FrozenLake_Q-learning_Gym.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "59822653-c23f-4703-865c-2e34a5dfa532",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import gym\n",
    "import random\n",
    "import time\n",
    "from IPython.display import clear_output\n",
    "from PIL import Image\n",
    "import matplotlib.pyplot as plt\n",
    "import imageio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "0f37bf7a-7152-4328-85fd-97d9d766759d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: imageio in ./myenv/lib/python3.8/site-packages (2.33.0)\n",
      "Requirement already satisfied: numpy in ./myenv/lib/python3.8/site-packages (from imageio) (1.24.3)\n",
      "Requirement already satisfied: pillow>=8.3.2 in ./myenv/lib/python3.8/site-packages (from imageio) (10.0.1)\n"
     ]
    }
   ],
   "source": [
    "!pip install imageio"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3a63481-b7d8-47fd-88b2-0b12f78c97f9",
   "metadata": {},
   "source": [
    "### Frozen Lake environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "447385b9-5b81-4223-ba9b-bbd34801a062",
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make('FrozenLake-v1',render_mode=\"rgb_array\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c0c49cb-4862-45f3-be2a-d15a54cfaab1",
   "metadata": {},
   "source": [
    "### Hyper-parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "47fb5d28-053e-4224-b935-fbdd9ec13b77",
   "metadata": {},
   "outputs": [],
   "source": [
    "action_space_size = env.action_space.n\n",
    "state_space_size = env.observation_space.n\n",
    "# print(action_space_size,state_space_size)\n",
    "q_table = np.zeros((state_space_size, action_space_size)) # q-learning\n",
    "\n",
    "num_episodes = 10000\n",
    "max_steps_per_episode = 100\n",
    "learning_rate = 0.1\n",
    "discount_rate = 0.99\n",
    "exploration_rate = 1\n",
    "max_exploration_rate = 1\n",
    "min_exploration_rate = 0.01\n",
    "exploration_decay_rate = 0.001"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ce85dfa-95a4-4bc1-bc3c-cb60b701607a",
   "metadata": {},
   "source": [
    "### Q-Learning training using Epsilon-greedy strategy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "922b6c30-139c-4530-bfa4-7e6fb664a27a",
   "metadata": {},
   "outputs": [],
   "source": [
    "rewards_all_episodes = []\n",
    "\n",
    "for episode in range(num_episodes):\n",
    "    state = env.reset()[0]\n",
    "    terminated = False\n",
    "    rewards_current_episode = 0\n",
    "\n",
    "    for step in range(max_steps_per_episode):\n",
    "        exp_exp_tradeoff = random.uniform(0, 1) # epsilon-greedy\n",
    "        if exp_exp_tradeoff > exploration_rate:\n",
    "            action = np.argmax(q_table[state,:])\n",
    "        else:\n",
    "            action = env.action_space.sample()\n",
    "        # print( env.step(action), state,action)\n",
    "        new_state, reward, terminated, truncated, info = env.step(action)\n",
    "        # print(new_state)\n",
    "        \n",
    "        q_table[state, action] = (1 - learning_rate) * q_table[state, action] + learning_rate * (reward + discount_rate * np.max(q_table[new_state, :]))\n",
    "        \n",
    "        rewards_current_episode += reward\n",
    "        state = new_state\n",
    "        if terminated == True: \n",
    "            break\n",
    "    exploration_rate = min_exploration_rate + (max_exploration_rate - min_exploration_rate) * np.exp(-exploration_decay_rate * episode) \n",
    "    rewards_all_episodes.append(rewards_current_episode)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cec7253a-ddb7-4a31-9420-65719361b5ba",
   "metadata": {},
   "source": [
    "### Plotting average rewards of every 100 episodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "3dec62e5-2dd1-4170-bfe2-bc5ed2432349",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "temp = np.split(np.array(rewards_all_episodes),100)\n",
    "temp = [np.mean(i) for i in temp]\n",
    "plt.plot(temp) # average rewards per 100 episodes\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "b9926541-cd65-42b9-9f98-6bdc59057c30",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.4743944  0.4727432  0.47177106 0.47256396]\n",
