session3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Session 3: GET a Taxi with Temporal Difference Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Colab Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# #uncomment only if you're running from google colab\n",
    "# !git clone https://github.com/Datatouille/rl-workshop\n",
    "# !mv rl-workshop/* .\n",
    "# !ls\n",
    "# !pip install gym #For full installations, see https://github.com/openai/gym#installation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import gym\n",
    "import numpy as np\n",
    "from collections import defaultdict\n",
    "import matplotlib.pyplot as plt\n",
    "import pickle\n",
    "from tqdm import trange\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "from random import random\n",
    "from datetime import datetime\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "#cross check with our solutions once you finish\n",
    "from solutions.agents import TaxiAgent, BJAgent\n",
    "\n",
    "MODEL_PATH = 'models/'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Recap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Monte Carlo Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For an arbitrary number of episodes, do:\n",
    "* **Step 1** Run the episode until the end and get a list of transitions $[(s_0,a_0,r_1,s_1), (s_1,a_1,r_2,s_2),...]$ with a random policy\n",
    "* **Step 2** Loop through those transition tuples,\n",
    "    * **Step 2.1** Count number of times a state-action pair appears in the current episode `n_q` (only if it is the first time we saw this state-action pair)\n",
    "    * **Step 2.2** Calculate discounted rewards from the current transition until the end `g` (only if it is the first time we saw this state-action pair)\n",
    "    * **Step 2.3** Add learning rate times the difference between the discounted rewards we just calculate `g` and the existing action value `q`\n",
    "* **Step 3** Update the current policy after a few episodes or after we have trained all episodes\n",
    "\n",
    "**Conceptual Assignment** Is this good enough? How can we do better?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mc_control_glie(self,n_episode=500000,lr=0.,update_every=1):\n",
    "    for t in trange(n_episode):\n",
    "        traversed = []\n",
    "        e = self.get_epsilon(t)\n",
    "        \n",
    "        #step 1\n",
    "        transitions = self.run_episode(e)\n",
    "        states,actions,rewards,next_states,dones = zip(*transitions)\n",
    "\n",
    "        #step 2\n",
    "        for i in range(len(transitions)):\n",
    "            traversed.append((states[i],actions[i]))\n",
    "            #step 2.1\n",
    "            self.n_q[states[i]][actions[i]]+=1\n",
    "            #step 2.2\n",
    "            discounts = np.array([self.gamma**j for j in range(len(transitions)+1)])\n",
    "            g = sum(rewards[i:]*discounts[:-(1+i)])\n",
    "            #step 2.3\n",
    "            alpha = lr if lr > 0 else (1/self.n_q[states[i]][actions[i]])\n",
    "            self.q[states[i]][actions[i]]+= alpha * (g - self.q[states[i]][actions[i]])\n",
    "\n",
    "        #step 3\n",
    "        if t % int(update_every * n_episode - 1)==0:\n",
    "            self.update_policy_q()\n",
    "\n",
    "    self.update_policy_q()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What Can We Improve About Monte Carlo: Temporal Difference Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Temporal difference (TD) learning is another value-based method for solving a reinforcement learning problem. Main differences between this and the Monte Carlo method we learned are that:\n",
    "\n",
    "* TD updates the Q-values at every time step; we do not need to run an entire episode beforehand\n",
    "* TD updates the policy at every timestep\n",
    "\n",
    "That is probably why it is called **temporal difference** learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Taxi-v2](https://github.com/openai/gym/blob/master/gym/envs/toy_text/taxi.py)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taxi-v2 is a reinforcment learning environment described in [Dietterich (2000)](https://arxiv.org/abs/cs/9905014) to demonstrate some issues with hierarchical reinforcement learning. The environment features a 5x5 grid with four locations denoted as red, blue, green and yellow. Our agent is a taxi started at any random position. The goal of the environment is to go pick up a passenger at an arbitrary location then send them to their destination as fast as possible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make('Taxi-v2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Coding Assignment** Find out what are the following elements\n",
    "\n",
    "* States:\n",
    "* Actions:\n",
    "* Rewards: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nUse this cell to try execute the following functions:\\n* env.reset() - reset the environment and return the current state\\n* env.step(action) - take an action at the current state; returns a tuple of (state, reward, done, info)\\n'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Use this cell to try execute the following functions:\n",
    "* env.reset() - reset the environment and return the current state\n",
    "* env.step(action) - take an action at the current state; returns a tuple of (state, reward, done, info)\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Observation Space (State Space)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The state is a single integer from 0 to 499. This is a result of all combinations of:\n",
