RL/tictactoe_RL.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reinforcement Learning: Learning to Play Tic-Tac-Toe with Q-Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction \n",
    " \n",
    "The goal of reinforcement learning is to interact with the environment and use trial-and-error to learn the best action for each state. Prescribing an action for a state is called a policy. The optimal policy is the policy that maximizes the sum of\n",
    "all future expected rewards. \n",
    "\n",
    "The optimal action in a state $s$ can be determined from the Q-values $Q(s, a)$ which is the expected utility of\n",
    "choosing $a$ in $s$ and the following the current policy till a terminal state is reached. The optimal action is the \n",
    "action with the largest Q-value for the state. The policy implementing this idea is called a greedy policy. \n",
    "\n",
    "For small problems, the Q-value function can be expressed as a table. \n",
    "We implement here the table-based TD(0) algorithm as described in Chapter 6 of Sutton and Barto (2020). \n",
    "\n",
    "**Algorithm: Q-learning (off-policy TD control) for estimating $\\pi^*$**\n",
    "\n",
    "Parameters: step size $\\alpha \\in (0, 1]$, small $\\epsilon > 0$, a discount factor $\\gamma$\n",
    "\n",
    "Initialize $Q(s, a) = 0$, for all $s \\in S^+, a \\in A(s)$\n",
    "\n",
    "Loop for each episode:\n",
    "  * Initialize $s$\n",
    "  * Loop for each step of episode:\n",
    "    *  Choose $a$ for $s$ (the state in the current step) using a policy derived from $Q$ (e.g., $\\epsilon$-greedy)\n",
    "    *  Take action $a$, observe the reward $r$ and the next state $s'$\n",
    "    *  $Q(s, a) \\leftarrow Q(s, a) + \\alpha [r +  \\gamma \\max_a' Q(s', a') - Q(s, a)]$\n",
    "    *  $s \\leftarrow s'$\n",
    "  * until $s$ is terminal\n",
    " \n",
    "The idea of this iterative algorithm is to make in every step $Q(s, a)$ a little more similar to \n",
    "the immediate reward plus the expected utility of the best action in the next state expressed as $r + Q(s', a')$. The algorithm is called temporal differencing since it used the \n",
    "difference between Q-values at state $s$ and the next (i.e., later) state $s'$. This difference is also\n",
    "called the TD-error.\n",
    "\n",
    "Different to the description in Sutton and Batro (2020), we will implement the algorithm as an agent function that can interact with an environment. An example is shown in AIMA Figure 22.8.\n",
    "\n",
    "Also, there is no immediate reward in games like tic-tac-toe. A reward is only available when the game ends. This makes the problem actually harder."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q-Table Size\n",
    "\n",
    "First, we need to establish that the Q-table will fit in memory. The table implements the function $Q: S \\times A \\rightarrow \\mathbb{R}$ so it has number of states times number of actions entries.\n",
    "\n",
    "We can estimate this in the following way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "level\tboards\tactions\tQ table entries\n",
      "0 \t 1 \t 9 \t 9\n",
      "1 \t 9 \t 8 \t 72\n",
      "2 \t 72 \t 7 \t 504\n",
      "3 \t 252 \t 6 \t 1512\n",
      "4 \t 756 \t 5 \t 3780\n",
      "5 \t 1260 \t 4 \t 5040\n",
      "6 \t 1680 \t 3 \t 5040\n",
      "7 \t 1260 \t 2 \t 2520\n",
      "8 \t 630 \t 1 \t 630\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "19107"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "print(\"level\\tboards\\tactions\\tQ table entries\")\n",
    "sum = 0\n",
    "\n",
    "for i in range(0,9):\n",
    "    boards = math.comb(9, i) * math.comb(i, math.floor(i/2))\n",
    "    actions = 9 - i\n",
    "    print(i, \"\\t\", \n",
    "          boards, \"\\t\",\n",
    "          actions, \"\\t\",\n",
    "          boards * actions)\n",
    "    sum += boards * actions\n",
    "\n",
    "sum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This game has no cycles so all of the boards are unique.\n",
    "However, the number is an upper bound since some boards are not reachable since the game is over once one player wins. Given this analysis, the Q-table should easily fit in memory and\n",
