Section_4_on_policy_constant_alpha_mc_complete.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "pycharm": {
          "name": "#%%\n"
        },
        "id": "7gzJnFaonawG"
      },
      "source": [
        "<div style=\"text-align:center\">\n",
        "    <h1>\n",
        "        On-policy Monte Carlo Control\n",
        "    </h1>\n",
        "</div>\n",
        "<br>\n",
        "\n",
        "<div style=\"text-align:center\">\n",
        "    <p>\n",
        "        In this notebook we are going to implement one of the two major strategies that exist when learning a policy by interacting with the environment, called on-policy learning. The agent will perform the task from start to finish and based on the sample experience generated, update its estimates of the q-values of each state-action pair Q(s,a).\n",
        "    </p>\n",
        "</div>\n",
        "\n",
        "\n",
        "<br>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Setup code (not important) - Run this cell by pressing \"Shift + Enter\"\n",
        "\n",
        "\n",
        "\n",
        "!pip install -qq gym==0.23.0\n",
        "\n",
        "\n",
        "from typing import Tuple, Dict, Optional, Iterable, Callable\n",
        "\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "import matplotlib\n",
        "from matplotlib import animation\n",
        "\n",
        "from IPython.display import HTML\n",
        "\n",
        "import gym\n",
        "from gym import spaces\n",
        "from gym.error import DependencyNotInstalled\n",
        "\n",
        "import pygame\n",
        "from pygame import gfxdraw\n",
        "\n",
        "\n",
        "class Maze(gym.Env):\n",
        "\n",
        "    def __init__(self, exploring_starts: bool = False,\n",
        "                 shaped_rewards: bool = False, size: int = 5) -> None:\n",
        "        super().__init__()\n",
        "        self.exploring_starts = exploring_starts\n",
        "        self.shaped_rewards = shaped_rewards\n",
        "        self.state = (size - 1, size - 1)\n",
        "        self.goal = (size - 1, size - 1)\n",
        "        self.maze = self._create_maze(size=size)\n",
        "        self.distances = self._compute_distances(self.goal, self.maze)\n",
        "        self.action_space = spaces.Discrete(n=4)\n",
        "        self.action_space.action_meanings = {0: 'UP', 1: 'RIGHT', 2: 'DOWN', 3: \"LEFT\"}\n",
        "        self.observation_space = spaces.MultiDiscrete([size, size])\n",
        "\n",
        "        self.screen = None\n",
        "        self.agent_transform = None\n",
        "\n",
        "    def step(self, action: int) -> Tuple[Tuple[int, int], float, bool, Dict]:\n",
        "        reward = self.compute_reward(self.state, action)\n",
        "        self.state = self._get_next_state(self.state, action)\n",
        "        done = self.state == self.goal\n",
        "        info = {}\n",
        "        return self.state, reward, done, info\n",
        "\n",
        "    def reset(self) -> Tuple[int, int]:\n",
        "        if self.exploring_starts:\n",
        "            while self.state == self.goal:\n",
        "                self.state = tuple(self.observation_space.sample())\n",
        "        else:\n",
        "            self.state = (0, 0)\n",
        "        return self.state\n",
        "\n",
        "    def render(self, mode: str = 'human') -> Optional[np.ndarray]:\n",
        "        assert mode in ['human', 'rgb_array']\n",
        "\n",
        "        screen_size = 600\n",
        "        scale = screen_size / 5\n",
        "\n",
        "        if self.screen is None:\n",
        "            pygame.init()\n",
        "            self.screen = pygame.Surface((screen_size, screen_size))\n",