    "* 25 taxi positions\n",
    "* 5 possible locations of the passenger (including the case when the passenger is the taxi)\n",
    "* 4 destination locations. \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Discrete(500)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.observation_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "492"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.reset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Action Space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 6 discrete deterministic actions:\n",
    "- 0: move south\n",
    "- 1: move north\n",
    "- 2: move east \n",
    "- 3: move west \n",
    "- 4: pickup passenger\n",
    "- 5: dropoff passenger"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Discrete(6)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.action_space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reward"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* -1 for each action; to finish the task as fast as possible\n",
    "* +20 for delivering passenger\n",
    "* -10 for doing `pickup` (4) and `dropoff` (5) illegally\n",
    "* No penalty for illegal move (the taxi will remain at the same tile)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State: 271\n",
      "Action: 0, Next state: 371, Reward: -1\n"
     ]
    }
   ],
   "source": [
    "print(f'State: {env.reset()}')\n",
    "next_tuple = env.step(0)\n",
    "print(f'Action: 0, Next state: {next_tuple[0]}, Reward: {next_tuple[1]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(471, -1, False, {'prob': 1.0})"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.step(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rendering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- blue: passenger\n",
    "- magenta: destination\n",
    "- yellow: empty taxi\n",
    "- green: full taxi\n",
    "- other letters: locations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|R: | : :G|\n",
      "| : : : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "|\u001b[34;1mY\u001b[0m| : |\u001b[35m\u001b[43mB\u001b[0m\u001b[0m: |\n",
      "+---------+\n",
      "  (South)\n"
     ]
    }
   ],
   "source": [
    "env.render(mode = 'human')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make('Taxi-v2').env"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "frames = []\n",
    "illegal_moves = 0\n",
    "illegal_others = 0\n",
    "cumu_reward = 0\n",
    "\n",
    "#get initial state\n",
    "state = env.reset()\n",
    "\n",
    "while True:\n",
    "    #random action\n",
    "    action = env.action_space.sample()\n",
    "    \n",
    "    #step the environment to get (next_state, reward, done, info)\n",
    "    next_state,reward,done,info =  env.step(action)\n",
    "    \n",
    "    #keep records\n",
    "    if state==next_state: illegal_moves+=1\n",
    "    if reward==-10: illegal_others+=1\n",
    "    cumu_reward+=reward\n",
    "    frames.append({\n",
    "        'frame': env.render(mode='ansi'),\n",
    "        'state': state,\n",
    "        'action': action,\n",
    "        'reward': reward,\n",
    "        'cumulative_reward': cumu_reward,\n",
    "        'illegal_moves': illegal_moves,\n",
    "        'illegal_others': illegal_others\n",
    "        })\n",
    "    \n",
    "    #set current state to next state\n",
    "    state = next_state\n",
    "    \n",
    "    #stop game if done; there's a bug with taxi-v2 that cuts your game over if you have not solved it in 200 timesteps\n",
    "    if done: break\n",
    "#     if reward==20: break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#stolen from https://www.learndatasci.com/tutorials/reinforcement-q-learning-scratch-python-openai-gym/\n",
    "from IPython.display import clear_output\n",
    "import time\n",
    "\n",
    "def print_frames(frames,wait_time=0.2):\n",
    "    for i, frame in enumerate(frames):\n",
    "        clear_output(wait=True)\n",
    "        print(frame['frame'].getvalue())\n",
    "        print(f\"Timestep: {i + 1}\")\n",
    "        print(f\"State: {frame['state']}\")\n",
    "        print(f\"Action: {frame['action']}\")\n",
    "        print(f\"Reward: {frame['reward']}\")\n",
    "        print(f\"Cumulative Reward: {frame['cumulative_reward']}\")\n",
    "        print(f\"Illegal Moves: {frame['illegal_moves']}\")\n",
    "        print(f\"Illegal Others: {frame['illegal_others']}\")\n",
    "        time.sleep(wait_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "151"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(frames)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|R: | : :G|\n",
      "| : : : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "|\u001b[35m\u001b[42mY\u001b[0m\u001b[0m| : |B: |\n",
      "+---------+\n",
      "  (Dropoff)\n",
      "\n",
      "Timestep: 151\n",
      "State: 418\n",
      "Action: 5\n",
      "Reward: 20\n",
      "Cumulative Reward: -472\n",
      "Illegal Moves: 66\n",
      "Illegal Others: 38\n"
     ]
    }
   ],
   "source": [
    "print_frames(frames[:200])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Human Play"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Play a couple of rounds with your own natural neural networks to get a hang of the environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|R: | : :G|\n",
      "| : : : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "|Y| : |\u001b[35m\u001b[42mB\u001b[0m\u001b[0m: |\n",
