(action)## TO DO ## Take a step according to the action\n",
    "\n",
    "        epochs += 1\n",
    "        frames.append(env.display(action))\n",
    "        \n",
    "    all_frames.append(frames)\n",
    "    \n",
    "    points.append(env.points)\n",
    "    errors.append(env.penalties)\n",
    "    eps.append(epochs)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "| : | : : |\n",
      "| : : : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "| | : |T: |\n",
      "+---------+\n",
      "Points: 7\n",
      "Action: Dropped Off Passenger\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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OeADYDZxbVXvmqHZJ0jgmDfeqevs4i04dZ/2LgYsHKUqSNBjfoSpJDTLcJalBhrskNWiml0JKmmPDvOR1y6VnDG3fmh0euUtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGeSnkAPx0Rkn7K4/cJalBhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgPzhM0j6G9aF4/u/W2eORuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDRroOvckW4BdwB5gd1UtT3IE8ClgKbAFeFtV/f1gZUqSpmM2jtz/ZVWdWFXLu/sXAOurahmwvrsvSXoBzcW0zEpgXXd7HXDWHOxDkjSBQcO9gM8nuSvJmq7t6KraBtB9P2qsDZOsSbIhyYadO3cOWIYkqd+gny1zclVtTXIUcGuSb0x1w6paC6wFWL58eQ1YhySpz0BH7lW1tfu+A7gRWAFsT3IMQPd9x6BFSpKmZ8bhnuQlSQ7dexv4V8D9wM3A6m611cBNgxYpSZqeQaZljgZuTLK3nz+vqr9OcidwXZJzgEeAtw5epiRpOmYc7lX1TeB1Y7R/Gzh1kKIkSYPxHaqS1CDDXZIaZLhLUoMMd0lqUBP/IHtY/8xXkvZXHrlLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNauKzZSS1YVifE7Xl0jOGst+55JG7JDXIcJekBjktI+mH3jA/NnyupoQ8cpekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkho0Z+Ge5PQkDybZnOSCudqPJGlfcxLuSRYA/x14E3A88PYkx8/FviRJ+5qrI/cVwOaq+mZVPQdcC6yco31JkkaZq4/8XQQ82nd/BPiZ/hWSrAHWdHf/IcmDA+zvSODxAbbfX7QyDnAs+6NWxgENjSX/ZaCxvHK8BXMV7hmjrX7gTtVaYO2s7CzZUFXLZ6OvYWplHOBY9ketjAMcy1TM1bTMCLCk7/5iYOsc7UuSNMpchfudwLIkxyb5EWAVcPMc7UuSNMqcTMtU1e4k7wH+F7AAuLKqNs7FvjqzMr2zH2hlHOBY9ketjAMcy6RSVZOvJUmaV3yHqiQ1yHCXpAbN23BPsiTJl5JsSrIxyXnDrmlQSRYk+T9JPjvsWgaR5GVJrk/yje7n87PDrmkmkvxm97t1f5JrkvzosGuaqiRXJtmR5P6+tiOS3Jrkoe774cOscarGGcuHu9+ve5PcmORlw6xxqsYaS9+y305SSY6cjX3N23AHdgPnV9VrgJOAcxv4iIPzgE3DLmIW/BHw11X1auB1zMMxJVkEvBdYXlWvpXdhwKrhVjUtVwGnj2q7AFhfVcuA9d39+eAq9h3LrcBrq+ongb8FLnyhi5qhq9h3LCRZArwReGS2djRvw72qtlXV3d3tXfQCZNFwq5q5JIuBM4BPDLuWQSQ5DPjnwBUAVfVcVT053Kpm7ADgxUkOAA5mHr1Xo6q+AjwxqnklsK67vQ446wUtaobGGktVfb6qdnd3b6P3Xpr93jg/F4DLgP/IqDd7DmLehnu/JEuB1wO3D7eSgXyM3g/3+WEXMqAfB3YCf9pNMX0iyUuGXdR0VdVjwB/SO5LaBjxVVZ8fblUDO7qqtkHv4Ag4asj1zJZfAz437CJmKsmZwGNV9fXZ7Hfeh3uSQ4AbgPdV1dPDrmcmkvwSsKOq7hp2LbPgAOANwOVV9XrgO8yf0//v6+ajVwLHAq8AXpLkncOtSqMl+R16U7RXD7uWmUhyMPA7wO/Odt/zOtyTHEgv2K+uqk8Pu54BnAycmWQLvU/Q/IUknxxuSTM2AoxU1d6zqOvphf1884vAw1W1s6q+B3wa+Lkh1zSo7UmOAei+7xhyPQNJshr4JeAdNX/fsPMqegcQX+/+/hcDdyd5+aAdz9twTxJ687qbquqjw65nEFV1YVUtrqql9F60+2JVzcujxKr6FvBokuO6plOBB4ZY0kw9ApyU5ODud+1U5uELw6PcDKzubq8GbhpiLQNJcjrwn4Azq+qZYdczU1V1X1UdVVVLu7//EeAN3d/RQOZtuNM72n0XvaPce7qvNw+7KAHwG8DVSe4FTgQuGXI909adeVwP3A3cR+9vZd685T3JNcDXgOOSjCQ5B7gUeGOSh+hdmXHpMGucqnHG8t+AQ4Fbu7/9Px5qkVM0zljmZl/z92xGkjSe+XzkLkkah+EuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGvT/AYxTGsupTeItAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "# Print out a solution\n",
    "for frame in all_frames[-1]:\n",
    "    clear_output(wait=True)\n",
    "    print(frame)\n",