        "\n",
        "        surf = pygame.Surface((screen_size, screen_size))\n",
        "        surf.fill((22, 36, 71))\n",
        "\n",
        "\n",
        "        for row in range(5):\n",
        "            for col in range(5):\n",
        "\n",
        "                state = (row, col)\n",
        "                for next_state in [(row + 1, col), (row - 1, col), (row, col + 1), (row, col - 1)]:\n",
        "                    if next_state not in self.maze[state]:\n",
        "\n",
        "                        # Add the geometry of the edges and walls (i.e. the boundaries between\n",
        "                        # adjacent squares that are not connected).\n",
        "                        row_diff, col_diff = np.subtract(next_state, state)\n",
        "                        left = (col + (col_diff > 0)) * scale - 2 * (col_diff != 0)\n",
        "                        right = ((col + 1) - (col_diff < 0)) * scale + 2 * (col_diff != 0)\n",
        "                        top = (5 - (row + (row_diff > 0))) * scale - 2 * (row_diff != 0)\n",
        "                        bottom = (5 - ((row + 1) - (row_diff < 0))) * scale + 2 * (row_diff != 0)\n",
        "\n",
        "                        gfxdraw.filled_polygon(surf, [(left, bottom), (left, top), (right, top), (right, bottom)], (255, 255, 255))\n",
        "\n",
        "        # Add the geometry of the goal square to the viewer.\n",
        "        left, right, top, bottom = scale * 4 + 10, scale * 5 - 10, scale - 10, 10\n",
        "        gfxdraw.filled_polygon(surf, [(left, bottom), (left, top), (right, top), (right, bottom)], (40, 199, 172))\n",
        "\n",
        "        # Add the geometry of the agent to the viewer.\n",
        "        agent_row = int(screen_size - scale * (self.state[0] + .5))\n",
        "        agent_col = int(scale * (self.state[1] + .5))\n",
        "        gfxdraw.filled_circle(surf, agent_col, agent_row, int(scale * .6 / 2), (228, 63, 90))\n",
        "\n",
        "        surf = pygame.transform.flip(surf, False, True)\n",
        "        self.screen.blit(surf, (0, 0))\n",
        "\n",
        "        return np.transpose(\n",
        "                np.array(pygame.surfarray.pixels3d(self.screen)), axes=(1, 0, 2)\n",
        "            )\n",
        "\n",
        "    def close(self) -> None:\n",
        "        if self.screen is not None:\n",
        "            pygame.display.quit()\n",
        "            pygame.quit()\n",
        "            self.screen = None\n",
        "\n",
        "    def compute_reward(self, state: Tuple[int, int], action: int) -> float:\n",
        "        next_state = self._get_next_state(state, action)\n",
        "        if self.shaped_rewards:\n",
        "            return - (self.distances[next_state] / self.distances.max())\n",
        "        return - float(state != self.goal)\n",
        "\n",
        "    def simulate_step(self, state: Tuple[int, int], action: int):\n",
        "        reward = self.compute_reward(state, action)\n",
        "        next_state = self._get_next_state(state, action)\n",
        "        done = next_state == self.goal\n",
        "        info = {}\n",
        "        return next_state, reward, done, info\n",
        "\n",
        "    def _get_next_state(self, state: Tuple[int, int], action: int) -> Tuple[int, int]:\n",
        "        if action == 0:\n",
        "            next_state = (state[0] - 1, state[1])\n",
        "        elif action == 1:\n",
        "            next_state = (state[0], state[1] + 1)\n",
        "        elif action == 2:\n",
        "            next_state = (state[0] + 1, state[1])\n",
        "        elif action == 3:\n",
        "            next_state = (state[0], state[1] - 1)\n",