      "+---------+\n",
      "  (Dropoff)\n",
      "Reward: 20\n",
      "Cumulative Reward: 7\n"
     ]
    }
   ],
   "source": [
    "state = env.reset()\n",
    "env.render()\n",
    "\n",
    "cumu_reward = 0\n",
    "\n",
    "while True:\n",
    "    action = int(input('Choose action: '))\n",
    "    state, reward, done, info = env.step(action)\n",
    "    cumu_reward+=reward\n",
    "    clear_output(wait=False)\n",
    "    env.render()\n",
    "    print(f'Reward: {reward}')\n",
    "    print(f'Cumulative Reward: {cumu_reward}')\n",
    "    if reward==20: break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 0: Down\n",
    "- 1: Up\n",
    "- 2: Right\n",
    "- 3: Left\n",
    "- 4: Pickup\n",
    "- 5: Dropoff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computer Play"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our benchmark will be the final cumulative reward, from now on called `score`, at the end of an episode over time. For instance, when we do 1,000 episodes, as our agent becomes smarter, the cumulative rewards should get better and better. OpenAI uses 100-episode average score as their benchmark for \"solving\" the environment. **The solving score for this environment is 8.5.**\n",
    "\n",
    "**Concept Assignment** Why is it a bad idea to use Monte Carlo method for this environment?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 200/200 [00:05<00:00, 37.89it/s]\n"
     ]
    }
   ],
   "source": [
    "scores = []\n",
    "ts = []\n",
    "illegal_moves = []\n",
    "illegal_others = []\n",
    "moving_scores = []\n",
    "moving_nb = 100\n",
    "solved_score = 8.5\n",
    "start_time = datetime.now()\n",
    "\n",
    "for i in trange(200):\n",
    "    #for the record\n",
    "    score = 0\n",
    "    t= 0\n",
    "    illegal_move = 0\n",
    "    illegal_other = 0\n",
    "    \n",
    "    #initiate state\n",
    "    state = env.reset()\n",
    "    while True:\n",
    "        \n",
    "        #get action\n",
    "        action = env.action_space.sample()\n",
    "        \n",
    "        #step environment\n",
    "        next_state, reward, done, info = env.step(action)\n",
    "        \n",
    "        #records\n",
    "        score+=reward\n",
    "        t+=1\n",
    "        if state==next_state: illegal_move+=1\n",
    "        if reward==-10: illegal_other+=1\n",
    "        \n",
    "        #move to next state\n",
    "        state = next_state\n",
    "        \n",
    "        #end if drop off at destination\n",
    "        if reward==20: break\n",
    "            \n",
    "    #record\n",
    "    scores.append(score)\n",
    "    ts.append(t)\n",
    "    illegal_moves.append(illegal_move)\n",
    "    illegal_others.append(illegal_other)\n",
    "    \n",
    "    if i > moving_nb:\n",
    "        moving_score = np.mean(scores[i-moving_nb:i])\n",
    "        moving_scores.append(moving_score)\n",
    "    else:\n",
    "        moving_scores.append(0)\n",
    "        \n",
    "    #break if solved\n",
    "    if moving_scores[-1] > solved_score: \n",
    "        print(f'Solved at Play {i}: {datetime.now() - start_time} Moving average: {moving_scores[-1]}')\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100-episode average score: -9447.97\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(scores)\n",
    "plt.plot(moving_scores)\n",
    "print(f'100-episode average score: {moving_scores[-1]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100-episode average timesteps: 2330.54\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts)\n",
    "print(f'100-episode average timesteps: {np.mean(ts[:-100])}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Illegal moves: 390; Illegal drop-offs/pickups: 254\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(illegal_moves)\n",
    "plt.plot(illegal_others)\n",
    "print(f'Illegal moves: {illegal_moves[-1]}; Illegal drop-offs/pickups: {illegal_others[-1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What Does A TD Agent Order at A Mexican Restaurant?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SARSA is the most basic of temporal difference learning. It got its name from the tuples we used for the learning:\n",
    "\n",
    "$$S_0 \\rightarrow A_0 \\rightarrow R_1 \\rightarrow S_1 \\rightarrow A_1 \\rightarrow R_2 \\rightarrow S_2 \\rightarrow ... \\rightarrow S_{t-1} \\rightarrow A_{t-1} \\rightarrow R_t \\rightarrow S_{t}$$\n",
    "\n",
    "Remember in Monte Carlo, you estimate the action values by:\n",
    "\n",
    "$$G_t = R_{t} + \\gamma R_{t+1} + ... $$\n",
    "\n",
    "$$Q(s_t,a_t) = \\frac{\\sum_{i=1}^{N(s_t,a_t)} G_i}{N(s_t,a_t)} = E[G(s_t,a_t)]$$\n",
    "\n",
    "where:\n",
    "* $G_t$ is discounted rewards\n",
    "* $R_t$ is the reward for each time step\n",
    "* $Q(s_t,a_t)$ is the action value for that state-action pair\n",
    "* $N(s_t,a_t)$ is the number of time we have seen that state-action pair\n",
    "\n",
    "We need to run the entire episode before updating Q because we need to calculate:\n",
    "\n",
    "$$G_t = R_{t} + \\gamma R_{t+1} + \\gamma^2 R_{t+2} + \\gamma^3 R_{t+3} + ... $$\n",
    "\n",
    "But actually\n",
    "\n",
    "$$G_{t+1} = R_{t+1} + \\gamma R_{t+2} + \\gamma^2 R_{t+3} + ...$$\n",
    "\n",
    "$$G_t = R_t + \\gamma (R_{t+1} + \\gamma R_{t+2} + \\gamma^2 R_{t+3} + ...) = R_t + \\gamma (G_{t+1}) = R_{t+1} + \\gamma Q(s_{t+1},a_{t+1})$$\n",
    "\n",