    "learning all these values should not take too much time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding a Policy using Q-Learning\n",
    "\n",
    "The code for the basic functions used for search are implemented in [tictactoe.py](tictactoe.py)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tictactoe import empty_board, actions, result, terminal, utility, other, show_board\n",
    "from tictactoe import random_player, play "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Define the immediate reward for a board and a player. Remember, the reward is only defined in this game for the terminal state and `utility()` return `None` otherwise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "def reward (board, player):\n",
    "    \"\"\"Return the reward for the board position.\"\"\"\n",
    "    \n",
    "    u = utility(board, player)\n",
    "    if u == None:\n",
    "        return 0\n",
    "    \n",
    "    return u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need argmax with randomly breaking ties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def argmax_rand(b):\n",
    "    return np.random.choice(np.flatnonzero(b == np.max(b)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "class QAgent:\n",
    "    def __init__(self, epsilon = 0.1, alpha = 0.1, gamma = 0.9, player = 'x'):\n",
    "        self.epsilon = epsilon\n",
    "        self.alpha = alpha\n",
    "        self.gamma = gamma\n",
    "        self.player = player\n",
    "        self.reset()\n",
    "        \n",
    "    def reset(self):\n",
    "        self.Q = dict() # Q-table, empty means all entries are initially 0\n",
    "        self.s = None\n",
    "        self.a = None\n",
    "        if DEBUG:\n",
    "                print(\"Resetting QAgent\")\n",
    "\n",
    "    def play(self, s, r, player):\n",
    "        global DEBUG\n",
    "        \n",
    "        if player != self.player:\n",
    "            print(\"Error: I was not trained to play as\", player)\n",
    "            return None\n",
    "\n",
    "        # Update Q-table with final reward, no more actions possible\n",
    "        if (r != None):\n",
    "            # we directly set the Q-value with to the final reward\n",
    "            self.Q[(tuple(self.s), self.a)] = r\n",
    "            if DEBUG:\n",
    "                print(\"Updating Q-table for state\", self.s, \"and action\", self.a, \"with reward\", r)\n",
    "\n",
    "            self.s = None\n",
    "            self.a = None\n",
    "            return None\n",
    "\n",
    "        \n",
    "        # Update Q-table while game is not over\n",
    "        \n",
    "        # We use in the update a zero immediate reward \n",
    "        r = 0\n",
    "        s_prime = s\n",
    "\n",
    "        if self.s is not None and self.a is not None:\n",
    "            max_Q_sp_a = np.max([self.Q.get((tuple(s_prime), x), 0) for x in actions(s_prime)])\n",
    "            Q_sa = self.Q.get((tuple(self.s), self.a), 0)\n",
    "            self.Q[(tuple(self.s), self.a)] = Q_sa + self.alpha * (r + self.gamma * max_Q_sp_a - Q_sa)\n",
    "\n",
    "            if DEBUG:\n",
    "                print(\"Updating Q-table for state\", self.s, \"and action\", self.a, \"to\", self.Q[(tuple(self.s), self.a)])\n",
    "\n",
    "\n",
    "        # Determine new action using epsilon-greedy strategy\n",
    "        if np.random.uniform() < self.epsilon:\n",
    "            # random action\n",
    "            a = np.random.choice(actions(s))\n",
    "            if DEBUG:\n",
    "                print(\"Chosen random action:\", a)\n",
    "        else:\n",
    "            # greedy action (best action given current Q-values)\n",
    "            a = actions(s)[argmax_rand([self.Q.get((tuple(s), x), 0) for x in actions(s)])]\n",
    "            if DEBUG:\n",
    "                print(\"Chosen greedy action:\", a)\n",
    "\n",
    "        # remember state and action\n",
    "        self.s = s_prime\n",
    "        self.a = a\n",
    "\n",