        "        else:\n",
        "            raise ValueError(\"Action value not supported:\", action)\n",
        "        if next_state in self.maze[state]:\n",
        "            return next_state\n",
        "        return state\n",
        "\n",
        "    @staticmethod\n",
        "    def _create_maze(size: int) -> Dict[Tuple[int, int], Iterable[Tuple[int, int]]]:\n",
        "        maze = {(row, col): [(row - 1, col), (row + 1, col), (row, col - 1), (row, col + 1)]\n",
        "                for row in range(size) for col in range(size)}\n",
        "\n",
        "        left_edges = [[(row, 0), (row, -1)] for row in range(size)]\n",
        "        right_edges = [[(row, size - 1), (row, size)] for row in range(size)]\n",
        "        upper_edges = [[(0, col), (-1, col)] for col in range(size)]\n",
        "        lower_edges = [[(size - 1, col), (size, col)] for col in range(size)]\n",
        "        walls = [\n",
        "            [(1, 0), (1, 1)], [(2, 0), (2, 1)], [(3, 0), (3, 1)],\n",
        "            [(1, 1), (1, 2)], [(2, 1), (2, 2)], [(3, 1), (3, 2)],\n",
        "            [(3, 1), (4, 1)], [(0, 2), (1, 2)], [(1, 2), (1, 3)],\n",
        "            [(2, 2), (3, 2)], [(2, 3), (3, 3)], [(2, 4), (3, 4)],\n",
        "            [(4, 2), (4, 3)], [(1, 3), (1, 4)], [(2, 3), (2, 4)],\n",
        "        ]\n",
        "\n",
        "        obstacles = upper_edges + lower_edges + left_edges + right_edges + walls\n",
        "\n",
        "        for src, dst in obstacles:\n",
        "            maze[src].remove(dst)\n",
        "\n",
        "            if dst in maze:\n",
        "                maze[dst].remove(src)\n",
        "\n",
        "        return maze\n",
        "\n",
        "    @staticmethod\n",
        "    def _compute_distances(goal: Tuple[int, int],\n",
        "                           maze: Dict[Tuple[int, int], Iterable[Tuple[int, int]]]) -> np.ndarray:\n",
        "        distances = np.full((5, 5), np.inf)\n",
        "        visited = set()\n",
        "        distances[goal] = 0.\n",
        "\n",
        "        while visited != set(maze):\n",
        "            sorted_dst = [(v // 5, v % 5) for v in distances.argsort(axis=None)]\n",
        "            closest = next(x for x in sorted_dst if x not in visited)\n",
        "            visited.add(closest)\n",
        "\n",
        "            for neighbour in maze[closest]:\n",
        "                distances[neighbour] = min(distances[neighbour], distances[closest] + 1)\n",
        "        return distances\n",
        "\n",
        "\n",
        "def plot_policy(probs_or_qvals, frame, action_meanings=None):\n",
        "    if action_meanings is None:\n",
        "        action_meanings = {0: 'U', 1: 'R', 2: 'D', 3: 'L'}\n",
        "    fig, axes = plt.subplots(1, 2, figsize=(8, 4))\n",
        "    max_prob_actions = probs_or_qvals.argmax(axis=-1)\n",
        "    probs_copy = max_prob_actions.copy().astype(object)\n",
        "    for key in action_meanings:\n",
        "        probs_copy[probs_copy == key] = action_meanings[key]\n",
        "    sns.heatmap(max_prob_actions, annot=probs_copy, fmt='', cbar=False, cmap='coolwarm',\n",
        "                annot_kws={'weight': 'bold', 'size': 12}, linewidths=2, ax=axes[0])\n",
        "    axes[1].imshow(frame)\n",
        "    axes[0].axis('off')\n",
        "    axes[1].axis('off')\n",
        "    plt.suptitle(\"Policy\", size=18)\n",
        "    plt.tight_layout()\n",
        "\n",
        "\n",
        "def plot_values(state_values, frame):\n",
        "    f, axes = plt.subplots(1, 2, figsize=(10, 4))\n",
        "    sns.heatmap(state_values, annot=True, fmt=\".2f\", cmap='coolwarm',\n",
