Sarsa.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sarsa\n",
    "\n",
    "Implement Sarsa to learn how to play Tic-tac-toe against a random player. Produce a learning curve. Discuss the learning curves. The pseudo-code for SARSA is reproduced below from the textbook (Reinforcement Learning, Sutton & Barto, 1998, Section 6.4).\n",
    "<img src=\"images/SARSA.png\" style=\"width: 600px;\"/>\n",
    "\n",
    "### compare with Q-learning agent\n",
    "\n",
    "The pseudo-code for Q-learning is reproduced below from the textbook (Reinforcement Learning, Sutton & Barto, 1998, Section 6.5).\n",
    "<img src=\"images/q_learning.png\" style=\"width: 600px;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Game Tic-Tac-Toe\n",
    "\n",
    "Tic-Tac-Toe is a paper-and-pencil game for two players, O and X, who take turns marking the spaces in a 3×3 grid. The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row wins the game. The following example game is won by player X (example from [Wikipedia](https://en.wikipedia.org/wiki/Tic-tac-toe)):\n",
    "<img src=\"images/tic-tac-toe_WIKI.png\" style=\"width: 600px;\"/> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import itertools\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Game Tic-Tac-Toe environment\n",
    "class Board:\n",
    "    def __init__(self, player_1, player_2):\n",
    "        self.board = np.array([[' ', ' ', ' '], [' ', ' ', ' '], [' ', ' ', ' ']])\n",
    "        self.player1_marker = player_1.marker\n",
    "        self.player2_marker = player_2.marker\n",
    "        self.active = False\n",
    "        self.winner = None\n",
    "    \n",
    "    # get the possible choices for next step\n",
    "    def get_possible_step(self):\n",
    "        pos_step = []\n",
    "        for i in itertools.product(np.arange(0,3),np.arange(0,3)):\n",
    "            if self.board[i] == ' ':\n",
    "                pos_step.append(i)\n",
    "        return pos_step\n",
    "   \n",
    "    # print the current state of the board\n",
    "    def print_board(self):\n",
    "        print_cor = (((0,0),(0,1),(0,2)),((1,0),(1,1),(1,2)),((2,0),(2,1),(2,2)))\n",
    "        for i in print_cor:\n",
    "            print(self.board[i[0]] + '|' + self.board[i[1]] + '|' + self.board[i[2]])\n",
    "    \n",
    "    # check if the game is end\n",
    "    def check(self):\n",
    "        # check who is win\n",
    "        win_conditions = (((0,0),(0,1),(0,2)),((1,0),(1,1),(1,2)),((2,0),(2,1),(2,2)),\n",
    "                          ((0,0),(1,0),(2,0)),((0,1),(1,1),(2,1)),((0,2),(1,2),(2,2)),\n",
    "                          ((0,0),(1,1),(2,2)),((0,2),(1,1),(2,0)))\n",
    "        for each in win_conditions:\n",
    "            if self.board[each[0]] == self.board[each[1]]  == self.board[each[2]]:\n",
    "                if self.board[each[0]] != ' ':\n",
    "                    self.winner = self.board[each[0]]\n",
    "        \n",
    "        if self.winner == self.player1_marker:\n",
    "            player1_reward = 1\n",
    "            player2_reward = -1\n",
    "            self.active = False\n",
    "            return player1_reward, player2_reward\n",
    "\n",
    "        if self.winner == self.player2_marker:\n",
    "            player1_reward = -1\n",
    "            player2_reward = 1\n",
    "            self.active = False\n",
    "            return player1_reward, player2_reward\n",
    "        \n",
    "        # check if it's draw\n",
    "        if len(self.get_possible_step()) == 0 and self.winner is None:\n",
    "            player1_reward = 0\n",
    "            player2_reward = 0\n",
    "            self.active = False\n",
    "            return player1_reward, player2_reward\n",
    "        \n",
    "        # if the game is not end \n",
    "        player1_reward = 0\n",
    "        player2_reward = 0\n",
    "        return player1_reward, player2_reward\n",
    "    \n",
    "    # make step function\n",
    "    def make_step(self, player, step_coordinate):\n",
    "        self.board[step_coordinate] = player.marker\n",
    "        player1_reward, player2_reward = self.check()\n",