    "        return a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Environment and a Random Baseline Player\n",
    "\n",
    "The environment for RL is slightly different, since the agent gets in addition to the percepts \n",
    "also the immediate reward information `r`.\n",
    "\n",
    "**Note:** In this game, there is no immediate reward till the game is done. \n",
    "We call the agent function when the game is done with the reward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "def switch_player(player, x, o):\n",
    "    if player == 'x':\n",
    "        return 'o', o\n",
    "    else:\n",
    "        return 'x', x\n",
    "\n",
    "def play(x, o, N = 100):\n",
    "    \"\"\"Let two agents play each other N times. x starts. x and y are agent functions that \n",
    "    get the board as the percept and return their next action.\"\"\"\n",
    "    results = {'x': 0, 'o': 0, 'd': 0}\n",
    "    \n",
    "    for i in range(N):\n",
    "        board = empty_board()\n",
    "        player, fun = 'x', x\n",
    "        \n",
    "        while True:\n",
    "            a = fun(board, None, player)\n",
    "            board = result(board, player, a)\n",
    "            \n",
    "            u = utility(board, player = 'x')   # reward; returns None if the game is not done.\n",
    "            \n",
    "            if u != None:\n",
    "                if (u == 1):\n",
    "                    results['x'] += 1\n",
    "                elif (u == -1):\n",
    "                    results['o'] += 1\n",
    "                elif (u == 0):\n",
    "                    results['d'] += 1       \n",
    "                \n",
    "                # show agents their final reward\n",
    "                x(board, u, 'x')\n",
    "                o(board, u * -1, 'o')\n",
    "                break\n",
    "            \n",
    "            player, fun = switch_player(player, x, o)   \n",
    "    \n",
    "    return results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement a completely randomized player agent can be used as a weak baseline. Immediate reward is ignored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_player(board, r, player = None):\n",
    "    \"\"\"Simple player that chooses a random empty square (equal probability of all permissible actions). \n",
    "    player is unused.\"\"\"\n",
    "    if (r != None):\n",
    "        return None    \n",
    "    \n",
    "    return np.random.choice(actions(board))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q-Learning Agent vs. Random\n",
    "\n",
    "The agent learns for every game that it plays. \n",
    "We start with the first 100 games to see how bad it initially is.\n",
    "For the final 1000 games, we set $\\epsilon = 0$ so the \n",
    "agent only makes greedy moves.\n",
    "\n",
    "The hyperparameters $\\epsilon$ and $\\alpha$ could be tuned.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train a Q-learning agent for playing x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q-Learning vs. Random:\n",
      "Initially, the performance is not better than a random player!\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'x': 52, 'o': 34, 'd': 14}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Play to learn how to play against a random player.\n"
     ]
    },
    {
     "data": {
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       "{'x': 3925, 'o': 692, 'd': 383}"
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       "{'x': 4424, 'o': 321, 'd': 255}"
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       "{'x': 4475, 'o': 328, 'd': 197}"
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     "text": [
      "Set epsilon to zero to make the agent greedy and play again:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'x': 997, 'o': 0, 'd': 3}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q-table size: 6862\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{((' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '), 6): 0.7598002311400952,\n",
       " ((' ', ' ', ' ', ' ', ' ', ' ', 'x', ' ', 'o'), 1): 0.14730026452992,\n",