        "                annot_kws={'weight': 'bold', 'size': 12}, linewidths=2, ax=axes[0])\n",
        "    axes[1].imshow(frame)\n",
        "    axes[0].axis('off')\n",
        "    axes[1].axis('off')\n",
        "    plt.tight_layout()\n",
        "\n",
        "\n",
        "def display_video(frames):\n",
        "    # Copied from: https://colab.research.google.com/github/deepmind/dm_control/blob/master/tutorial.ipynb\n",
        "    orig_backend = matplotlib.get_backend()\n",
        "    matplotlib.use('Agg')\n",
        "    fig, ax = plt.subplots(1, 1, figsize=(5, 5))\n",
        "    matplotlib.use(orig_backend)\n",
        "    ax.set_axis_off()\n",
        "    ax.set_aspect('equal')\n",
        "    ax.set_position([0, 0, 1, 1])\n",
        "    im = ax.imshow(frames[0])\n",
        "    def update(frame):\n",
        "        im.set_data(frame)\n",
        "        return [im]\n",
        "    anim = animation.FuncAnimation(fig=fig, func=update, frames=frames,\n",
        "                                    interval=50, blit=True, repeat=False)\n",
        "    return HTML(anim.to_html5_video())\n",
        "\n",
        "\n",
        "def test_agent(environment, policy, episodes=10):\n",
        "    frames = []\n",
        "    for episode in range(episodes):\n",
        "        state = env.reset()\n",
        "        done = False\n",
        "        frames.append(env.render(mode=\"rgb_array\"))\n",
        "\n",
        "        while not done:\n",
        "            p = policy(state)\n",
        "            if isinstance(p, np.ndarray):\n",
        "                action = np.random.choice(4, p=p)\n",
        "            else:\n",
        "                action = p\n",
        "            next_state, reward, done, extra_info = env.step(action)\n",
        "            img = env.render(mode=\"rgb_array\")\n",
        "            frames.append(img)\n",
        "            state = next_state\n",
        "\n",
        "    return display_video(frames)\n",
        "\n",
        "\n",
        "def plot_action_values(action_values):\n",
        "\n",
        "    text_positions = [\n",
        "        [(0.35, 4.75), (1.35, 4.75), (2.35, 4.75), (3.35, 4.75), (4.35, 4.75),\n",
        "         (0.35, 3.75), (1.35, 3.75), (2.35, 3.75), (3.35, 3.75), (4.35, 3.75),\n",
        "         (0.35, 2.75), (1.35, 2.75), (2.35, 2.75), (3.35, 2.75), (4.35, 2.75),\n",
        "         (0.35, 1.75), (1.35, 1.75), (2.35, 1.75), (3.35, 1.75), (4.35, 1.75),\n",
        "         (0.35, 0.75), (1.35, 0.75), (2.35, 0.75), (3.35, 0.75), (4.35, 0.75)],\n",
        "        [(0.6, 4.45), (1.6, 4.45), (2.6, 4.45), (3.6, 4.45), (4.6, 4.45),\n",
        "         (0.6, 3.45), (1.6, 3.45), (2.6, 3.45), (3.6, 3.45), (4.6, 3.45),\n",
        "         (0.6, 2.45), (1.6, 2.45), (2.6, 2.45), (3.6, 2.45), (4.6, 2.45),\n",
        "         (0.6, 1.45), (1.6, 1.45), (2.6, 1.45), (3.6, 1.45), (4.6, 1.45),\n",
        "         (0.6, 0.45), (1.6, 0.45), (2.6, 0.45), (3.6, 0.45), (4.6, 0.45)],\n",
        "        [(0.35, 4.15), (1.35, 4.15), (2.35, 4.15), (3.35, 4.15), (4.35, 4.15),\n",
        "         (0.35, 3.15), (1.35, 3.15), (2.35, 3.15), (3.35, 3.15), (4.35, 3.15),\n",
        "         (0.35, 2.15), (1.35, 2.15), (2.35, 2.15), (3.35, 2.15), (4.35, 2.15),\n",
        "         (0.35, 1.15), (1.35, 1.15), (2.35, 1.15), (3.35, 1.15), (4.35, 1.15),\n",
        "         (0.35, 0.15), (1.35, 0.15), (2.35, 0.15), (3.35, 0.15), (4.35, 0.15)],\n",
        "        [(0.05, 4.45), (1.05, 4.45), (2.05, 4.45), (3.05, 4.45), (4.05, 4.45),\n",
        "         (0.05, 3.45), (1.05, 3.45), (2.05, 3.45), (3.05, 3.45), (4.05, 3.45),\n",
        "         (0.05, 2.45), (1.05, 2.45), (2.05, 2.45), (3.05, 2.45), (4.05, 2.45),\n",
        "         (0.05, 1.45), (1.05, 1.45), (2.05, 1.45), (3.05, 1.45), (4.05, 1.45),\n",