    "And since action value $Q(s,a)$ is **expected** discounted rewards, we can substitute $Q(s_{t+1},a_{t+1})$ for $G_{t+1}$. And with each time step, we update the action values as:\n",
    "\n",
    "$$Q(s_t,a_t) = Q(s_t,a_t) + \\alpha (R_{t+1} + \\gamma Q(s_{t+1},a_{t+1}) - Q(s_t,a_t))$$\n",
    "\n",
    "where $\\alpha$ is the learning rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fill in The Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import numpy as np\n",
    "# from collections import defaultdict\n",
    "# import sys\n",
    "# import random\n",
    "# from tqdm import trange\n",
    "\n",
    "# class TaxiAgent:\n",
    "#     def __init__(self, env, gamma = 0.8, alpha = 1e-1,\n",
    "#                  start_epsilon = 1, end_epsilon = 1e-2, epsilon_decay = 0.999):\n",
    "        \n",
    "#         self.env = env\n",
    "#         self.n_action = self.env.action_space.n\n",
    "#         self.gamma = gamma\n",
    "#         self.alpha = alpha\n",
    "        \n",
    "#         #action values\n",
    "#         self.q = defaultdict(lambda: np.zeros(self.n_action)) #action value\n",
    "        \n",
    "#         #epsilon greedy parameters\n",
    "#         self.start_epsilon = start_epsilon\n",
    "#         self.end_epsilon = end_epsilon\n",
    "#         self.epsilon_decay = epsilon_decay\n",
    "\n",
    "#     #get epsilon\n",
    "#     def get_epsilon(self,n_episode):\n",
    "#         epsilon = max(self.start_epsilon * (self.epsilon_decay ** n_episode), self.end_epsilon)\n",
    "#         return(epsilon)\n",
    "    \n",
    "#     #select action based on epsilon greedy\n",
    "#     def select_action(self,state,epsilon):\n",
    "#         #implicit policy; if we have action values for that state, choose the largest one, else random\n",
    "#         best_action = np.argmax(self.q[state]) if state in self.q else self.env.action_space.sample()\n",
    "#         if random.random() > epsilon:\n",
    "#             action = best_action\n",
    "#         else:\n",
    "#              action = self.env.action_space.sample()\n",
    "#         return(action)\n",
    "    \n",
    "#     def sarsa_update(self, state, action, reward, next_state, n_episode):\n",
    "#         #get next action\n",
    "#         next_action = self.select_action(next_state, self.get_epsilon(n_episode)) \n",
    "#         #get new q\n",
    "#         new_q = reward + (self.gamma * self.q[next_state][next_action])\n",
    "#         #calculate update equation\n",
    "#         self.q[state][action] = self.q[state][action] + (self.alpha * (new_q - self.q[state][action]))\n",
    "        \n",
    "#     def sarsa_max_update(self, state, action, reward, next_state):\n",
    "#         \"\"\"\n",
    "#         Implement your code here\n",
    "#         \"\"\"\n",
    "        \n",
    "#     def sarsa_expected_update(self, state, action, reward, next_state, n_episode):\n",
    "#         #get next action\n",
    "#         next_action = self.select_action(next_state, self.get_epsilon(n_episode)) \n",
    "#         #get current epsilon\n",
    "#         eps = self.get_epsilon(n_episode)\n",
    "#         #get q value of random portion\n",
    "#         random_q = eps * np.sum((1/self.n_action) * self.q[next_state])\n",
    "#         #get q value of best action\n",
    "#         best_q = (1-eps) * self.q[next_state][next_action]\n",
    "#         #get new q\n",
    "#         new_q = reward + self.gamma * (random_q+best_q)\n",
    "#         #calculate update equation\n",
    "#         self.q[state][action] = self.q[state][action] + (self.alpha * (new_q - self.q[state][action]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SARSA\n",
    "\n",
    "For every **timestep**\n",
    "* **Step 1** Given state $s_t$, choose an action $a_t$ using epsilon greedy policy\n",
    "* **Step 2** Take that action and observe next state ($s_{t+1}$) and reward ($r_{t+1}$)\n",
    "* **Step 3** Update the action value $Q(s_t,a_t)$ using the equation above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = TaxiAgent(env, gamma = 0.8, alpha = 1e-1,\n",
    "                 start_epsilon = 1, end_epsilon = 1e-2, epsilon_decay = 0.999)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 82%|████████▏ | 82495/100000 [00:37<00:07, 2194.31it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solved at Play 82695: 0:00:37.657127 Moving average: 8.56\n"
     ]
    }
   ],
   "source": [
    "scores = []\n",
    "ts = []\n",
    "illegal_moves = []\n",
    "illegal_others = []\n",
    "moving_scores = []\n",
    "\n",
    "moving_nb = 100\n",
    "solved_score = 8.5\n",
    "start_time = datetime.now()\n",
    "\n",
    "for i in trange(100000):\n",
    "    #for the record\n",
    "    score = 0\n",
    "    t= 0\n",
    "    illegal_move = 0\n",
    "    illegal_other = 0\n",
    "    \n",
    "    #initiate state\n",
    "    state = env.reset()\n",
    "    while True:\n",
    "        \n",
    "        #get action\n",
    "        action = a.select_action(state, a.get_epsilon(i))\n",
    "        \n",
    "        #step environment\n",
    "        next_state, reward, done, info = env.step(action)\n",
    "        \n",
    "        #update agent\n",
    "        a.sarsa_update(state, action, reward, next_state, i)\n",
    "        \n",
    "        #records\n",
    "        score+=reward\n",
    "        t+=1\n",
    "        if state==next_state: illegal_move+=1\n",
    "        if reward==-10: illegal_other+=1\n",
    "        \n",
    "        #move to next state\n",
    "        state = next_state\n",
    "        \n",