       " ((' ', 'x', ' ', ' ', ' ', 'o', 'x', ' ', 'o'), 0): 0.0,\n",
       " (('x', 'x', ' ', ' ', 'o', 'o', 'x', ' ', 'o'), 2): 1,\n",
       " ((' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '), 5): 0.7685979206499914,\n",
       " ((' ', ' ', ' ', ' ', 'o', 'x', ' ', ' ', ' '), 7): 0.144781759881216,\n",
       " ((' ', ' ', ' ', ' ', 'o', 'x', 'o', 'x', ' '), 0): -1,\n",
       " (('x', ' ', ' ', ' ', 'o', 'x', 'o', 'x', 'o'), 3): -1,\n",
       " ((' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '), 4): 0.7686303538309619,\n",
       " ((' ', ' ', ' ', ' ', 'x', ' ', ' ', ' ', 'o'), 7): 0.6772572367257601,\n",
       " ((' ', ' ', ' ', 'o', 'x', ' ', ' ', 'x', 'o'), 0): 0.0,\n",
       " (('x', ' ', ' ', 'o', 'x', 'o', ' ', 'x', 'o'), 2): 0.0,\n",
       " (('x', 'o', 'x', 'o', 'x', 'o', ' ', 'x', 'o'), 6): 1,\n",
       " ((' ', ' ', ' ', ' ', 'x', ' ', ' ', ' ', 'o'), 3): 0.5238228197352447,\n",
       " ((' ', ' ', ' ', 'x', 'x', ' ', ' ', 'o', 'o'), 6): 0.5903424,\n",
       " ((' ', ' ', ' ', 'x', 'x', 'o', 'x', 'o', 'o'), 1): -1,\n",
       " ((' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '), 2): 0.8047739123470543,\n",
       " (('o', ' ', 'x', ' ', ' ', ' ', ' ', ' ', ' '), 5): 0.8532615479940651,\n",
       " (('o', ' ', 'x', 'o', ' ', 'x', ' ', ' ', ' '), 6): 0.8978239335246937,\n",
       " (('o', ' ', 'x', 'o', ' ', 'x', 'x', 'o', ' '), 8): 1,\n",
       " ((' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '), 1): 0.7525754208836217,\n",
       " ((' ', 'x', ' ', 'o', ' ', ' ', ' ', ' ', ' '), 0): 0.5266970682163201,\n",
       " (('x', 'x', ' ', 'o', 'o', ' ', ' ', ' ', ' '), 7): 0.18000000000000002,\n",
       " (('x', 'x', 'o', 'o', 'o', ' ', ' ', 'x', ' '), 5): 0.0,\n",
       " (('x', 'x', 'o', 'o', 'o', 'x', ' ', 'x', 'o'), 6): 0,\n",
       " ((' ', 'o', 'x', ' ', ' ', ' ', ' ', ' ', ' '), 4): 0.8565329705210961,\n",
       " ((' ', 'o', 'x', ' ', 'x', ' ', 'o', ' ', ' '), 3): 0.64594560393216,\n",
       " (('o', 'o', 'x', 'x', 'x', ' ', 'o', ' ', ' '), 8): 0.18000000000000002,\n",
       " (('o', 'o', 'x', 'x', 'x', ' ', 'o', 'o', 'x'), 5): 1,\n",
       " ((' ', 'x', ' ', ' ', 'o', ' ', 'x', ' ', 'o'), 7): -1,\n",
       " ((' ', ' ', 'o', ' ', 'o', 'x', ' ', 'x', ' '), 6): 0.05313600000000001,\n",
       " (('o', ' ', 'o', ' ', 'o', 'x', 'x', 'x', ' '), 8): 1,\n",
       " ((' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '), 7): 0.7320527271608921,\n",
       " ((' ', ' ', ' ', 'o', ' ', ' ', ' ', 'x', ' '), 5): 0.02606801356800001,\n",
       " (('o', ' ', ' ', 'o', ' ', 'x', ' ', 'x', ' '), 1): 0.0,\n",
       " (('o', 'x', ' ', 'o', ' ', 'x', ' ', 'x', 'o'), 6): -0.62,\n",
       " (('o', ' ', 'x', 'o', ' ', 'x', ' ', ' ', ' '), 7): -1,\n",
       " (('o', 'o', 'x', 'o', ' ', 'x', ' ', 'x', ' '), 4): -1,\n",
       " (('o', 'o', 'x', 'o', 'x', 'x', ' ', 'x', 'o'), 6): 1,\n",
       " ((' ', ' ', ' ', ' ', 'x', ' ', ' ', ' ', 'o'), 5): 0.5119932288614402,\n",
       " ((' ', ' ', 'o', ' ', 'x', 'x', ' ', ' ', 'o'), 6): 0.0,\n",
       " (('o', ' ', 'o', ' ', 'x', 'x', 'x', ' ', 'o'), 7): -1,\n",
       " ((' ', 'x', ' ', ' ', 'o', ' ', ' ', ' ', ' '), 2): 0.7795780672763051,\n",
       " ((' ', 'x', 'x', ' ', 'o', ' ', 'o', ' ', ' '), 8): 0.8930271307401378,\n",
       " ((' ', 'x', 'x', ' ', 'o', 'o', 'o', ' ', 'x'), 3): 0.18000000000000002,\n",
       " ((' ', 'x', 'x', 'x', 'o', 'o', 'o', 'o', 'x'), 0): 1,\n",
       " ((' ', ' ', ' ', 'o', 'x', ' ', ' ', ' ', ' '), 7): 0.39510272668262997,\n",
       " (('o', ' ', ' ', 'o', 'x', ' ', ' ', 'x', ' '), 6): 0.18000000000000002,\n",
       " (('o', ' ', 'o', 'o', 'x', ' ', 'x', 'x', ' '), 8): 1,\n",
       " ((' ', ' ', ' ', ' ', ' ', ' ', ' ', 'x', 'o'), 3): 0.09565345979780827,\n",
       " ((' ', ' ', ' ', 'x', 'o', ' ', ' ', 'x', 'o'), 0): 0.18000000000000002,\n",
       " (('x', ' ', 'o', 'x', 'o', ' ', ' ', 'x', 'o'), 5): -1,\n",
       " ((' ', ' ', ' ', ' ', ' ', 'x', 'o', ' ', ' '), 7): 0.052861248,\n",
       " ((' ', ' ', ' ', ' ', ' ', 'x', 'o', 'x', 'o'), 1): 0.0,\n",
       " (('o', 'x', ' ', ' ', ' ', 'x', 'o', 'x', 'o'), 4): 1,\n",
