taxi_demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "given-segment",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Inspired from https://www.learndatasci.com/tutorials/reinforcement-q-learning-scratch-python-openai-gym/\n",
    "import os\n",
    "import time\n",
    "import gym\n",
    "import numpy as np\n",
    "from tqdm.notebook import trange, tqdm\n",
    "from IPython.display import clear_output"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "encouraging-surname",
   "metadata": {},
   "source": [
    "# Taxi-v3\n",
    "This task was introduced in [Dietterich2000] to illustrate some issues in hierarchical reinforcement learning. There are 4 locations (labeled by different letters) and your job is to pick up the passenger at one location and drop him off in another. You receive +20 points for a successful dropoff, and lose 1 point for every timestep it takes. There is also a 10 point penalty for illegal pick-up and drop-off actions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "unlimited-friendly",
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make(\"Taxi-v3\").env"
   ]
  },
  {
   "attachments": {
    "1276b9d6-2303-45a0-8241-e5831ae44269.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "after-gallery",
   "metadata": {},
   "source": [
    "![Taxi environment](images/taxi_env.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "duplicate-registration",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|R: | : :\u001b[34;1mG\u001b[0m|\n",
      "| : | : : |\n",
      "| : : : : |\n",
      "| | :\u001b[43m \u001b[0m| : |\n",
      "|\u001b[35mY\u001b[0m| : |B: |\n",
      "+---------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "env.render()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sudden-manitoba",
   "metadata": {},
   "source": [
    "* **`env.reset`**: Resets the environment and returns a random initial state.\n",
    "* **`env.step(action)`**: Step the environment by one timestep. Returns\n",
    "    * **observation**: Observations of the environment\n",
    "    * **reward**: If your action was beneficial or not\n",
    "    * **done**: Indicates if we have successfully picked up and dropped off a passenger, also called one episode\n",
    "    * **info**: Additional info such as performance and latency for debugging purposes\n",
    "* **`env.render`**: Renders one frame of the environment (helpful in visualizing the environment)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dried-inclusion",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|R: | : :G|\n",
      "| : | : : |\n",
      "| :\u001b[43m \u001b[0m: : : |\n",
      "| | : | : |\n",
      "|\u001b[34;1mY\u001b[0m| : |\u001b[35mB\u001b[0m: |\n",
      "+---------+\n",
      "\n",
      "Action Space Discrete(6)\n",
      "State Space Discrete(500)\n"
     ]
    }
   ],
   "source": [
    "env.reset()  # reset environment to a new, random state\n",
    "env.render()\n",
    "\n",
    "print(\"Action Space {}\".format(env.action_space))\n",
    "print(\"State Space {}\".format(env.observation_space))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "expensive-course",
   "metadata": {},
   "source": [
    "* 0 = south\n",
    "* 1 = north\n",
    "* 2 = east\n",
    "* 3 = west\n",
    "* 4 = pickup\n",
    "* 5 = dropoff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "external-inventory",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "State: 328\n",
      "+---------+\n",
      "|\u001b[35mR\u001b[0m: | : :G|\n",
      "| : | : : |\n",
      "| : : : : |\n",
      "| |\u001b[43m \u001b[0m: | : |\n",
      "|\u001b[34;1mY\u001b[0m| : |B: |\n",
      "+---------+\n",
      "\n"
     ]
    }
   ],
   "source": [
    "state = env.encode(3, 1, 2, 0) # (taxi row, taxi column, passenger index, destination index)\n",
    "print(\"State:\", state)\n",
    "\n",
    "env.s = state\n",
    "env.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "removed-smooth",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: [(1.0, 428, -1, False)],\n",
       " 1: [(1.0, 228, -1, False)],\n",
       " 2: [(1.0, 348, -1, False)],\n",
       " 3: [(1.0, 328, -1, False)],\n",
       " 4: [(1.0, 328, -10, False)],\n",
       " 5: [(1.0, 328, -10, False)]}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.P[328]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "brutal-uganda",
   "metadata": {},
   "source": [
    "$$Q(state,action)\\leftarrow (1 - \\alpha)Q(state, action)+\\alpha(reward+\\gamma max_a Q(next state, all actions))$$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $\\large\\alpha$ (alpha) is the learning rate ($0<\\alpha\\leq 1$) - Just like in supervised learning settings, α is the extent to which our Q-values are being updated in every iteration.\n",
    "\n",
    "- $\\large\\gamma$ (gamma) is the discount factor ($0\\leq\\gamma\\leq 1$) - determines how much importance we want to give to future rewards. A high value for the discount factor (close to 1) captures the long-term effective award, whereas, a discount factor of 0 makes our agent consider only immediate reward, hence making it greedy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "technological-charge",
