double_q_learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Double Q-Learning\n",
    "\n",
    "This notebook shows the tabular reinforcement learning algorithm, Double Q-Learning applied to the Taxi problem (it also works on CliffWalking and FrozenLake) from Open AI's gym. Double Q-Learning is an off-policy Temporal Difference control algorithm. Two action value functions, $Q_1$ and $Q_2$ are used for this method, which are both used for estimating the discounted return and selecting the optimal action, hence the name double learning. This algorithm improves on the standard Q-Learning algorithm by reducing the impact of maximization bias. Maximimization bias can occur when there is uncertainty in the return of the actions in a given state. For example if the return of all the actions in a state is 0, but the estimated returns are non-zero, (some positive and others negative), then the maximum of the values will be positive. This results in a positive bias, which we call a maximization bias.  \n",
    "\n",
    "The action $A$ is selected by using the $\\epsilon$-greedy policy on $(Q_1 + Q_2) / 2$, then with 50% probability the following update is performed:\n",
    "$$Q_1(S_t, A_t) \\leftarrow Q_1(S_t, A_t) + \\alpha [R_{t + 1} + \\gamma Q_2(S_{t + 1}, \\argmax_{a}Q_1(S_{t + 1}, a)) - Q_1(S_t, A_t)]$$\n",
    ", otherwise the following update is performed:\n",
    "$$Q_2(S_t, A_t) \\leftarrow Q_2(S_t, A_t) + \\alpha [R_{t + 1} + \\gamma Q_1(S_{t + 1}, \\argmax_{a}Q_2(S_{t + 1}, a)) - Q_2(S_t, A_t)]$$\n",
    ", where $Q1$ and $Q2$ are the learned action-value functions, $R$ is the reward, $A$ is the action, $\\alpha$ is the step size, $\\gamma$ is the discount rate and $t$ is the time step.\n",
    "\n",
    "The learned action-value functions $Q1$ and $Q2$ directly approximates the optimal action-value function $q_*$ independent of the policy being followed. For more information on Double Q-Learning see section 6.7 of [Reinforcement Learning: An Introduction](http://incompleteideas.net/book/RLbook2018.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import gymnasium as gym\n",
    "import numpy as np\n",
    "import random\n",
    "from IPython.display import Video\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Type of environment, options include:\n",
    "# Taxi-v3, CliffWalking-v0, FrozenLake-v1\n",
    "ENV_TYPE = \"Taxi-v3\"\n",
    "\n",
    "# Save videos from training\n",
    "SAVE_VIDEOS = False\n",
    "VIDEOS_ROOT_DIR = './videos/double_q_learning/'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the environment\n",
    "env = gym.make(ENV_TYPE, render_mode=\"rgb_array\")\n",
    "\n",
    "# Number of possible states and actions\n",
    "num_states = env.observation_space.n \n",
    "num_actions = env.action_space.n\n",
    "\n",
    "# Action-value function, \n",
    "# initialized to 0 for all states and actions\n",
    "Q1 = np.zeros([num_states, num_actions])\n",
    "Q2 = np.zeros([num_states, num_actions])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create An $\\epsilon$-Greedy Policy "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def policy_fn(state, Q, epsilon, num_actions):\n",
    "    # Create a distribution of actions and divide the epsilon probability between all actions\n",
    "    action_dist = np.ones(num_actions, dtype=float) * epsilon / num_actions\n",
    "    # Find the best action\n",
    "    best_action = np.argmax(Q[state, :])\n",
    "    # Set probability for the best action to (1 - epsilon)\n",
    "    action_dist[best_action] += (1.0 - epsilon)\n",
    "    return action_dist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learn The Optimal Action-Value Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 10 Return: -19\n",
      "Episode: 20 Return: -510\n",
      "Episode: 30 Return: -420\n",
      "Episode: 40 Return: -1022\n",
      "Episode: 50 Return: -27\n",
      "Episode: 60 Return: -23\n",
      "Episode: 70 Return: -56\n",
      "Episode: 80 Return: -35\n",
      "Episode: 90 Return: -52\n",
      "Episode: 100 Return: -357\n",
      "Episode: 110 Return: -140\n",
      "Episode: 120 Return: -17\n",
      "Episode: 130 Return: -583\n",
      "Episode: 140 Return: -205\n",
      "Episode: 150 Return: -6\n",
      "Episode: 160 Return: 7\n",
      "Episode: 170 Return: -46\n",
      "Episode: 180 Return: -129\n",
      "Episode: 190 Return: 3\n",
      "Episode: 200 Return: 13\n",
      "Episode: 210 Return: 8\n",
      "Episode: 220 Return: 6\n",
      "Episode: 230 Return: -11\n",
      "Episode: 240 Return: 13\n",
      "Episode: 250 Return: -66\n",
      "Episode: 260 Return: 15\n",
      "Episode: 270 Return: -81\n",
      "Episode: 280 Return: 9\n",
      "Episode: 290 Return: -55\n",
      "Episode: 300 Return: 6\n",
      "Episode: 310 Return: 8\n",
      "Episode: 320 Return: 1\n",
      "Episode: 330 Return: -8\n",
      "Episode: 340 Return: 5\n",
      "Episode: 350 Return: 8\n",
      "Episode: 360 Return: 7\n",