      " [0.24385758 0.3420455  0.26434853 0.45114734]\n",
      " [0.3898758  0.38032431 0.40723607 0.44076535]\n",
      " [0.32698708 0.31425315 0.19557099 0.4322145 ]\n",
      " [0.48069422 0.34131311 0.31884741 0.30001737]\n",
      " [0.         0.         0.         0.        ]\n",
      " [0.1841373  0.13020282 0.30888988 0.08878824]\n",
      " [0.         0.         0.         0.        ]\n",
      " [0.36508988 0.43590724 0.35973797 0.50630471]\n",
      " [0.36245885 0.53883774 0.4405232  0.40634921]\n",
      " [0.54824651 0.37179491 0.31220101 0.37601513]\n",
      " [0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.        ]\n",
      " [0.47753778 0.58700501 0.61950592 0.55708904]\n",
      " [0.75907208 0.79746169 0.76822363 0.75015722]\n",
      " [0.         0.         0.         0.        ]]\n"
     ]
    }
   ],
   "source": [
    "print(q_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "f65b4c0a-533f-4041-a157-0e787ca5aba9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: gym[toy_text] in ./myenv/lib/python3.8/site-packages (0.26.2)\n",
      "Requirement already satisfied: gym-notices>=0.0.4 in ./myenv/lib/python3.8/site-packages (from gym[toy_text]) (0.0.8)\n",
      "Requirement already satisfied: numpy>=1.18.0 in ./myenv/lib/python3.8/site-packages (from gym[toy_text]) (1.24.3)\n",
      "Requirement already satisfied: cloudpickle>=1.2.0 in ./myenv/lib/python3.8/site-packages (from gym[toy_text]) (3.0.0)\n",
      "Requirement already satisfied: importlib-metadata>=4.8.0; python_version < \"3.10\" in ./myenv/lib/python3.8/site-packages (from gym[toy_text]) (6.8.0)\n",
      "Collecting pygame==2.1.0; extra == \"toy_text\"\n",
      "  Downloading pygame-2.1.0-cp38-cp38-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (18.3 MB)\n",
      "\u001b[K     |████████████████████████████████| 18.3 MB 110.7 MB/s eta 0:00:01\n",
      "\u001b[?25hRequirement already satisfied: zipp>=0.5 in ./myenv/lib/python3.8/site-packages (from importlib-metadata>=4.8.0; python_version < \"3.10\"->gym[toy_text]) (3.17.0)\n",
      "Installing collected packages: pygame\n",
      "Successfully installed pygame-2.1.0\n"
     ]
    }
   ],
   "source": [
    "!pip install gym[toy_text]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41430315-eca4-48ed-9ff8-f1f9755ca79b",
   "metadata": {},
   "source": [
    "### Rendering the environment using optimized Q-table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "7fea5729-6e81-49cb-a03e-045cd57d53e8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "****************************************************\n",
      "EPISODE  0\n",
      "Number of steps 76\n"
     ]
    }
   ],
   "source": [
    "env.reset()\n",
    "frames = []\n",
    "num_steps = 0\n",
    "for episode in range(1):\n",
    "    state = env.reset()[0]\n",
    "    done = False\n",
    "    print(\"****************************************************\")\n",
    "    print(\"EPISODE \", episode)\n",
    "\n",
    "    for step in range(max_steps_per_episode):\n",
    "        # plt.imshow(env.render())\n",
    "        # print(state)\n",
    "        frame = env.render()\n",
    "        frames.append(frame)\n",
    "        action = np.argmax(q_table[state,:])\n",
    "        \n",
    "        new_state, reward, done, truncated, info = env.step(action)\n",
    "        \n",
    "        if done:\n",
    "            print(\"Number of steps\", step)\n",
    "            num_steps = step\n",
    "            frames.append(env.render())\n",
    "            break\n",
    "        state = new_state\n",
    "env.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85c1b92c-96a5-4d4d-8fb5-762b06909848",
   "metadata": {},
   "source": [
    "### Saving the frames as a gif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "46065140-6c7f-40aa-a419-f1a48951ecce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GIF saved at episode.gif\n"
     ]
    }
   ],
   "source": [
    "image_path = \"episode.gif\"\n",
    "imageio.mimsave(image_path, frames, duration=0.2*num_steps)\n",
    "print(f\"GIF saved at {image_path}\")"
   ]
  }
 ],
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