       " ((' ', ' ', ' ', ' ', ' ', ' ', ' ', ' ', ' '), 0): 0.7621591365774433,\n",
       " (('x', ' ', ' ', 'o', ' ', ' ', ' ', ' ', ' '), 1): 0.494366976,\n",
       " (('x', 'x', ' ', 'o', 'o', ' ', ' ', ' ', ' '), 5): 0.0,\n",
       " (('x', 'x', ' ', 'o', 'o', 'x', ' ', ' ', 'o'), 6): 0.0,\n",
       " (('x', 'x', ' ', 'o', 'o', 'x', 'x', 'o', 'o'), 2): 1,\n",
       " (('x', 'o', ' ', ' ', ' ', ' ', ' ', ' ', ' '), 3): 0.31202849433600005,\n",
       " (('x', 'o', ' ', 'x', ' ', ' ', ' ', ' ', 'o'), 6): 1,\n",
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       " (('o', ' ', 'x', ' ', ' ', ' ', 'o', 'x', ' '), 5): -1,\n",
       " (('o', 'x', ' ', ' ', 'o', ' ', ' ', 'x', ' '), 8): 0.46234024916954947,\n",
       " (('o', 'x', 'o', ' ', 'o', ' ', ' ', 'x', 'x'), 5): -1,\n",
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       " (('x', 'x', ' ', ' ', 'o', 'o', 'o', 'x', ' '), 3): -1,\n",
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       " ((' ', ' ', 'x', 'o', ' ', 'o', ' ', 'x', ' '), 8): -0.98,\n",
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       " ((' ', ' ', ' ', 'x', ' ', 'o', ' ', 'x', 'o'), 4): 0.0,\n",
       " ((' ', 'o', ' ', 'x', 'x', 'o', ' ', 'x', 'o'), 6): 0.0,\n",
       " (('o', 'o', ' ', 'x', 'x', 'o', 'x', 'x', 'o'), 2): 1,\n",
       " (('o', ' ', 'x', ' ', 'o', ' ', ' ', 'x', ' '), 6): -0.8,\n",
       " (('o', ' ', 'x', ' ', 'o', 'o', 'x', 'x', ' '), 1): -1,\n",
       " ((' ', ' ', 'x', ' ', ' ', ' ', 'o', 'x', 'o'), 5): -0.06923966735071055,\n",
       " ((' ', ' ', 'x', 'o', ' ', 'x', 'o', 'x', 'o'), 0): 0.22960157650845697,\n",
       " (('x', ' ', 'x', 'o', 'o', 'x', 'o', 'x', 'o'), 1): 1,\n",
       " ((' ', ' ', ' ', ' ', ' ', 'o', ' ', 'x', ' '), 4): 0.3709875456,\n",
       " (('o', ' ', ' ', ' ', 'x', 'o', ' ', 'x', ' '), 6): 0.5903424,\n",
       " (('o', 'o', ' ', ' ', 'x', 'o', 'x', 'x', ' '), 2): 1,\n",
       " (('x', ' ', 'o', ' ', ' ', 'o', ' ', 'x', ' '), 6): 0.0,\n",
       " (('x', 'o', 'o', ' ', ' ', 'o', 'x', 'x', ' '), 3): 1,\n",
       " ((' ', ' ', 'o', ' ', ' ', ' ', ' ', ' ', 'x'), 3): 0.20202048000000003,\n",
       " ((' ', 'o', 'o', 'x', ' ', ' ', ' ', ' ', 'x'), 0): 0.0,\n",
       " (('x', 'o', 'o', 'x', ' ', 'o', ' ', ' ', 'x'), 4): 1,\n",
       " (('x', ' ', ' ', 'o', 'o', ' ', ' ', 'x', ' '), 8): -0.62,\n",
       " ((' ', ' ', 'x', ' ', 'o', 'o', ' ', 'x', ' '), 0): 0.14780783301791248,\n",
       " (('x', ' ', 'x', ' ', 'o', 'o', 'o', 'x', ' '), 3): 0.19955284701924558,\n",
       " (('x', ' ', 'x', 'x', 'o', 'o', 'o', 'x', 'o'), 1): 1,\n",
       " ((' ', ' ', ' ', ' ', 'x', ' ', ' ', 'o', ' '), 3): 0.316858752,\n",
       " (('o', ' ', ' ', 'x', 'x', ' ', ' ', 'o', ' '), 8): 0.2603808,\n",
       " (('o', ' ', ' ', 'x', 'x', ' ', 'o', 'o', 'x'), 5): 1,\n",
       " ((' ', ' ', ' ', 'o', ' ', ' ', ' ', 'x', ' '), 4): 0.45570424588370395,\n",
       " ((' ', ' ', ' ', 'o', 'x', ' ', 'o', 'x', ' '), 8): 0.324,\n",
       " ...}"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Q-Learning vs. Random:\")\n",
    "\n",
    "DEBUG = False\n",
    "\n",
    "qplayer_x = QAgent(player = 'x', epsilon = 0.3, alpha = 0.2)\n",
    "qplayer_x.reset()\n",
    "\n",
    "print(\"Initially, the performance is not better than a random player!\")\n",
    "display(play(qplayer_x.play, random_player, N = 100))\n",
    "\n",
    "print(\"Play to learn how to play against a random player.\")\n",
    "display(play(qplayer_x.play, random_player, N = 5000))\n",
    "display(play(qplayer_x.play, random_player, N = 5000))\n",
    "display(play(qplayer_x.play, random_player, N = 5000))\n",
    "display(play(qplayer_x.play, random_player, N = 5000))\n",
    "display(play(qplayer_x.play, random_player, N = 5000))\n",
    "display(play(qplayer_x.play, random_player, N = 5000))\n",
    "display(play(qplayer_x.play, random_player, N = 5000))\n",
    "display(play(qplayer_x.play, random_player, N = 5000))\n",
    "display(play(qplayer_x.play, random_player, N = 5000))\n",
    "display(play(qplayer_x.play, random_player, N = 5000))\n",
    "\n",
    "print(\"Set epsilon to zero to make the agent greedy and play again:\")\n",