    "        #end if drop off at destination\n",
    "        if reward==20: break\n",
    "            \n",
    "    #record\n",
    "    scores.append(score)\n",
    "    ts.append(t)\n",
    "    illegal_moves.append(illegal_move)\n",
    "    illegal_others.append(illegal_other)\n",
    "    \n",
    "    if i > moving_nb:\n",
    "        moving_score = np.mean(scores[i-moving_nb:i])\n",
    "        moving_scores.append(moving_score)\n",
    "    else:\n",
    "        moving_scores.append(0)\n",
    "        \n",
    "    #break if solved\n",
    "    if moving_scores[-1] > solved_score: \n",
    "        print(f'Solved at Play {i}: {datetime.now() - start_time} Moving average: {moving_scores[-1]}')\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100-episode average score: 8.56\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(moving_scores[:2500])\n",
    "print(f'100-episode average score: {moving_scores[-1]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100-episode average timesteps: 23.061346796455034\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts)\n",
    "print(f'100-episode average timesteps: {np.mean(ts[:-100])}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Illegal moves: 1; Illegal drop-offs/pickups: 0\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(illegal_moves)\n",
    "plt.plot(illegal_others)\n",
    "print(f'Illegal moves: {illegal_moves[-1]}; Illegal drop-offs/pickups: {illegal_others[-1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q-learning aka SARSAMAX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q-learning or SARSAMAX is perhaps the most well-known RL algorithm due to Deepminds' [Playing Atari with Deep Reinforcement Learning](https://www.cs.toronto.edu/~vmnih/docs/dqn.pdf) paper in 2013. There are some significant contributions made by that paper such as using deep learning as function approximation instead of a dictionary, experience replay, and fixed target for learning. But the principle of the learning remains largely the same as the algorithm we will learn today.\n",
    "\n",
    "For every **timestep**\n",
    "* **Step 1** Given state $s_t$, choose an action $a_t$ using epsilon greedy policy\n",
    "* **Step 2** Update the action value $Q(s_t,a_t)$ using the following equation:\n",
    "\n",
    "$Q(s_t,a_t) = Q(s_t,a_t) + \\alpha (R_{t+1} + \\gamma max_{a}Q(s_{t+1},a) - Q(s_t,a_t))$\n",
    "\n",
    "where $max_{a}Q(s_{t+1},a)$ is the highest action value given state $s_{t+1}$. \n",
    "\n",
    "This is very similar to SARSA except for the fact that we will always choose the best action value as opposed to epsilon-greedy action selection of SARSA. For this reason, SARSA is called **on-policy** and Q-learning **off-policy**.\n",
    "\n",
    "**Coding Assignment** Implement Q-learning in `sarsa_max_update` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = TaxiAgent(env, gamma = 0.8, alpha = 1e-1,\n",
    "                 start_epsilon = 1, end_epsilon = 1e-2, epsilon_decay = 0.999)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solved at Play 4712: 0:00:05.267496 Moving average: 8.51\n"
     ]
    }
   ],
   "source": [
    "scores = []\n",
    "ts = []\n",
    "illegal_moves = []\n",
    "illegal_others = []\n",
    "moving_scores = []\n",
    "moving_nb = 100\n",
    "solved_score = 8.5\n",
    "start_time = datetime.now()\n",
    "\n",
    "for i in range(100000):\n",
    "    #for the record\n",
    "    score = 0\n",
    "    t= 0\n",
    "    illegal_move = 0\n",
    "    illegal_other = 0\n",
    "    \n",
    "    #initiate state\n",
    "    state = env.reset()\n",
    "    while True:\n",
    "        \n",
    "        #get action\n",
    "        action = a.select_action(state, a.get_epsilon(i))\n",
    "        \n",
    "        #step environment\n",
    "        next_state, reward, done, info = env.step(action)\n",
    "        \n",
    "        #update agent\n",
    "        a.sarsa_max_update(state, action, reward, next_state)\n",
    "        \n",
    "        #records\n",
    "        score+=reward\n",
    "        t+=1\n",
    "        if state==next_state: illegal_move+=1\n",
    "        if reward==-10: illegal_other+=1\n",
    "        \n",
    "        #move to next state\n",
    "        state = next_state\n",
    "        \n",
    "        #end if drop off at destination\n",
    "        if reward==20: break\n",
    "            \n",
    "    #record\n",
    "    scores.append(score)\n",
    "    ts.append(t)\n",
    "    illegal_moves.append(illegal_move)\n",
    "    illegal_others.append(illegal_other)\n",
    "    \n",
    "    if i > moving_nb:\n",
    "        moving_score = np.mean(scores[i-moving_nb:i])\n",
    "        moving_scores.append(moving_score)\n",
    "    else:\n",
    "        moving_scores.append(0)\n",
    "        \n",
    "    #break if solved\n",
    "    if moving_scores[-1] > solved_score: \n",
    "        print(f'Solved at Play {i}: {datetime.now() - start_time} Moving average: {moving_scores[-1]}')\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100-episode average score: 8.51\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(scores)\n",
    "plt.plot(moving_scores)\n",
    "print(f'100-episode average score: {moving_scores[-1]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100-episode average timesteps: 49.05701278994147\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts)\n",
    "print(f'100-episode average timesteps: {np.mean(ts[:-100])}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Illegal moves: 1; Illegal drop-offs/pickups: 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(illegal_moves)\n",