    "    sleep(0.5)\n",
    "\n",
    "plt.hist(points)\n",
    "plt.title('Trained Score Distribution')\n",
    "plt.show()\n",
    "\n",
    "plt.hist(eps)\n",
    "plt.title('Trained Epoch Distribution')\n",
    "plt.show()\n",
    "\n",
    "plt.hist(errors)\n",
    "plt.title('Trained Mistake Distribution')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "| : | : : |\n",
      "| : : : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "| | : |T: |\n",
      "+---------+\n",
      "Points: 7\n",
      "\n",
      "[18.  8.  8. 18.  8. 38.]\n"
     ]
    }
   ],
   "source": [
    "print(env)\n",
    "print(q_table[state_num])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Questions: \n",
    "1. Why do some indices other than the dropoff index (index 5) in the q_table have high rewards in the final state (printed above)? If we are only getting positive points for dropping off the passenger in this state, shouldn't all other rewards be negative?\n",
    "2. What specifically are each of the three hyperparameters ($\\alpha$, $\\gamma$ and $\\epsilon$) accomplishing?\n",
    "3. Is the trained model being as efficient as possible? Is it taking any incorrect steps after training?\n",
    "4. If you move some of the walls in the environment by changing the env.walls attribute, will the trained agent still be able to accomplish the task? Why or why not?\n",
    "\n",
    "# Answers:\n",
    "1. This is because when we update the Q-Table, we are updating it with the reward for our previous move and the expected reward from the next move. In the Q-Table above, when we move south or east, the next move we drop off the passenger, meaning we get 20 points. As a result, we see high values for indices 0 and 3 in the above table even though dropping off the passenger is the only action that would give us points in this state. \n",
    "2. Alpha is telling us how much to care about past/future Q-Table values. We see this because we are weighting the old Q-Table value by (1- alpha) and the next value by just alpha. Gamma is the discount on future rewards. We multiply the future reward by gamma so we don't overvalue the reward given by the next action. Epsilon is the probability that we take a random action. We want to make sure that our agent both explores the environment but also exploits the information that it already knows. Putting in the epsilon term ensures that all possible actions will eventually be explored. \n",
    "3. Yes, after training, the agent takes no incorrect actions, suggesting that our training has allowed the agent to explore and learn the entire state space. \n",
    "4. If we completely remove the walls, the agent will still be able to accomplish the task. This is because the agent can still take all optimal actions without any problems. However, if we move some of the walls to new locations, the agent won't be able to accomplish the task without retraining. This is because it has learned where the walls are during training. Adding walls will lead to repeated movements into the wall if the a wall is blocking an 'optimal' action as defined in the Q-Table."
   ]
  }
 ],
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