    "qplayer_x.epsilon = 0.0\n",
    "display(play(qplayer_x.play, random_player, N = 1000))\n",
    "\n",
    "print(\"Q-table size:\", len(qplayer_x.Q))\n",
    "qplayer_x.Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train a Q-learning agent for playing o."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random vs. Q-Learning:\n",
      "Initially, the performance is not better than a random player!\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'x': 53, 'o': 31, 'd': 16}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Play to learn how to play against a random player.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'x': 1898, 'o': 2493, 'd': 609}"
      ]
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     "metadata": {},
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    {
     "data": {
      "text/plain": [
       "{'x': 1245, 'o': 3182, 'd': 573}"
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     "metadata": {},
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    },
    {
     "data": {
      "text/plain": [
       "{'x': 1074, 'o': 3331, 'd': 595}"
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     "metadata": {},
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    {
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      "text/plain": [
       "{'x': 961, 'o': 3472, 'd': 567}"
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    {
     "data": {
      "text/plain": [
       "{'x': 851, 'o': 3559, 'd': 590}"
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    {
     "data": {
      "text/plain": [
       "{'x': 766, 'o': 3651, 'd': 583}"
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     "metadata": {},
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    },
    {
     "data": {
      "text/plain": [
       "{'x': 807, 'o': 3596, 'd': 597}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'x': 753, 'o': 3608, 'd': 639}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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       "{'x': 784, 'o': 3607, 'd': 609}"
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     "metadata": {},
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    },
    {
     "data": {
      "text/plain": [
       "{'x': 824, 'o': 3582, 'd': 594}"
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     "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Set epsilon to zero to make the agent greedy and play again:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'x': 5, 'o': 924, 'd': 71}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q-table size: 7172\n"
     ]
    },
    {
     "data": {
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       " (('o', 'x', 'x', ' ', 'x', 'o', ' ', ' ', ' '), 6): -1,\n",
       " ((' ', 'o', 'x', 'x', ' ', ' ', ' ', ' ', ' '), 0): 0.0,\n",
       " (('o', 'o', 'x', 'x', ' ', ' ', 'x', ' ', ' '), 8): 0.18000000000000002,\n",
       " (('o', 'o', 'x', 'x', ' ', ' ', 'x', 'x', 'o'), 5): -1,\n",
       " ((' ', ' ', ' ', 'o', ' ', 'x', 'x', ' ', ' '), 4): 0.031372262259565076,\n",
       " ((' ', 'x', ' ', 'o', 'o', 'x', 'x', ' ', ' '), 0): -0.025704916992000032,\n",
       " (('o', 'x', 'x', 'o', 'o', 'x', 'x', ' ', ' '), 8): 1,\n",
       " ((' ', ' ', ' ', ' ', 'x', 'o', 'x', ' ', ' '), 0): -0.41635093283746316,\n",
       " (('o', 'x', ' ', ' ', 'x', 'o', 'x', ' ', ' '), 8): -1,\n",
       " ((' ', ' ', ' ', 'o', ' ', 'x', 'x', ' ', ' '), 2): 0.0,\n",
       " ((' ', ' ', 'o', 'o', ' ', 'x', 'x', 'x', ' '), 4): -0.8,\n",
       " ((' ', 'x', ' ', ' ', 'x', ' ', ' ', 'o', ' '), 2): 0.0,\n",
       " ((' ', 'x', 'o', ' ', 'x', ' ', ' ', 'o', 'x'), 5): -0.8,\n",
       " ((' ', 'x', 'o', 'x', 'x', 'o', ' ', 'o', 'x'), 6): -1,\n",
       " ((' ', ' ', 'x', ' ', 'o', ' ', 'x', ' ', ' '), 0): 0.4412696991267909,\n",
       " (('o', ' ', 'x', ' ', 'o', ' ', 'x', ' ', 'x'), 5): -1,\n",
       " (('x', ' ', 'x', ' ', ' ', ' ', ' ', ' ', 'o'), 7): -0.07279999999999995,\n",
       " (('x', ' ', 'x', 'x', ' ', ' ', ' ', 'o', 'o'), 6): 1,\n",
       " (('x', 'o', 'x', ' ', 'o', ' ', 'x', ' ', ' '), 3): 0.8837870413414661,\n",