    "plt.plot(illegal_others)\n",
    "print(f'Illegal moves: {illegal_moves[-1]}; Illegal drop-offs/pickups: {illegal_others[-1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Expected SARSA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Expected SARSA is another way we can update the Q values, not with maximum action values but with all the actions value weighted by their probability (in our case of the epsilon-greedy policy).\n",
    "\n",
    "For every **timestep**\n",
    "* **Step 1** Given state $s_t$, choose an action $a_t$ using epsilon greedy policy\n",
    "* **Step 2** Update the action value $Q(s_t,a_t)$ using the following equation:\n",
    "\n",
    "$$Q(s_t,a_t) = Q(s_t,a_t) + \\alpha (R_{t+1} + \\gamma \\sum_{a}\\pi(a|s_{t+1})Q(s_{t+1},a) - Q(s_t,a_t))$$\n",
    "\n",
    "where $\\pi(a|s_{t+1})$ is the probability of taking an action $a$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solved at Play 27049: 0:00:30.621846 Moving average: 8.6\n"
     ]
    }
   ],
   "source": [
    "scores = []\n",
    "ts = []\n",
    "illegal_moves = []\n",
    "illegal_others = []\n",
    "moving_scores = []\n",
    "moving_nb = 100\n",
    "solved_score = 8.5\n",
    "start_time = datetime.now()\n",
    "\n",
    "for i in range(100000):\n",
    "    #for the record\n",
    "    score = 0\n",
    "    t= 0\n",
    "    illegal_move = 0\n",
    "    illegal_other = 0\n",
    "    \n",
    "    #initiate state\n",
    "    state = env.reset()\n",
    "    while True:\n",
    "        \n",
    "        #get action\n",
    "        action = a.select_action(state, a.get_epsilon(i))\n",
    "        \n",
    "        #step environment\n",
    "        next_state, reward, done, info = env.step(action)\n",
    "        \n",
    "        #update agent\n",
    "        a.sarsa_expected_update(state, action, reward, next_state, i)\n",
    "        \n",
    "        #records\n",
    "        score+=reward\n",
    "        t+=1\n",
    "        if state==next_state: illegal_move+=1\n",
    "        if reward==-10: illegal_other+=1\n",
    "        \n",
    "        #move to next state\n",
    "        state = next_state\n",
    "        \n",
    "        #end if drop off at destination\n",
    "        if reward==20: break\n",
    "            \n",
    "    #record\n",
    "    scores.append(score)\n",
    "    ts.append(t)\n",
    "    illegal_moves.append(illegal_move)\n",
    "    illegal_others.append(illegal_other)\n",
    "    \n",
    "    if i > moving_nb:\n",
    "        moving_score = np.mean(scores[i-moving_nb:i])\n",
    "        moving_scores.append(moving_score)\n",
    "    else:\n",
    "        moving_scores.append(0)\n",
    "        \n",
    "    #break if solved\n",
    "    if moving_scores[-1] > solved_score: \n",
    "        print(f'Solved at Play {i}: {datetime.now() - start_time} Moving average: {moving_scores[-1]}')\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100-episode average score: 8.6\n"
     ]
    },
    {
     "data": {
      "image/png": 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93NjpfYhIdkjqjGhmTwOxZvFZ4O5PhjILgEbgn2OU61JmNg+YB1BRUdHp/RSE5FEffj3dMXFERjp17QXzRJOBWiAiJ66kzoruPq2t9Wb2OeBjwFQ/djV2GxA9hGh4iBEnvhsoNbO80PqILt+6PouARQDV1dWdPrflW2h5ePdLGl0lmR64XgW5/NlFJ/PH44d1XYW60M+vn8S+Q/WZroZIVkvZ2dHMZgLfAi5294NRq5YCj5jZ3cAwoAp4nsgX3yozG0kkOcwBPu3ubma/JnLN5FFgLvBkquoNUHi05ZGvoasxmBm3XH56pqsR1wVVAzNdBZGsl8qv1vcBhcCK0EWy0t1vcPcNZvY48CqR7qyb3L0JwMxuBpYDucBid98Q9vVt4FEz+z7wEvBQCutN3tFrHrl87vzKVL6ViEiPlMrRVnGfmOfutwO3x4gvA5bFiG/m2IislMujCYBGchlfUdpO6QwxKCnI5WB9U2c3FxHpND3bKob8qORxbmV65jC/7YpxCW/Tt+jYM6Z++rlzE9s4y4cdi0hqKXnEcKTl0dCdn97SajhAcUFiT/lV6hCRZHTjs2Pm5IXRVo0xJoM60dxw8Sns/VAjl0SkJSWPGJ5s+iP+JPd3vODpm6vi43HmzkiVWJNBxerJamuucxE5cSl5xPBs81lU1j2S1vcsLUnwWY9J9jvpkoeIJEPXPE5Qyh0ikgwlDxERSZiSRzfzxI3n86M541P+Puq2EpFkKHl0M2dXlDF7fDnnVpZR0sbw22TP/amaQnZE/2K+NCXu/aEikiV0wbyb+tcbzk+ofMKpIEUtj99+a0pqdiwi3YpaHmnUpyj9ufruT57FN2ekb8ixiJwYlDzS6KvTTu3S/XkHZtQ4c3g/brr0+G6kWA2PVHVliUj2UfLIkK9ddir/+aULOr19she8s31KXRFJLV3zyJAvT63K6PsrdYhIMtTyOEH0K85v8Tov9/j0kejDFUXkxKXkkeUK8yIJ4ZVbpzPt9MFH4xX9SwDIzTmWRFonGBGReFKePMzs62bmZjYwvDYzu9fMasxsrZlNiCo718w2hZ+5UfFzzGxd2OZe66Ed9l1Z6/Yubo8e0od/+MwERoQkEc+4YX27rlIicsJIafIwsxHAdOCdqPAsIvOWVwHzgAdC2f7ArcAkIrMG3mpmZWGbB4AvRG03M5X1TpV0Zry+xfnMHNfySb23XTH2WF16Zv4VkW4i1S2Pe4Bv0XLqotnAEo9YCZSa2VBgBrDC3fe4+15gBTAzrOvr7ivd3YElwBUprndWGtqvONNVEJEskbLkYWazgW3u/kqrVeXAlqjXW0OsrfjWGPGM605zXaglISLplFTyMLOnzWx9jJ/ZwF8A3+2aana4PvPMbLWZrd61a1fK3++Gi09hRP/MfJtPNlf0CiOrysvUGhGRxCV1n4e7T4sVN7MzgJHAK+Eb8XDgRTObCGwDRkQVHx5i24BLWsV/E+LDY5SPVZ9FwCKA6urq9m+/TrOubh14W0fYztFXDe7DA9dO4IKqgSxb926X1ktEsl9Kuq3cfZ27D3L3SnevJNLVNMHd3wWWAteFUVeTgf3uvgNYDkw3s7JwoXw6sDysO2Bmk8Moq+uAJ1NR79ZyOnCu78mP9Jh1xlD6FGl4rogkLhN3mC8DLgdqgIPA5wHcfY+Z3Qa8EMp9z933hOUbgX8CioFfhZ8eR5clRCRbpCV5hNbHkWUHbopTbjGwOEZ8NTAuVfWLpyP9Xt01IXTkoYkiIp2lO8yTlKm7srsyZ1WfVNZ+IRGRKHowYpIyMUfHEV3V6lly/UR219Z3zc5E5ISg5NGGNkczdUI6e7j+aNTADpctKcijpL/+FESk49RtlUbpvArx5SmZfeS7iGQ3JY8eqvU9I9EvC/NyyOnIOGMRkU5S8khSIvd5pPp03l1HfolI9lHySFJCJ2yd3UUkSyh5dLGSNM7G19UX9EVEOkrJo4sV5ulXKiLZT2e6LjaoT1GmqyAiknJKHm3I68SIpUxd1nBXN5aIpI+SRxv+40sXdOn+0pVXdF1eRFJNyaMNpw/t226ZRObo6MqTuvKDiGSSkkcaqVtJRLKFkkcXy1SCUFeViKSTkkeSdM4WkRNRSpOHmX3JzF43sw1mdldU/BYzqzGzjWY2Iyo+M8RqzGx+VHykma0K8cfMrCCV9U4VtQ5EJFukLHmY2aXAbOAsdx8L/DDExwBzgLHATODHZpZrZrnA/cAsYAxwTSgLcCdwj7uPAvYC16eq3qnUpV1alt6n9IqIREtly+OLwB3ufhjA3XeG+GzgUXc/7O5vEpnLfGL4qXH3ze5eDzwKzLbIcKYpwC/C9g8DV6Sw3ikzaWT/TFdBRKRLpDJ5nApcGLqb/tfMzg3xcmBLVLmtIRYvPgDY5+6NreLdQuuuqHhdU0/ceD5Vg/ukvkIiImmQ1PRxZvY0MCTGqgVh3/2BycC5wONmdnIy79eB+swD5gFUVFSk8q2OvWcHy51doXnCRSR7JJU83H1avHVm9kXgl+7uwPNm1gwMBLYBI6KKDg8x4sR3A6VmlhdaH9HlW9dnEbAIoLq6ultcErhqQjmzxg3t8v3q2ruIZFIqu63+HbgUwMxOBQqA94GlwBwzKzSzkUAV8DzwAlAVRlYVELmovjQkn18DV4f9zgWeTGG9k9L6ovjdnxzPZWMGZ6YyIiIpklTLox2LgcVmth6oB+aGRLDBzB4HXgUagZvcvQnAzG4GlgO5wGJ33xD29W3gUTP7PvAS8FAK6y0iIu1IWfIII6Y+E2fd7cDtMeLLgGUx4puJjMbqdhJ5tlUqdY9aiMiJQneYJylTJ+3ukrRE5MSk5JFFXLcNikiaKHlkIVMnloikmJJHhs2fNZqSgtxObfvZySd1cW1ERDpGySNJyV56uOHiU3j1ezM79b5fnlrFOSfp5kMRST8ljy6m69giciJI5X0eJ6TuPlvgA9dO4KUt+zJdDRHp4ZQ8ktazmhqzzhjKrDO6/nEpInJiUfJIkXMryyjM69yF8I44krK8uzd1RCQrKXkkKd41jtuuGMfoIX0zXg8RkVTQBXMREUmYkoeIiCRMyaOL/GjOeFZ/J+70JiIiWUXJI0mfqo7MX1Vd2Z+BvQtT+l6Xn3Fs0kY9GFFEMknJI0nTxgzmrTs+SnlpMQDlZZF/i1Iw0urH157DGrVuRKQb0GirLnbPp8bz2027qBzYK9NVERFJmZS1PMxsvJmtNLOXzWy1mU0McTOze82sxszWmtmEqG3mmtmm8DM3Kn6Oma0L29xr3bjPpl9xPh87c1jK9t+7KJLvb7zklJS9h4hIe1LZ8rgL+Ct3/5WZXR5eXwLMIjJveRUwCXgAmGRm/YFbgWrAgTVmttTd94YyXwBWEZlpcCbwqxTWvdsqzMvlrTs+mulqiMgJLpXXPBw4cpdcP2B7WJ4NLPGIlUCpmQ0FZgAr3H1PSBgrgJlhXV93XxnmQF8CXJHCevco0feX62ZzEUmXVLY8/hxYbmY/JJKkzg/xcmBLVLmtIdZWfGuMuLRwrCev+3bqiUi2SCp5mNnTwJAYqxYAU4Gvuvu/mdkngYeAlA4VMrN5wDyAioqKVL6ViMgJLank4e5xk4GZLQG+El7+K/BgWN4GjIgqOjzEthG5JhId/02ID49RPlZ9FgGLAKqrq9WJIyKSIqm85rEduDgsTwE2heWlwHVh1NVkYL+77wCWA9PNrMzMyoDpwPKw7oCZTQ6jrK4DnkxhvUVEpB2pvObxBeBHZpYH1BG6k4iMlrocqAEOAp8HcPc9ZnYb8EIo9z133xOWbwT+CSgmMsrqhBxpJSLSXaQsebj774BzYsQduCnONouBxTHiq4FxXV1HERHpHD2eREREEqbkISIiCVPy6OF0Y6CIZIKSR5bQjYEikk5KHiIikjAlDxERSZiSh4iIJEzJQ0REEqbkISIiCVPyEBGRhCl5ZBHd8iEi6aLkkYV0y4eIpJqSRw+n1oaIZIKSR5ZQa0NE0knJQ0REEqbkkYXUlSUiqabkkUXUdSUi6ZJU8jCzT5jZBjNrNrPqVutuMbMaM9toZjOi4jNDrMbM5kfFR5rZqhB/zMwKQrwwvK4J6yuTqbOIiCQv2ZbHeuAq4NnooJmNAeYAY4GZwI/NLNfMcoH7gVnAGOCaUBbgTuAedx8F7AWuD/Hrgb0hfk8oJyIiGZRU8nD319x9Y4xVs4FH3f2wu78J1AATw0+Nu29293rgUWC2mRkwBfhF2P5h4IqofT0cln8BTA3lRUQkQ1J1zaMc2BL1emuIxYsPAPa5e2OreIt9hfX7Q/njmNk8M1ttZqt37drVRYciIiKt5bVXwMyeBobEWLXA3Z/s+ip1nrsvAhYBVFdXa9CRiEiKtJs83H1aJ/a7DRgR9Xp4iBEnvhsoNbO80LqILn9kX1vNLA/oF8oLaBJzEcmIVHVbLQXmhJFSI4Eq4HngBaAqjKwqIHJRfam7O/Br4Oqw/Vzgyah9zQ3LVwP/E8pLFF0GEpF0Snao7pVmthU4D3jKzJYDuPsG4HHgVeC/gJvcvSm0Km4GlgOvAY+HsgDfBr5mZjVErmk8FOIPAQNC/GvA0eG9IiKSGe12W7XF3Z8Anoiz7nbg9hjxZcCyGPHNREZjtY7XAZ9Ipp4iItK1dId5lnB3PZZERNJGyaOni3GtQ1c/RCTVlDxERCRhSh4iIpIwJQ8REUmYkoeIiCRMyaOn0/2SIpIBSh5ZQneYi0g6KXmIiEjClDxERCRhSh5xXHV2efuFREROUEoerXzu/EoAxpX3y2xFRES6MSUPERFJmJKHiIgkTMkjDo18FRGJT8lDREQSluxMgp8wsw1m1mxm1VHxy8xsjZmtC/9OiVp3TojXmNm9Fu5uM7P+ZrbCzDaFf8tC3EK5GjNba2YTkqlzttH95SKSCcm2PNYDVwHPtoq/D3zc3c8gMv/4z6LWPQB8gci85lXAzBCfDzzj7lXAMxybbnZWVNl5YXtpxYhMCCUikg5JJQ93f83dN8aIv+Tu28PLDUCxmRWa2VCgr7uv9MiZbglwRSg3G3g4LD/cKr7EI1YCpWE/EoceVSIiqZaOax5/Arzo7oeBcmBr1LqtIQYw2N13hOV3gcFhuRzYEmebFsxsnpmtNrPVu3bt6qr6i4hIK3ntFTCzp4EhMVYtcPcn29l2LHAnMD2RSrm7m1nCfTDuvghYBFBdXd2pPhx1/YiItK/d5OHu0zqzYzMbDjwBXOfub4TwNmB4VLHhIQbwnpkNdfcdoVtqZ9Q2I+JskzLq+BERiS8l3VZmVgo8Bcx39/87Eg/dUgfMbHIYZXUdcKT1spTIxXXCv9Hx68Koq8nA/qjuLRERyYBkh+peaWZbgfOAp8xseVh1MzAK+K6ZvRx+BoV1NwIPAjXAG8CvQvwO4DIz2wRMC68BlgGbQ/mfhO1FRCSD2u22aou7P0Gka6p1/PvA9+NssxoYFyO+G5gaI+7ATcnUU0REupbuMBcRkYQpefRwGhwmIpmg5NFKTz0X675AEUknJY84dJe2iEh8Sh4iIpIwJQ8REUmYkoeIiCRMyUNERBKm5JFFeupIMRHpeZQ8WsmG+yY0TkxEUk3JIw6N1BURiU/Jo4dzdVaJSAYoeWQJU2eViKSRkoeIiCRMyUNERBKm5CEiIglLdibBT5jZBjNrNrPqGOsrzKzWzL4RFZtpZhvNrMbM5kfFR5rZqhB/zMwKQrwwvK4J6yuTqbOIiCQv2ZbHeuAq4Nk46+/m2DSzmFkucD8wCxgDXGNmY8LqO4F73H0UsBe4PsSvB/aG+D2hXMrceOkpnH/KAGafVZ7KtxER6dGSSh7u/pq7b4y1zsyuAN4ENkSFJwI17r7Z3euBR4HZFnn++RTgF6Hcw8AVYXl2eE1YP9VS+Lz0of2KeeQLk+lXkp+qtxAR6fFScs3DzHoD3wb+qtWqcmBL1OutITYA2Ofuja3iLbYJ6/eH8iIikiF57RUws6eBITFWLXD3J+NstpBIF1RtOidVMrN5wDyAioqKtL2viMiJpt3k4e7TOrHfScDVZnYXUAo0m1kdsAYYEVVuOLAN2A2UmlleaF0ciRP+HQFsNbM8oF8oH6uui4BFANXV1SfErdfZ8CwuEel52k0eneHuFx4s6j/0AAAHB0lEQVRZNrOFQK273xdO/lVmNpJIUpgDfNrd3cx+DVxN5DrIXOBIq2ZpeP1cWP8/7jpltqZncYlIOiU7VPdKM9sKnAc8ZWbL2yofWhU3A8uB14DH3f3IBfVvA18zsxoi1zQeCvGHgAEh/jVgPiIiklFJtTzc/QngiXbKLGz1ehmwLEa5zURGY7WO1wGfSKaeIiLStVLSbSWZ0bsgjzPK+/HlqVWZroqIZDkljyySk2P8x5cuyHQ1ROQEoGdbiYhIwpQ8REQkYUoeIiKSMCUPERFJmJJHD6fbJUUkE5Q8REQkYUoeIiKSMCUPERFJmJKHiIgkTMlDREQSpuQhIiIJU/IQEZGEKXmIiEjClDx6uKL8yEeYo6kERSSNkp1J8BNmtsHMms2sutW6M83subB+nZkVhfg54XWNmd1rFjnrmVl/M1thZpvCv2UhbqFcjZmtNbMJydQ529x/7QS+MrWK04f2yXRVROQEkmzLYz1wFfBsdDDMVf5z4AZ3HwtcAjSE1Q8AXwCqws/MEJ8PPOPuVcAzHJtudlZU2XlhewmG9ivmq5ediqnlISJplFTycPfX3H1jjFXTgbXu/koot9vdm8xsKNDX3Ve6uwNLgCvCNrOBh8Pyw63iSzxiJVAa9iMiIhmSqmsepwJuZsvN7EUz+1aIlwNbo8ptDTGAwe6+Iyy/CwyO2mZLnG1ERCQD2p2G1syeBobEWLXA3Z9sY78XAOcCB4FnzGwNsL8jlXJ3N7OEnxdrZvOIdG1RUVGR6OYiItJB7SYPd5/Wif1uBZ519/cBzGwZMIHIdZDhUeWGA9vC8ntmNtTdd4RuqZ0hvg0YEWeb1nVdBCwCqK6u1sPKRURSJFXdVsuBM8ysJFw8vxh4NXRLHTCzyWGU1XXAkdbLUmBuWJ7bKn5dGHU1Gdgf1b0lIiIZkOxQ3SvNbCtwHvCUmS0HcPe9wN3AC8DLwIvu/lTY7EbgQaAGeAP4VYjfAVxmZpuAaeE1wDJgcyj/k7C9iIhkkHmWTkVXXV3tq1evznQ1RER6FDNb4+7V7ZXTHeYiIpKwrG15mNku4O1Obj4QeL8Lq9MdZfsx6vh6tmw/Pui+x3iSu3+kvUJZmzySYWarO9Js68my/Rh1fD1bth8f9PxjVLeViIgkTMlDREQSpuQR26JMVyANsv0YdXw9W7YfH/TwY9Q1DxERSZhaHiIikjAlj1bMbKaZbQyTT81vf4vuw8zeChNtvWxmq0Ms4Um2zGxuKL/JzObGe780HM9iM9tpZuujYl12PPEmJsvw8S00s23hM3zZzC6PWndLqOtGM5sRFY/5N2tmI81sVYg/ZmYF6Ts6MLMRZvZrM3vVIpPCfSXEs+kzjHeMWfM5xuXu+gk/QC6RR6acDBQArwBjMl2vBOr/FjCwVewuYH5Yng/cGZYvJ/JoGAMmA6tCvD+Rx8H0B8rCclmGjuciIg/UXJ+K4wGeD2UtbDurGxzfQuAbMcqOCX+PhcDI8Hea29bfLPA4MCcs/wPwxTQf31BgQljuA/whHEc2fYbxjjFrPsd4P2p5tDQRqHH3ze5eDzxKZDKqnizRSbZmACvcfY9HnlG2gmOzPaaVuz8L7GkV7pLjsbYnJkuLOMcXz2zgUXc/7O5vEnnW20Ti/M2Gb+BTgF+E7aN/V2nh7jvc/cWw/AHwGpG5eLLpM4x3jPH0uM8xHiWPlnr6xFMO/LeZrbHI3CaQ+CRb3f130FXH09bEZJl2c+i2WXykS4fEj28AsM/dG1vFM8LMKoGzgVVk6WfY6hghCz/HaEoe2eUCd59AZN73m8zsouiV4dtZ1gyvy7bjCR4ATgHGAzuAv81sdZJnZr2BfwP+3N0PRK/Lls8wxjFm3efYmpJHSx2eeKo7cvdt4d+dwBNEmsLvheY91rFJtrr776Crjmcb8Scmyxh3f8/dm9y9mcgUBBPDqkSPbzeRbp+8VvG0MrN8IifVf3b3X4ZwVn2GsY4x2z7HWJQ8WnoBqAqjGwqAOUQmo+r2zKyXmfU5sgxMB9aT+CRby4HpZlYWmtrTQ6y76JLj8bYnJsuYIyfV4EoinyFEjm+OmRWa2UigisjF4ph/s+Eb/a+Bq8P20b+rtAi/14eA19z97qhVWfMZxjvGbPoc48r0Ffvu9kNkxMcfiIx8WJDp+iRQ75OJjNB4BdhwpO5E+kyfATYBTwP9Q9yA+8NxrgOqo/b1p0Qu5NUAn8/gMf0LkSZ/A5G+3uu78niAaiL/qd8A7iPcNJvh4/tZqP9aIieaoVHlF4S6biRqVFG8v9nwN/F8OO5/BQrTfHwXEOmSWktkUriXQ12z6TOMd4xZ8znG+9Ed5iIikjB1W4mISMKUPEREJGFKHiIikjAlDxERSZiSh4iIJEzJQ0REEqbkISIiCVPyEBGRhP1/9Vzz5SVBrNIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(scores)\n",