      "Episode: 370 Return: 0\n",
      "Episode: 380 Return: 3\n",
      "Episode: 390 Return: 3\n",
      "Episode: 400 Return: 5\n"
     ]
    }
   ],
   "source": [
    "# Number of episodes to train on\n",
    "episodes = 401\n",
    "# Sliding window for episode evaluation (needs to be less than episodes)\n",
    "episode_window = 5\n",
    "# Return (accumulation of all rewards over an episode)\n",
    "G = 0\n",
    "returns = []\n",
    "# Discount ratio\n",
    "gamma = 0.99\n",
    "# Step size\n",
    "alpha = 0.618\n",
    "# Probability of taking a non-greedy action\n",
    "epsilon = 0.01\n",
    "\n",
    "env = gym.make(ENV_TYPE, render_mode=\"rgb_array\")\n",
    "env = gym.wrappers.RecordEpisodeStatistics(env, buffer_length=episodes)\n",
    "\n",
    "if SAVE_VIDEOS:\n",
    "    os.makedirs(VIDEOS_ROOT_DIR, exist_ok=True)\n",
    "    env = gym.wrappers.RecordVideo(\n",
    "        env=env, \n",
    "        video_folder=VIDEOS_ROOT_DIR,\n",
    "        episode_trigger=lambda episode: episode % 100 == 0,\n",
    "        video_length=0,\n",
    "        name_prefix=ENV_TYPE\n",
    "        )\n",
    "        \n",
    "\n",
    "for episode in range(1, episodes+1):\n",
    "    terminated, truncated = False, False\n",
    "    G, reward = 0, 0\n",
    "    state, info = env.reset()\n",
    "    while not terminated:\n",
    "        # Select the action following the epsilon-greedy policy\n",
    "        action_dist1 = policy_fn(state, Q1, epsilon, num_actions)\n",
    "        action_dist2 = policy_fn(state, Q2, epsilon, num_actions)\n",
    "        action_dist = (action_dist1 + action_dist2) / 2\n",
    "        action = np.random.choice(np.arange(num_actions), p=action_dist)\n",
    "        # Take the action and observe reward and next state\n",
    "        next_state, reward, terminated, truncated, info = env.step(action)\n",
    "        # Randomly update action value function Q1 or Q2\n",
    "        rand_value = random.uniform(0, 1)\n",
    "        if rand_value > 0.5:\n",
    "            # Update the expected return for the action-value function Q1\n",
    "            Q1[state, action] += alpha * (reward + gamma * Q2[next_state, np.argmax(Q1[next_state, :])] - Q1[state, action]) \n",
    "        else:\n",
    "            # Update the expected return for the action-value function Q2\n",
    "            Q2[state, action] += alpha * (reward + gamma * Q1[next_state, np.argmax(Q2[next_state, :])] - Q2[state, action]) \n",
    "        G += reward\n",
    "        state = next_state\n",
    "\n",
    "    returns.append(G)\n",
    "\n",
    "    if episode % 10 == 0:\n",
    "        print(f'Episode: {episode} Return: {G}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot The Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(episodes), returns)\n",
    "plt.title(\"Returns Over Episodes\")\n",
    "plt.xlabel(\"Episodes\")\n",
    "plt.ylabel(\"Returns\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training Episode Videos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/double_q_learning//Taxi-v3-episode-0.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-0.mp4\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/double_q_learning//Taxi-v3-episode-100.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-100.mp4\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/double_q_learning//Taxi-v3-episode-200.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-200.mp4\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 300"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/double_q_learning//Taxi-v3-episode-300.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-300.mp4\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 400"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/double_q_learning//Taxi-v3-episode-400.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-400.mp4\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Render Final Model On An Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total Reward: 7, Steps Taken: 14\n"
     ]
    }
   ],
   "source": [
    "# Run the algorithm in inferencing mode and \n",
    "# observe its performance\n",
    "env = gym.make(ENV_TYPE, render_mode=\"human\")\n",
    "state, info = env.reset(seed=65)\n",
    "G = 0\n",
    "num_steps = 0\n",
    "terminated = False\n",
    "\n",
    "while not terminated and not truncated:\n",
    "    action = np.argmax((Q1[state, :] + Q2[state, :]) / 2) \n",
    "    state, reward, terminated, truncated, info = env.step(action)\n",
    "    G += reward\n",
    "    num_steps += 1\n",
    "\n",
    "print(f'Total Reward: {G}, Steps Taken: {num_steps}')\n",
    "\n",
    "env.close()"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "flax",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
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  "orig_nbformat": 4,
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   "interpreter": {
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