ch12TabularQ-LearningCoinGame.ipynb

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    "# Chaper 12: Tabular Q-Learning in the Coin Game\n",
    "\n",
    "\n",
    "\n",
    "***\n",
    "*“Reinforcement learning is the idea of being able to assign credit or blame to all the actions you took along the way while you were getting that reward signal.”*\n",
    "\n",
    "-- Jeff Dean, Chief Scientist at Google\n",
    "***\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "Reinforcement learning is the idea of being able to assign credit or blame to all the actions you took along the way while you were getting that reward signal. Jeff Dean, Chief Scientist at Google\n",
    "\n",
    "This chapter introduces you to the basics of reinforcement learning. You'll use one type of reinforcement learning, namely tabular Q-learning, to solve the coin game. Along the way, you'll learn the concepts of dynamic programming and the Bellman equation, and on how to implement tabular Q-learning.\n",
    "\n",
    "Machine learning can be classified into three areas: Supervised learning, unsupervised learning, and reinforcement learning. The deep learning method we covered in the last few chapters belongs to supervised learning. Generally, supervised learning models learn from examples of input-output pairs. In the process, the model extracts features from the input data (dog and cat pictures, for example) and associate them with the output labels (this image is a dog and that one is a cat). In contrast, in unsupervised learning, the model doesn't have access to pre-assigned target variables (labels) in the training data. Instead, unsupervised learning models use naturally-occurring patterns in the data. Methods used in unsupervised learning include clustering, principal component analysis, and data visualization. \n",
    "\n",
    "The third type of machine leanring, reinforcement learning (RL), uses trials and errors to achieve optimal outcomes. Typically, an agent operates in an environment and selects different actions. The environment provides feedback in the form of rewards and punishments. The agent learns to select actions leading to high rewards to maximize cumulated payoffs. This chapter covers one type of RL, tabular Q-learning. Later in the book, you'll learn other types of RL such as the policy gradient method.\n",
    "\n",
    "In this chapter, you’ll use the Coin game as an example to learn how RL works. Your’ll learn to train a Q-table by trial and error: the agent plays the coin game many times and adjusts the values in the Q-table based on the rewards: increase the Q-value if an action leads to positive rewards and decrease the Q-value otherwise. Once the Q-table is trained, you’ll use it to play and win the coin game. You'll win 100% of the time when you move second, even when playing against the perfect rule-based AI that we developed in Chapter 1."
   ]
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   "source": [
    "# 1. What Is Reinforcement Learning?\n"
   ]
  },
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   "source": [
    "# 2. Use Q Values to Play the Coin Game"
   ]
  },
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   "source": [
    "## 2.1. The Logic Behind Q Learning\n"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "c68d72e4",
   "metadata": {},
   "source": [
    "![fig13.1.png](attachment:fig13.1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d68c4b83",
   "metadata": {},
   "source": [
    "## 2.2. A Python Program to Win the Coin Game\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7b862cf5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "def AI(state):\n",
    "    if state%3 != 0:\n",
    "        move = state%3\n",
    "    else:\n",
    "        move = random.choice([1,2])\n",
    "    return move"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "42e4d2bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "state is 21; Player 1 chooses action 1\n",
      "state is 20; Player 2 chooses action 2\n",
      "state is 18; Player 1 chooses action 2\n",
      "state is 16; Player 2 chooses action 1\n",
      "state is 15; Player 1 chooses action 1\n",
      "state is 14; Player 2 chooses action 2\n",
      "state is 12; Player 1 chooses action 1\n",
      "state is 11; Player 2 chooses action 2\n",
      "state is 9; Player 1 chooses action 2\n",
      "state is 7; Player 2 chooses action 1\n",
      "state is 6; Player 1 chooses action 2\n",
      "state is 4; Player 2 chooses action 1\n",
      "state is 3; Player 1 chooses action 1\n",
      "state is 2; Player 2 chooses action 2\n",
      "Player 2 won!\n"
     ]
    }
   ],
   "source": [
    "from utils.coin_env import coin_game\n",
    "import numpy as np\n",
    "import time\n",
    "\n",
    "# initiate the game environment\n",
    "env=coin_game()\n",
    "# create a Q-table by using values from the CSV file\n",
    "file=\"files/coin_Qs.csv\"\n",
    "Q=np.loadtxt(file, delimiter=\",\")\n",
    "\n",
    "# play a full game\n",
    "state=env.reset()\n",
    "# turn on the graphical rendering\n",
    "env.render()\n",
    "while True:\n",
    "    # Rule-based AI moves first\n",
    "    m1=AI(state)\n",
    "    print(f\"state is {state}; Player 1 chooses action {m1}\")\n",
    "    state, reward, done, _ = env.step(m1)\n",
    "    env.render()\n",
    "    time.sleep(1)\n",
    "    if done==True:\n",
    "        print('Player 1 won!')\n",
    "        break          \n",
    "    # pick the action with the higher Q value\n",
    "    m2=np.argmax(Q[state, :])+1\n",