    "        new_state = self.board\n",
    "        \n",
    "        return player1_reward, player2_reward, new_state\n",
    "    \n",
    "    # reset the game\n",
    "    def reset_game(self):\n",
    "        self.active = True\n",
    "        self.winner = None\n",
    "        self.board = np.array([[' ', ' ', ' '], [' ', ' ', ' '], [' ', ' ', ' ']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Random Agent\n",
    "class random_agent:\n",
    "    def __init__(self, marker):\n",
    "        self.marker = marker\n",
    "        \n",
    "    def choose_step(self, board):\n",
    "        pos_step = board.get_possible_step()\n",
    "        chosen_step = pos_step[np.random.choice(len(pos_step))]\n",
    "        return chosen_step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Q Agent\n",
    "class Q_Agent:\n",
    "    def __init__(self, marker, alpha = 0.1, greedy = 0.1):\n",
    "        self.marker = marker\n",
    "        self.alpha = alpha\n",
    "        self.greedy = greedy\n",
    "        self.q = {}\n",
    "    \n",
    "    # get q value, if the key is not exist (since initial the q table as empty dictionary), initial its value as 0\n",
    "    def getQ(self, state, step):\n",
    "        if self.q.get((state, step)) is None:\n",
    "            self.q[(state, step)] = 1\n",
    "        return self.q.get((state, step))\n",
    "    \n",
    "    def choose_step(self, env):\n",
    "        current_state = tuple(map(tuple, env.board))\n",
    "        pos_step = env.get_possible_step()\n",
    "        if np.random.rand(1) < self.greedy:\n",
    "            # choose not greedy action \n",
    "            chosen_step = pos_step[np.random.choice(len(pos_step))]\n",
    "        else:\n",
    "            # choose greedy action according to Q table\n",
    "            # get the maximum Q value of the current state\n",
    "            max_q = np.array([self.getQ(current_state, p_step) for p_step in pos_step]).max()\n",
    "            # create= a current dictionary which is a part of Q table to avoid of different state, but same q value\n",
    "            current_key = [(current_state, p_step) for p_step in pos_step]\n",
    "            new_d = {key:self.q[key] for key in current_key}\n",
    "            # choose the action, if there are several actions, choose randomly\n",
    "            choices = [key for key in new_d.keys() if new_d[key]==max_q]  \n",
    "            chosen_step = choices[np.random.choice(len(choices))][1]\n",
    "            \n",
    "        return chosen_step\n",
    "    \n",
    "    def Q_learn(self, old_state, new_state, step, reward, pos_step_after):\n",
    "        old_state = tuple(map(tuple, old_state))\n",
    "        new_state = tuple(map(tuple, new_state))\n",
    "        if len(pos_step_after) == 0:\n",
    "            pass\n",
    "        else:\n",
    "            max_value = np.array([self.getQ(new_state, p_step) for p_step in pos_step_after]).max()\n",
    "            self.q[(old_state,step)] = (1-self.alpha)*self.getQ(old_state,step)+self.alpha*(reward+max_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sarsa Agent\n",
    "class Sarsa_Agent:\n",
    "    def __init__(self, marker, alpha = 0.1, greedy = 0.1):\n",
    "        self.marker = marker\n",
    "        self.alpha = alpha\n",
    "        self.greedy = greedy\n",
    "        self.q = {}\n",
    "    \n",
    "    # get q value, if the key is not exist (since initial the q table as empty dictionary), initial its value as 0\n",
    "    def getQ(self, state, step):\n",
    "        if self.q.get((state, step)) is None:\n",
    "            self.q[(state, step)] = 1\n",
    "        return self.q.get((state, step))\n",
    "    \n",
    "    def choose_step(self, env):\n",
    "        current_state = tuple(map(tuple, env.board))\n",
    "        pos_step = env.get_possible_step()\n",
    "        if len(pos_step) == 0:\n",
    "            # chose (3,3) as an unexist step in the game, just to make the program pass\n",
    "            chosen_step = (3,3)\n",
    "        elif np.random.rand(1) < self.greedy:\n",