    "plt.plot(moving_scores)\n",
    "print(f'100-episode average score: {moving_scores[-1]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100-episode average timesteps: 44.42756957328386\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts)\n",
    "print(f'100-episode average timesteps: {np.mean(ts[:-100])}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Illegal moves: 1; Illegal drop-offs/pickups: 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(illegal_moves)\n",
    "plt.plot(illegal_others)\n",
    "print(f'Illegal moves: {illegal_moves[-1]}; Illegal drop-offs/pickups: {illegal_others[-1]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "#export q\n",
    "# pickle.dump(dict(a.q), open(f'{MODEL_PATH}taxi_optimal_q.pkl','wb'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## See A Smart Agent Play"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "frames = []\n",
    "illegal_moves = 0\n",
    "illegal_others = 0\n",
    "cumu_reward = 0\n",
    "\n",
    "#get initial state\n",
    "state = env.reset()\n",
    "\n",
    "while True:\n",
    "    #best action\n",
    "    action = a.select_action(state, a.get_epsilon(1e6))\n",
    "    \n",
    "    #step the environment to get (next_state, reward, done, info)\n",
    "    next_state,reward,done,info =  env.step(action)\n",
    "    \n",
    "    #keep records\n",
    "    if state==next_state: illegal_moves+=1\n",
    "    if reward==-10: illegal_others+=1\n",
    "    cumu_reward+=reward\n",
    "    frames.append({\n",
    "        'frame': env.render(mode='ansi'),\n",
    "        'state': state,\n",
    "        'action': action,\n",
    "        'reward': reward,\n",
    "        'cumulative_reward': cumu_reward,\n",
    "        'illegal_moves': illegal_moves,\n",
    "        'illegal_others': illegal_others\n",
    "        })\n",
    "    \n",
    "    #set current state to next state\n",
    "    state = next_state\n",
    "    \n",
    "    #stop game if done; there's a bug with taxi-v2 that cuts your game over if you have not solved it in 200 timesteps\n",
    "    if reward==20: break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(frames)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|\u001b[35m\u001b[42mR\u001b[0m\u001b[0m: | : :G|\n",
      "| : : : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "|Y| : |B: |\n",
      "+---------+\n",
      "  (Dropoff)\n",
      "\n",
      "Timestep: 12\n",
      "State: 16\n",
      "Action: 5\n",
      "Reward: 20\n",
      "Cumulative Reward: 9\n",
      "Illegal Moves: 1\n",
      "Illegal Others: 0\n"
     ]
    }
   ],
   "source": [
    "print_frames(frames)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coding Assignment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The OpenAI scoreboard lists 9.7 as the high score. This requires you to do some hyperparameter tuning over time of gamma, alpha and epsilon. Try to implement `get_alpha` and `get_gamma` methods in addition to `get_epsilon` and increase/decrease your hyperparameters as the training goes on. Here are some hints:\n",
    "\n",
    "* `gamma`: you would want to focus more on near-term rewards as time goes on as your agent is more aware of the action values of the states\n",
    "* `alpha`: you would want to learn more slowly as time goes on as your agent has already accumulated a lot of knowledge about the environment\n",
    "* `epsilon`: you would want to do less random action as time goes on as your best actions are probably really best.\n",
    "\n",
    "<img src=\"img/taxi_scores.PNG\" alt=\"OpenAI Learderboard\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Challenges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve an environment with continuous states using discretization, tile coding, or other advanced methods\n",
    "\n",
    "* Acrobat-v1\n",
    "* MountainCar-v0\n",
    "* CartPole-v0\n",
    "* LunarLander-v2\n",
    "    \n",
    "Points to consider\n",
    "* What are other ways of handling continuous states? (See tile coding)\n",
    "* What are the state space, action space, and rewards of the environment?\n",
    "* What algorithms did you use to solve the environment and why?\n",
    "* How many episodes did you solve it in? Can you improve the performance? (Tweaking discount factor, learning rate, Monte Carlo vs TD)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Dietterich, T. G. (2000). Hierarchical Reinforcement Learning with the MAXQ Value Function Decomposition. Journal of Artificial Intelligence Research, 13, 227-303. doi:10.1613/jair.639\n",
    "* Mnih, V., Kavukcuoglu, K., Silver, D., Graves, A., Antonoglou, I., Wierstra, D., and Riedmiller, M.\n",
    "(Dec 2013). Playing Atari with deep reinforcement learning. Technical Report arXiv:1312.5602\n",
    "[cs.LG], Deepmind Technologies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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