project_summary.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Project Summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import time\n",
    "from datetime import datetime\n",
    "\n",
    "from game import Game, Player\n",
    "from utils import investigate_game\n",
    "from utils.investigate_game import InvestigateGame\n",
    "from players.random_player import RandomPlayer\n",
    "from players.min_max import MinMaxPlayer, AlphaBetaMinMaxPlayer\n",
    "from players.monte_carlo_rl import MonteCarloRLPlayer\n",
    "from players.monte_carlo_tree_search import MCTSPlayer\n",
    "from players.human_player import HumanPlayer\n",
    "\n",
    "import sys\n",
    "\n",
    "# needed to load Seralized Monte Carlo RL Player\n",
    "sys.modules['investigate_game'] = investigate_game"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_training_stats(\n",
    "    rewards: list, state_value_dict_size: int, step_size: int, switch_ratio: int | None = None\n",
    ") -> None:\n",
    "    \"\"\"\n",
    "    Given a training list of rewards and the size of the player's State-Value dictionary,\n",
    "    this function plots the averages of the rewards using a given step size.\n",
    "\n",
    "    Args:\n",
    "        rewards: the rewards achieved during training time;\n",
    "        state_value_dict_size: the length of the State-Value dictionary of the player;\n",
    "        step: the step size to be used to plot an average value;\n",
    "        switch_ratio: define the moment in which minmax started playing-\n",
    "\n",
    "    Returns:\n",
    "        None.\n",
    "    \"\"\"\n",
    "\n",
    "    # https://stackoverflow.com/questions/15956309/averaging-over-every-n-elements-of-a-numpy-array\n",
    "    # compute the averages\n",
    "    averages = np.mean(np.array(rewards).reshape(-1, step_size), axis=1)\n",
    "\n",
    "    # define the width and height of the figure in inches\n",
    "    plt.figure(figsize=(10, 5))\n",
    "    # plot the averages\n",
    "    plt.plot(averages, color='red', marker='o', linestyle='dashed', label='Training')\n",
    "    # if minmax played\n",
    "    if switch_ratio is not None:\n",
    "        # compute the exact moment\n",
    "        switch_moment = int(len(rewards) / step_size * switch_ratio)\n",
    "        # print a vertical line at the moment minmax started playing\n",
    "        plt.axvline(x=switch_moment, color='green', label='MinMax Starts Playing')\n",
    "    # specify the title\n",
    "    plt.title('Training Summary')\n",
    "    # specify the x-axis label\n",
    "    plt.xlabel('# of the step')\n",
    "    # specify the y-axis label\n",
    "    plt.ylabel('Mean rewards value')\n",
    "    # show the legend\n",
    "    plt.legend()\n",
    "    # add information text\n",
    "    plt.text(\n",
    "        500,\n",
    "        0,\n",
    "        f'Number of visited states: {state_value_dict_size:,}',\n",
    "        color=\"white\",\n",
    "        bbox=dict(facecolor='red', boxstyle='round,pad=0.3,rounding_size=0.2'),\n",
    "        ha='right',\n",
    "        va='top',\n",
    "    )\n",
    "    # show the plot\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monte Carlo Reinforcement learning player\n",
    "\n",
    "To train a Reinforcement Learning player based on a Monte Carlo technique, we used a method referred as [**Temporal Difference learning (TD)**](https://en.wikipedia.org/wiki/Temporal_difference_learning#Mathematical_formulation). In short, the training is performed in such a way that the _State-Value_ function is updated as follows:\n",
    "$$\n",
    "V(S_{t})\\leftarrow (1-\\alpha )V(S_{t})+\\underbrace {\\alpha } _{\\text{learning rate}}[\\overbrace {R_{t+1}+\\gamma V(S_{t+1})} ^{\\text{The TD target}}]\n",
    "$$\n",
    "where $S_{t}$ is the state at time $t$, $\\gamma$ is the discount rate and $R_{t+1}$ is the reward at time $t+1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Show the training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "monte_carlo_rl_player = MonteCarloRLPlayer()\n",
    "monte_carlo_rl_player.load('trained_agents/monte_carlo_rl.pkl')\n",
    "plot_training_stats(monte_carlo_rl_player.rewards, len(monte_carlo_rl_player._state_values), step_size=1_000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Considering the above plot, we can see that the player is able to learn because of the implemented symmetries. Without the symmetries, the number of states is too large and the player would need a huge amount of matches to achieve the same learning performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train MinMax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/100 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Found states: 5,262,427: 100%|██████████| 100/100 [22:58<00:00, 13.78s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New found states after 100 games: 5,262,427\n"
     ]
    }
   ],
   "source": [
    "minmax_player = MinMaxPlayer(depth=3, enhance=True)\n",
    "minmax_player.train(n_games=100)\n",