       " (('x', 'o', 'x', 'o', 'o', ' ', 'x', 'x', ' '), 5): 1,\n",
       " ((' ', 'o', ' ', 'x', ' ', ' ', ' ', 'x', ' '), 6): 0.05832000000000001,\n",
       " ((' ', 'o', ' ', 'x', ' ', ' ', 'o', 'x', 'x'), 5): 0.0,\n",
       " (('x', 'o', ' ', 'x', ' ', 'o', 'o', 'x', 'x'), 2): -1,\n",
       " ((' ', ' ', ' ', ' ', 'x', 'o', 'x', ' ', ' '), 2): 0.5821226831874576,\n",
       " (('x', 'o', ' ', 'x', ' ', ' ', ' ', ' ', ' '), 8): -0.64,\n",
       " (('o', ' ', ' ', 'x', ' ', 'x', ' ', ' ', ' '), 1): -0.7416799999999999,\n",
       " (('o', 'o', 'x', 'x', ' ', 'x', ' ', ' ', ' '), 6): 0.0,\n",
       " (('o', 'o', 'x', 'x', ' ', 'x', 'o', 'x', ' '), 4): -1,\n",
       " (('x', 'o', ' ', ' ', 'x', 'x', ' ', 'o', ' '), 3): 0.0,\n",
       " (('x', ' ', ' ', ' ', 'o', 'o', 'x', 'x', ' '), 3): 1,\n",
       " ((' ', ' ', ' ', 'o', ' ', ' ', 'x', ' ', 'x'), 4): 0.08373525372928001,\n",
       " ((' ', 'x', ' ', ' ', 'x', 'o', ' ', ' ', ' '), 0): -0.388864,\n",
       " (('o', 'x', ' ', ' ', 'x', 'o', ' ', ' ', 'x'), 2): -1,\n",
       " (('o', 'x', 'o', ' ', 'x', 'o', 'x', ' ', 'x'), 7): 0,\n",
       " (('o', ' ', 'o', 'x', ' ', ' ', ' ', 'x', 'x'), 4): -0.31599999999999995,\n",
       " (('o', 'x', 'o', 'x', 'o', ' ', ' ', 'x', 'x'), 5): -1,\n",
       " (('x', 'o', ' ', ' ', ' ', ' ', ' ', ' ', 'x'), 6): -0.6140800000000001,\n",
       " (('x', 'o', ' ', ' ', ' ', 'x', 'o', ' ', 'x'), 4): 0.53136,\n",
       " ((' ', 'o', ' ', ' ', ' ', 'x', 'x', ' ', ' '), 4): 0.5386590720000001,\n",
       " (('x', 'o', ' ', ' ', 'o', 'x', 'x', ' ', ' '), 3): 0.29482204789148225,\n",
       " (('x', 'o', 'x', 'o', 'o', 'x', 'x', ' ', ' '), 8): 0,\n",
       " (('x', ' ', ' ', ' ', 'x', ' ', ' ', 'o', ' '), 5): 0.10635379200000003,\n",
       " (('x', ' ', 'x', ' ', 'x', 'o', ' ', 'o', ' '), 3): -1,\n",
       " ((' ', 'x', ' ', 'x', ' ', 'o', ' ', ' ', ' '), 8): 0.8178142409503788,\n",
       " ((' ', 'x', ' ', 'x', ' ', 'o', 'x', ' ', 'o'), 4): -1,\n",
       " ((' ', 'x', ' ', 'x', 'o', 'o', 'x', 'x', 'o'), 0): 1,\n",
       " ((' ', ' ', 'o', 'x', 'x', ' ', ' ', ' ', ' '), 0): -0.62,\n",
       " (('o', 'x', 'o', 'x', 'x', ' ', ' ', ' ', ' '), 8): -1,\n",
       " ...}"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Random vs. Q-Learning:\")\n",
    "\n",
    "DEBUG = False\n",
    "\n",
    "qplayer_o = QAgent(player = 'o', epsilon = 0.3, alpha = 0.2)\n",
    "qplayer_o.reset()\n",
    "\n",
    "print(\"Initially, the performance is not better than a random player!\")\n",
    "display(play(random_player, qplayer_o.play, N = 100))\n",
    "\n",
    "print(\"Play to learn how to play against a random player.\")\n",
    "display(play(random_player, qplayer_o.play, N = 5000))\n",
    "display(play(random_player, qplayer_o.play, N = 5000))\n",
    "display(play(random_player, qplayer_o.play, N = 5000))\n",
    "display(play(random_player, qplayer_o.play, N = 5000))\n",
    "display(play(random_player, qplayer_o.play, N = 5000))\n",
    "display(play(random_player, qplayer_o.play, N = 5000))\n",
    "display(play(random_player, qplayer_o.play, N = 5000))\n",
    "display(play(random_player, qplayer_o.play, N = 5000))\n",
    "display(play(random_player, qplayer_o.play, N = 5000))\n",
    "display(play(random_player, qplayer_o.play, N = 5000))\n",
    "\n",
    "print(\"Set epsilon to zero to make the agent greedy and play again:\")\n",
    "qplayer_o.epsilon = 0.0\n",
    "display(play(random_player, qplayer_o.play, N = 1000))\n",
    "\n",
    "print(\"Q-table size:\", len(qplayer_o.Q))\n",
    "qplayer_o.Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q-Learning vs. Q-Learning\n",
    "Let two Q-learning agents play each other. This is called self play. Note that both agents already have been trained against a random agent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q-Learning vs. Q-Learning:\n",