    "    print(f\"state is {state}; Player 2 chooses action {m2}\")\n",
    "    state, reward, done, _ = env.step(m2)\n",
    "    env.render()\n",
    "    time.sleep(1)\n",
    "    if done==True:\n",
    "        print('Player 2 won!')\n",
    "        break  \n",
    "time.sleep(5)\n",
    "env.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3968e663",
   "metadata": {},
   "source": [
    "# 3. Training the Q-Values\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8ba3931",
   "metadata": {},
   "source": [
    "## 3.1. What Is Q-Learning?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6334083a",
   "metadata": {},
   "source": [
    "## 3.2. Let the Learning Begin\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9ea32e74",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.      0.    ]\n",
      " [ 1.      1.    ]\n",
      " [-1.      1.    ]\n",
      " [-1.     -1.    ]\n",
      " [ 0.95   -1.    ]\n",
      " [-0.8804  0.95  ]\n",
      " [-0.95   -0.95  ]\n",
      " [ 0.9025 -0.921 ]\n",
      " [-0.8678  0.9025]\n",
      " [-0.9025 -0.9025]\n",
      " [ 0.8573 -0.8945]\n",
      " [-0.8368  0.8573]\n",
      " [-0.8574 -0.8574]\n",
      " [ 0.8144 -0.8541]\n",
      " [-0.8104  0.8144]\n",
      " [-0.8145 -0.8145]\n",
      " [ 0.7737 -0.8142]\n",
      " [-0.7728  0.7737]\n",
      " [-0.77   -0.7701]\n",
      " [ 0.735  -0.7737]\n",
      " [-0.7278  0.735 ]\n",
      " [ 0.      0.    ]]\n"
     ]
    }
   ],
   "source": [
    "# the learning rate\n",
    "lr=0.01\n",
    "# discount rate\n",
    "gamma=0.95\n",
    "# parameters to control exploration\n",
    "max_exp=0.9\n",
    "min_exp=0.1\n",
    "# maximum steps in a game\n",
    "max_steps=50\n",
    "# number of episodes to train Q-values\n",
    "max_episode=10000\n",
    "\n",
    "# Set Q-values to zeros at first \n",
    "Q=np.zeros((22, 2))\n",
    "# Train the Q-table\n",
    "for episode in range(max_episode):\n",
    "    # The initial state is the starting position (state 0)\n",
    "    state=env.reset() \n",
    "    # AI moves first\n",
    "    AIaction=AI(state)\n",
    "    state, reward, done, _ = env.step(AIaction)\n",
    "    # The cutoff value for exploration\n",
    "    cutoff=min_exp+(max_exp-min_exp)*episode/max_episode\n",
    "    # Play a game\n",
    "    for _ in range(max_steps):\n",
    "        # Exploitation\n",
    "        if np.random.uniform(0,1,1)>cutoff:\n",
    "            action=np.argmax(Q[state, :])\n",
    "        # Exploration\n",
    "        else:\n",
    "            action=random.choice(range(2))\n",
    "        # Use the selected action to make the move\n",
    "        # Important: convert 0 and 1 to 1 and 2\n",
    "        new_state,reward,done,_=env.step(action+1)\n",
    "        # Update Q values\n",
    "        if done==True:\n",
    "            # Q-agent moves second, -1 means winning\n",
    "            reward=-reward\n",
    "            Q[state,action]=reward\n",
    "            break    \n",
    "        else:\n",
    "            # AI payer's turn\n",
    "            AIaction=AI(new_state)\n",
    "            new_state,reward,done,_=env.step(AIaction)\n",
    "            # Q-agent moves second, -1 means winning\n",
    "            reward=-reward               \n",
    "            if done:\n",
    "                Q[state,action]=reward\n",
    "                break            \n",
    "            else:\n",
    "                Q[state,action]=lr*(reward+gamma*np.max(\\\n",
    "                    Q[new_state,:]))+(1-lr)*Q[state,action]\n",
    "                state=new_state \n",
    "\n",
    "# Print out and save the trained Q-table\n",
    "Q=np.round(Q,4)\n",
    "print(Q)\n",
    "np.savetxt(\"files/coin_Qs.csv\",Q,delimiter=',')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abc6f365",
   "metadata": {},
   "source": [
    "## 3.3. Test the Trained Q-Table\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "89cede39",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "game 1\n",
      "Player 2 wins the game!\n",
      "game 2\n",
      "Player 2 wins the game!\n",
      "game 3\n",
      "Player 2 wins the game!\n",
      "game 4\n",
      "Player 2 wins the game!\n",
      "game 5\n",
      "Player 2 wins the game!\n",
      "game 6\n",
      "Player 2 wins the game!\n",
      "game 7\n",
      "Player 2 wins the game!\n",
      "game 8\n",
      "Player 2 wins the game!\n",
      "game 9\n",
      "Player 2 wins the game!\n",
      "game 10\n",
      "Player 2 wins the game!\n"
     ]
    }
   ],
   "source": [
    "# test trained Q\n",
    "for t in range(10):\n",
    "    print(f\"game {t+1}\")\n",
    "    # The initial state is the starting position (state 0)\n",
    "    state=env.reset() \n",
    "    # AI move first\n",
    "    AIaction=AI(state)\n",
    "    state, reward, done, _ = env.step(AIaction)    \n",
    "    # Play a full game\n",
    "    for _ in range(max_steps):\n",
    "        action=np.argmax(Q[state, :])\n",
    "        # Use the selected action to make the move\n",
    "        new_state,reward,done,_=env.step(action+1)\n",
    "        if done==True:\n",
    "            print(\"Player 2 wins the game!\")\n",
    "            break    \n",
    "        else:\n",
    "            AIaction=AI(new_state)\n",
    "            new_state, reward, done, _ = env.step(AIaction)            \n",
    "            if done:\n",
    "                print(\"Player 1 wins the game!\")\n",
    "                break            \n",
    "            else:\n",
    "                state=new_state "
   ]
  }
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