    "minmax_player.save('trained_agents/minmax_depth3_player.pkl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train AlphaBetaMinMax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Found states: 3,467,383: 100%|██████████| 20/20 [27:21<00:00, 82.05s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New found states after 20 games: 3,467,383\n"
     ]
    }
   ],
   "source": [
    "alphabeta_minmax_player = AlphaBetaMinMaxPlayer(depth=4, enhance=True)\n",
    "alphabeta_minmax_player.train(n_games=20)\n",
    "alphabeta_minmax_player.save('trained_agents/alphabeta_minmax_depth4_player')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## View Games"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- BEGINNING OF THE GAME --\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "Player ❌ chose to move (0, 1) to the top\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "Player ⭕️ chose to move (2, 4) to the right\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⭕️\n",
      "Player ❌ chose to move (0, 1) to the bottom\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⭕️\n",
      "Player ⭕️ chose to move (0, 1) to the top\n",
      "⭕️⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⭕️\n",
      "Player ❌ chose to move (4, 0) to the left\n",
      "❌⭕️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⭕️\n",
      "Player ⭕️ chose to move (3, 0) to the right\n",
      "❌⭕️⬜️⬜️⭕️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⭕️\n",
      "Player ❌ chose to move (0, 2) to the top\n",
      "❌⭕️⬜️⬜️⭕️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "⬜️⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⭕️\n",
      "Player ⭕️ chose to move (0, 3) to the bottom\n",
      "❌⭕️⬜️⬜️⭕️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "⭕️⬜️⬜️⬜️⭕️\n",
      "Player ❌ chose to move (2, 4) to the left\n",
      "❌⭕️⬜️⬜️⭕️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "❌⬜️⬜️⬜️⬜️\n",
      "❌⭕️⬜️⬜️⭕️\n",
      "Winner: Player 0\n",
      "-- END OF THE GAME --\n"
     ]
    }
   ],
   "source": [
    "# create the first player\n",
    "player1 = MinMaxPlayer()\n",
    "# create the second player\n",
    "player2 = RandomPlayer()\n",
    "# create a new game\n",
    "game = InvestigateGame(Game())\n",
    "# LET'S BATTLE\n",
    "winner = game.play(player1, player2, max_steps_draw=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Play Games"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create the human player\n",
    "human_player = HumanPlayer()\n",
    "\n",
    "# create a mtcs player\n",
    "monte_carlo_tree_search = MCTSPlayer(n_simulations=500, random=True)\n",
    "\n",
    "# start the game\n",
    "g = InvestigateGame(Game())\n",
    "g.play(human_player, monte_carlo_tree_search, max_steps_draw=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing Players performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_game_statistics(player1: Player, player2: Player, n_games: int) -> None:\n",
    "    \"\"\"\n",
    "    Play a few games between two players and plot the calculated winning percentages.\n",
    "\n",
    "    Args:\n",
    "        players1: the first player;\n",
    "        players2: the second player;\n",
    "        n_games: how many games to play.\n",
    "\n",
    "    Returns:\n",
    "        None.\n",
    "    \"\"\"\n",
    "\n",
    "    # define the width and height of the figure in inches\n",
    "    plt.figure(figsize=(8, 5))\n",
    "\n",
    "    # let the players play both first and second\n",
    "    for plot, (player1, player2) in enumerate([(player1, player2), (player2, player1)]):\n",
    "        # count how many wins for the first player\n",
    "        player1_wins = 0\n",
    "\n",
    "        # for each game\n",
    "        for _ in range(n_games):\n",
    "            # create the game\n",
    "            game = Game()\n",
    "            # play the game\n",
    "            winner = game.play(player1, player2)\n",
    "            # if the first player wins\n",
    "            if winner == 0:\n",
    "                # increment the counter\n",
    "                player1_wins += 1\n",
    "\n",
    "        # create a subplot\n",
    "        plt.subplot(1, 2, plot + 1)\n",
    "        # plot the first player wins\n",
    "        bars = plt.bar([0, 0.6], [player1_wins, n_games - player1_wins], color=['royalblue', 'lightcoral'], width=0.4)\n",
    "        # for each bar\n",
    "        for bar in bars:\n",
    "            # get the winning percentage\n",
    "            percentage = bar.get_height() / n_games\n",
    "            # write the percentage on top of the bar\n",
    "            plt.text(\n",
    "                bar.get_x() + bar.get_width() / 2,\n",
    "                bar.get_height(),\n",
    "                f'{percentage:.2%}',\n",
    "                ha='center',\n",
    "                va='bottom',\n",
    "                fontsize='medium',\n",
    "            )\n",
    "        # plot the players' names\n",
    "        plt.xticks([0, 0.6], [player1.__class__.__name__, player2.__class__.__name__])\n",
    "        # delete y-axis ticks and labels\n",
    "        plt.tick_params(left=False, labelleft=False)\n",