      "exploration with epsilon = 0.3:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'x': 2055, 'o': 1320, 'd': 1625}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'x': 2114, 'o': 1135, 'd': 1751}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'x': 2090, 'o': 1167, 'd': 1743}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'x': 2107, 'o': 1115, 'd': 1778}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'x': 2113, 'o': 1106, 'd': 1781}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result exploration to epsilon = 0.2:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'x': 1629, 'o': 864, 'd': 2507}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'x': 1622, 'o': 929, 'd': 2449}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'x': 1617, 'o': 900, 'd': 2483}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "{'x': 1638, 'o': 948, 'd': 2414}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result with no exploration (epsilon = 0):\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'x': 26, 'o': 12, 'd': 962}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Q-Learning vs. Q-Learning:\")\n",
    "\n",
    "# turn on a little exploration\n",
    "print(\"exploration with epsilon = 0.3:\")\n",
    "qplayer_x.epsilon = 0.3\n",
    "qplayer_o.epsilon = 0.3\n",
    "\n",
    "display(play(qplayer_x.play, qplayer_o.play, N = 5000))\n",
    "display(play(qplayer_x.play, qplayer_o.play, N = 5000))\n",
    "display(play(qplayer_x.play, qplayer_o.play, N = 5000))\n",
    "display(play(qplayer_x.play, qplayer_o.play, N = 5000))\n",
    "display(play(qplayer_x.play, qplayer_o.play, N = 5000))\n",
    "\n",
    "# reduce exploration. The agent will now play fewer random moves.\n",
    "print(\"Result exploration to epsilon = 0.2:\")\n",
    "qplayer_x.epsilon = 0.2\n",
    "qplayer_o.epsilon = 0.2\n",
    "\n",
    "display(play(qplayer_x.play, qplayer_o.play, N = 5000))\n",
    "display(play(qplayer_x.play, qplayer_o.play, N = 5000))\n",
    "display(play(qplayer_x.play, qplayer_o.play, N = 5000))\n",
    "display(play(qplayer_x.play, qplayer_o.play, N = 5000))\n",
    "\n",
    "print(\"Result with no exploration (epsilon = 0):\")\n",
    "qplayer_x.epsilon = 0\n",
    "qplayer_o.epsilon = 0\n",
    "display(play(qplayer_x.play, qplayer_o.play, N = 1000))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At the end, no agent should be able to win."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Look at the Q-tables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q-table size of x: 7744\n",
      "Q-table size of o: 7322\n"
     ]
    }
   ],
   "source": [
    "print(\"Q-table size of x:\", len(qplayer_x.Q))\n",
    "print(\"Q-table size of o:\", len(qplayer_o.Q))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at Q-table entries for a few boards. We show the action and the Q-value from the table. `nan` (i.e., not a number) means the action has not been tried and there is no Q-value in the table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 192x192 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[[0, 0.07],\n",
       " [1, 0.07],\n",
       " [2, 0.07],\n",
       " [3, 0.07],\n",
       " [4, 0.14],\n",
       " [5, 0.07],\n",
       " [6, 0.07],\n",
       " [7, 0.07],\n",
       " [8, 0.07]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 192x192 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[[2, 0.61], [5, 0.0], [6, 0.18], [7, 0.03], [8, 1]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 192x192 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[[3, -0.62], [5, -0.8], [6, -1], [7, 0.0], [8, -1]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q = qplayer_x.Q\n",
    "\n",
    "def find_q(s):\n",
    "    return [[x, round(Q.get((tuple(s), x), np.nan),2)] for x in actions(s)]\n",
    "\n",
    "\n",
    "board = empty_board()\n",
    "show_board(board)\n",
    "display(find_q(board))\n",
    "\n",
    "\n",
    "board = empty_board() \n",
    "board[0] = 'x'\n",
    "board[1] = 'o'\n",
    "board[3] = 'o'\n",
    "board[4] = 'x'\n",
    "show_board(board)\n",
    "display(find_q(board))\n",
    "\n",
    "\n",
    "board = empty_board() \n",
    "board[0] = 'x'\n",
    "board[1] = 'o'\n",
    "board[2] = 'x'\n",
    "board[4] = 'o'\n",
    "show_board(board)\n",
    "display(find_q(board))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}