    "            # choose not greedy action \n",
    "            chosen_step = pos_step[np.random.choice(len(pos_step))]\n",
    "        else:\n",
    "            # choose greedy action according to Q table\n",
    "            # get the maximum Q value of the current state\n",
    "            max_q = np.array([self.getQ(current_state, p_step) for p_step in pos_step]).max()\n",
    "            # create a current dictionary which is a part of Q table to avoid of different state, but same q value\n",
    "            current_key = [(current_state, p_step) for p_step in pos_step]\n",
    "            new_d = {key:self.q[key] for key in current_key}\n",
    "            # choose the action, if there are several actions, choose randomly\n",
    "            choices = [key for key in new_d.keys() if new_d[key]==max_q]  \n",
    "            chosen_step = choices[np.random.choice(len(choices))][1]\n",
    "            \n",
    "        return chosen_step\n",
    "    \n",
    "    def Sarsa_learn(self, old_state, new_state, old_step, new_step, reward):\n",
    "        old_state = tuple(map(tuple, old_state))\n",
    "        new_state = tuple(map(tuple, new_state))\n",
    "        mask1 = self.getQ(old_state, old_step)\n",
    "        mask2 = self.alpha * (reward + self.getQ(new_state, new_step) - mask1)\n",
    "        self.q[(old_state,old_step)] = mask1 + mask2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a function that simulate Q learning\n",
    "def simulate_game_Q(player_1, player_2, eposides):\n",
    "    # asumme player_1 is always the Q-learning Agent\n",
    "    env = Board(player_1, player_2)\n",
    "    player_1_record = np.zeros(eposides)\n",
    "    player_2_record = np.zeros(eposides)\n",
    "    player_1_total = 0\n",
    "    player_2_total = 0\n",
    "    for eposide in range(eposides): \n",
    "        \n",
    "        env.reset_game()\n",
    "        # switch player\n",
    "        player_first, player_second = (player_1, player_2) if np.random.choice(2) == 0 else (player_2, player_1)\n",
    "        # play the game\n",
    "        while env.active == True:\n",
    "            temp_reward = 0\n",
    "            old_state = env.board.copy()\n",
    "            player_first_step = player_first.choose_step(env)\n",
    "            player_1_reward, player_2_reward, new_state = env.make_step(player_first, player_first_step)\n",
    "            temp_reward += player_1_reward\n",
    "            player_1_total += player_1_reward\n",
    "            player_2_total += player_2_reward\n",
    "            if env.active == True:\n",
    "                player_second_step = player_second.choose_step(env)\n",
    "                player_1_reward, player_2_reward, new_state = env.make_step(player_second, player_second_step)\n",
    "                temp_reward += player_1_reward\n",
    "                player_1_total += player_1_reward\n",
    "                player_2_total += player_2_reward\n",
    "                pos_step_after = env.get_possible_step()\n",
    "                # check wihich player is q player\n",
    "                if player_1 == player_first:                 \n",
    "                    player_1.Q_learn(old_state, new_state, player_first_step, temp_reward, pos_step_after)\n",
    "                else:\n",
    "                    player_1.Q_learn(old_state, new_state, player_second_step, temp_reward, pos_step_after)\n",
    "            else:\n",
    "                pos_step_after = env.get_possible_step()\n",
    "                # check which player is q player\n",
    "                if player_1 == player_first:                 \n",
    "                    player_1.Q_learn(old_state, new_state, player_first_step, temp_reward, pos_step_after)\n",
    "                else:\n",
    "                    player_1.Q_learn(old_state, new_state, player_second_step, temp_reward, pos_step_after)\n",
    "                    \n",
    "        player_1_record[eposide] = player_1_total\n",
    "        player_2_record[eposide] = player_2_total\n",
    "        \n",