    "        # specify the y-axis label\n",
    "        plt.ylabel('Wins')\n",
    "        # specify the title shared between the subplots\n",
    "        plt.title(\n",
    "            f'{player1.__class__.__name__.replace(\"Player\",\"\")} VS {player2.__class__.__name__.replace(\"Player\",\"\")}',\n",
    "            fontsize=10,\n",
    "        )\n",
    "\n",
    "    # specify the title shared between the subplots\n",
    "    plt.suptitle(f'Summary of {n_games} games')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_game_statistics(RandomPlayer(), MCTSPlayer(n_simulations=500, random=True), 100)\n",
    "show_game_statistics(RandomPlayer(), monte_carlo_rl_player, 100)\n",
    "show_game_statistics(RandomPlayer(), MinMaxPlayer(depth=3, enhance=True), 100)\n",
    "show_game_statistics(RandomPlayer(), AlphaBetaMinMaxPlayer(depth=3, enhance=True), 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing MinMax implementations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_minmax_statistics(player: MinMaxPlayer, minute: bool = False) -> None:\n",
    "    \"\"\"\n",
    "    Play two games between the minmax player and a player that play randomly, and plot the duration time\n",
    "    of the game with different optimizations.\n",
    "\n",
    "    Args:\n",
    "        player: a minmax player to test.\n",
    "\n",
    "    Returns:\n",
    "        None.\n",
    "    \"\"\"\n",
    "\n",
    "    # define the width and height of the figure in inches\n",
    "    plt.figure(figsize=(8, 5))\n",
    "\n",
    "    # list to collect the duration time\n",
    "    data = []\n",
    "\n",
    "    # for each optimization\n",
    "    for label, (flag1, flag2) in {\n",
    "        'Hash table': (False, False),\n",
    "        'Parallization': (True, False),\n",
    "        'Symmetries': (False, True),\n",
    "        'Parallization\\n&\\nSymmetries': (True, True),\n",
    "        'Nothing': (False, False),\n",
    "    }.items():\n",
    "        # set the flags\n",
    "        player.parallelize(flag1)\n",
    "        player._symmetries = flag2\n",
    "        # create the game\n",
    "        game = Game()\n",
    "        # keep track of the start time\n",
    "        start = time.time()\n",
    "        # play the game\n",
    "        game.play(player, RandomPlayer())\n",
    "        # create the game\n",
    "        game = Game()\n",
    "        # play the game\n",
    "        game.play(RandomPlayer(), player)\n",
    "        # get the total time of a match\n",
    "        total_time = (time.time() - start) / 2\n",
    "        # append the data to plot\n",
    "        data.append((label, total_time))\n",
    "\n",
    "    # split labels and values\n",
    "    labels, values = zip(*sorted(data, key=lambda x: x[1]))\n",
    "    # plot the results\n",
    "    bars = plt.bar(labels, values, color=['deepskyblue'], width=0.5)\n",
    "    # for each bar\n",
    "    for i, bar in enumerate(bars):\n",
    "        # write the game duration on top of the bar\n",
    "        plt.text(\n",
    "            bar.get_x() + bar.get_width() / 2,\n",
    "            bar.get_height(),\n",
    "            (datetime.strftime(datetime.utcfromtimestamp(values[i]), \"%Mm %Ss %f\")[:-3] + \"ms\")\n",
    "            .replace('00m ', '')\n",
    "            .replace('00s ', '')\n",
    "            .replace(' 000ms', ''),\n",
    "            ha='center',\n",
    "            va='bottom',\n",
    "            fontsize='medium',\n",
    "        )\n",
    "\n",
    "    # delete y-axis ticks and labels\n",
    "    plt.tick_params(left=False, labelleft=False)\n",
    "    # specify the y-axis label\n",
    "    plt.ylabel('Time')\n",
    "    # specify the title\n",
    "    plt.title(f'How long does a game last?')\n",
    "    # add margins to the plot\n",
    "    plt.margins(y=0.2)\n",
    "    # add information text\n",
    "    plt.text(\n",
    "        -0.35,\n",
    "        values[-1] * (1.16),\n",
    "        f'{player.__class__.__name__} at depth {player._depth} VS RandomPlayer',\n",
    "        color=\"white\",\n",
    "        bbox=dict(facecolor='steelblue', boxstyle='round,pad=0.3,rounding_size=0.2'),\n",
    "        ha='left',\n",
    "        va='top',\n",
    "    )\n",
    "    # show the plot\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "minmax_player = MinMaxPlayer()\n",
    "minmax_player.load('trained_agents/minmax_depth3_player.pkl')\n",
    "alphabeta_minmax_player = AlphaBetaMinMaxPlayer()\n",
    "alphabeta_minmax_player.load('trained_agents/alphabeta_minmax_depth4_player.pkl')\n",
    "show_minmax_statistics(minmax_player)\n",
    "show_minmax_statistics(alphabeta_minmax_player)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen from the results, parallelization of the first level of the MinMax search tree leads to the best results. Against our expectations, however, symmetries do not produce time improvements, but worsen the overall performance of the players."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "ci",
   "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": "3.12.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}