   "metadata": {},
   "outputs": [],
   "source": [
    "q_table = np.zeros([env.observation_space.n, env.action_space.n])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "chronic-things",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 100000\n",
      "Training finished.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Hyperparameters\n",
    "alpha = 0.1\n",
    "gamma = 0.99\n",
    "epsilon = 0.1\n",
    "\n",
    "# For plotting metrics\n",
    "all_epochs = []\n",
    "all_penalties = []\n",
    "\n",
    "seed= 42\n",
    "rng =np.random.default_rng(seed)\n",
    "\n",
    "for i in range(1, 100001):\n",
    "    state = env.reset()\n",
    "\n",
    "    epochs, penalties, reward, = 0, 0, 0\n",
    "    done = False\n",
    "    \n",
    "    while not done:\n",
    "        if rng.random() < epsilon:\n",
    "            action = env.action_space.sample() # Explore action space\n",
    "        else:\n",
    "            action = np.argmax(q_table[state]) # Exploit learned values\n",
    "\n",
    "        next_state, reward, done, info = env.step(action) \n",
    "        \n",
    "        old_value = q_table[state, action]\n",
    "        next_max = np.max(q_table[next_state])\n",
    "        \n",
    "        new_value = (1 - alpha) * old_value + alpha * (reward + gamma * next_max)\n",
    "        q_table[state, action] = new_value\n",
    "\n",
    "        if reward == -10:\n",
    "            penalties += 1\n",
    "\n",
    "        state = next_state\n",
    "        epochs += 1\n",
    "        \n",
    "    if i % 1000 == 0:\n",
    "        clear_output(wait=True)\n",
    "        print(f\"Episode: {i}\")\n",
    "\n",
    "print(\"Training finished.\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "arctic-lawyer",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results after 100 episodes:\n",
      "Average timesteps per episode: 13.1\n",
      "Average penalties per episode: 0.0\n"
     ]
    }
   ],
   "source": [
    "\"\"\"Evaluate agent's performance after Q-learning\"\"\"\n",
    "\n",
    "total_epochs, total_penalties = 0, 0\n",
    "episodes = 100\n",
    "\n",
    "for _ in range(episodes):\n",
    "    state = env.reset()  # reset environment to a new, random state\n",
    "    epochs, penalties, reward = 0, 0, 0\n",
    "    \n",
    "    done = False\n",
    "    \n",
    "    while not done:\n",
    "        action = np.argmax(q_table[state])\n",
    "        state, reward, done, info = env.step(action)\n",
    "\n",
    "        if reward == -10:\n",
    "            penalties += 1\n",
    "\n",
    "        epochs += 1\n",
    "\n",
    "    total_penalties += penalties\n",
    "    total_epochs += epochs\n",
    "\n",
    "print(f\"Results after {episodes} episodes:\")\n",
    "print(f\"Average timesteps per episode: {total_epochs / episodes}\")\n",
    "print(f\"Average penalties per episode: {total_penalties / episodes}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "introductory-fashion",
   "metadata": {},
   "source": [
    "Hyperparameters and optimizations\n",
    "The values of ($\\large\\alpha$) `alpha`, ($\\large\\gamma$) `gamma`, and ($\\large\\epsilon$) `epsilon` were mostly based on intuition and some \"hit and trial\", but there are better ways to come up with good values.\n",
    "\n",
    "Ideally, all three should decrease over time because as the agent continues to learn, it actually builds up more resilient priors;\n",
    "\n",
    "$\\Large\\alpha$: (the learning rate) should decrease as you continue to gain a larger and larger knowledge base.\n",
    "\n",
    "$\\Large\\gamma$: as you get closer and closer to the deadline, your preference for near-term reward should increase, as you won't be around long enough to get the long-term reward, which means your gamma should decrease.\n",
    "\n",
    "$\\Large\\epsilon$: as we develop our strategy, we have less need of exploration and more exploitation to get more utility from our policy, so as trials increase, epsilon should decrease."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "rocky-initial",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "|R: | : :G|\n",
      "| : | : : |\n",
      "| : : : : |\n",
      "| | : | : |\n",
      "|Y| : |\u001b[35m\u001b[34;1m\u001b[43mB\u001b[0m\u001b[0m\u001b[0m: |\n",
      "+---------+\n",
      "  (Dropoff)\n",
      "20\n"
     ]
    }
   ],
   "source": [
    "# Play an episode\n",
    "\n",
    "state = env.reset()  # reset environment to a new, random state\n",
    "env.render()\n",
    "time.sleep(0.5)\n",
    "done = False\n",
    "\n",
    "while not done:\n",
    "    action = np.argmax(q_table[state])\n",
    "    state, reward, done, info = env.step(action)\n",
    "    clear_output(wait=True)\n",
    "    env.render()\n",
    "    print(reward)\n",
    "    time.sleep(0.5)"
   ]
  }
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