    "    return player_1_record, player_2_record"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a function that used to simulate Sarsa\n",
    "def simulate_game_Sarsa(player_1, player_2, eposides):\n",
    "    # asumme player_1 is always the SARSA Agent\n",
    "    env = Board(player_1, player_2)\n",
    "    player_1_record = np.zeros(eposides)\n",
    "    player_2_record = np.zeros(eposides)\n",
    "    player_1_total = 0\n",
    "    player_2_total = 0\n",
    "    for eposide in range(eposides): \n",
    "        env.reset_game()\n",
    "        # switch player\n",
    "        if np.random.choice(2) == 0: # when player 1 go first\n",
    "            old_player_1_step = player_1.choose_step(env)           \n",
    "        else:  # when player 2 go fisrt\n",
    "            player_2_step = player_2.choose_step(env)\n",
    "            player_1_reward, player_2_reward, _ = env.make_step(player_2, player_2_step)\n",
    "            player_1_total += player_1_reward\n",
    "            player_2_total += player_2_reward\n",
    "            old_player_1_step = player_1.choose_step(env)\n",
    "        # play the game\n",
    "        while env.active == True:\n",
    "            temp_reward = 0\n",
    "            old_state = env.board.copy()\n",
    "            player_1_reward, player_2_reward, new_state = env.make_step(player_1, old_player_1_step)\n",
    "            temp_reward += player_1_reward\n",
    "            player_1_total += player_1_reward\n",
    "            player_2_total += player_2_reward \n",
    "            if env.active == True:\n",
    "                player_2_step = player_2.choose_step(env)\n",
    "                player_1_reward, player_2_reward, new_state = env.make_step(player_2, player_2_step)\n",
    "                temp_reward += player_1_reward\n",
    "                player_1_total += player_1_reward\n",
    "                player_2_total += player_2_reward\n",
    "                new_player_1_step = player_1.choose_step(env)\n",
    "                player_1.Sarsa_learn(old_state, new_state, old_player_1_step, new_player_1_step, \n",
    "                                     temp_reward)\n",
    "                old_player_1_step = new_player_1_step\n",
    "            else:\n",
    "                # chose (3,3) as an unexist step in the game, just to make the program pass\n",
    "                new_player_1_step = (3,3)\n",
    "                player_1.Sarsa_learn(old_state, new_state, old_player_1_step, new_player_1_step, \n",
    "                                     temp_reward)\n",
    "                    \n",
    "        player_1_record[eposide] = player_1_total\n",
    "        player_2_record[eposide] = player_2_total\n",
    "        \n",
    "    return player_1_record, player_2_record"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UDx8+nPLly5OUlETLli1Zs2YN0dHR3HXXXRw8eJCwsDCmTp1K165d+e2333j6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\niPgJBTcRERERP6HgJiIiIuIn/g8+YtJqmt6TMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106c7bd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player_random = random_agent('X')\n",
    "eposides = 6000\n",
    "player_Q_record = []\n",
    "player_SARSA_record = []\n",
    "for i in range(5):\n",
    "    player_Q = Q_Agent('O')\n",
    "    player_SARSA = Sarsa_Agent('O')\n",
    "    \n",
    "    player_Q_record.append(simulate_game_Q(player_Q, player_random, eposides)[0])\n",
    "    player_SARSA_record.append(simulate_game_Sarsa(player_SARSA, player_random, eposides)[0])\n",
    "\n",
    "fig = plt.figure(figsize=(10, 8))\n",
    "\n",
    "plt.plot(np.arange(eposides), np.array(player_Q_record).mean(axis = 0), color = 'g', \n",
    "         label = '5 Q learning Players O averaged')\n",
    "plt.plot(np.arange(eposides), np.array(player_SARSA_record).mean(axis = 0), color = 'r', \n",
    "         label = '5 SARSA Players O averaged')\n",
    "\n",
    "\n",
    "plt.legend(loc = 'best')\n",
    "plt.xlabel('Eposides')\n",
    "plt.ylabel('Total rewards')\n",
    "plt.title('The comparing learning curves for 5 Sarsa Players and 5 Q Players')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}