        "         (0.05, 0.45), (1.05, 0.45), (2.05, 0.45), (3.05, 0.45), (4.05, 0.45)]]\n",
        "\n",
        "    fig, ax = plt.subplots(figsize=(7, 7))\n",
        "    tripcolor = quatromatrix(action_values, ax=ax,\n",
        "                             triplotkw={\"color\": \"k\", \"lw\": 1}, tripcolorkw={\"cmap\": \"coolwarm\"})\n",
        "    ax.margins(0)\n",
        "    ax.set_aspect(\"equal\")\n",
        "    fig.colorbar(tripcolor)\n",
        "\n",
        "    for j, av in enumerate(text_positions):\n",
        "        for i, (xi, yi) in enumerate(av):\n",
        "            plt.text(xi, yi, round(action_values[:, :, j].flatten()[i], 2), size=8, color=\"w\", weight=\"bold\")\n",
        "\n",
        "    plt.title(\"Action values Q(s,a)\", size=18)\n",
        "    plt.tight_layout()\n",
        "    plt.show()\n",
        "\n",
        "\n",
        "def quatromatrix(action_values, ax=None, triplotkw=None, tripcolorkw=None):\n",
        "    action_values = np.flipud(action_values)\n",
        "    n = 5\n",
        "    m = 5\n",
        "    a = np.array([[0, 0], [0, 1], [.5, .5], [1, 0], [1, 1]])\n",
        "    tr = np.array([[0, 1, 2], [0, 2, 3], [2, 3, 4], [1, 2, 4]])\n",
        "    A = np.zeros((n * m * 5, 2))\n",
        "    Tr = np.zeros((n * m * 4, 3))\n",
        "    for i in range(n):\n",
        "        for j in range(m):\n",
        "            k = i * m + j\n",
        "            A[k * 5:(k + 1) * 5, :] = np.c_[a[:, 0] + j, a[:, 1] + i]\n",
        "            Tr[k * 4:(k + 1) * 4, :] = tr + k * 5\n",
        "    C = np.c_[action_values[:, :, 3].flatten(), action_values[:, :, 2].flatten(),\n",
        "              action_values[:, :, 1].flatten(), action_values[:, :, 0].flatten()].flatten()\n",
        "\n",
        "    ax.triplot(A[:, 0], A[:, 1], Tr, **triplotkw)\n",
        "    tripcolor = ax.tripcolor(A[:, 0], A[:, 1], Tr, facecolors=C, **tripcolorkw)\n",
        "    return tripcolor\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "cellView": "form",
        "id": "LyTAkpthoZMu",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "87801a16-26f0-43d0-989f-14d7b715d51a"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[?25l     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/624.4 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K     \u001b[91m━━\u001b[0m\u001b[91m╸\u001b[0m\u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m41.0/624.4 kB\u001b[0m \u001b[31m1.2 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K     \u001b[91m━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[91m╸\u001b[0m\u001b[90m━━━━━━━━━━━━\u001b[0m \u001b[32m430.1/624.4 kB\u001b[0m \u001b[31m6.5 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m624.4/624.4 kB\u001b[0m \u001b[31m6.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "  Building wheel for gym (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "63oAK3JLnawK"
      },
      "source": [
        "## Import the necessary software libraries:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "0oYNpIN1nawK"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qtHqOrD4nawL"
      },
      "source": [
        "## Initialize the environment"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "ROYlzzQLnawM"
      },
      "outputs": [],
      "source": [
        "env = Maze()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "y_by7VW9nawM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "outputId": "bc46bde1-8597-4183-8dd5-f1891cdd2d6c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7cc4a5a41e10>"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAGFCAYAAAASI+9IAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAANIElEQVR4nO3dXYxU93nA4Xf2A8YsUNuLDGYNrDHEYG/9kdpOICQXaSGx3bq1kSsu7EaNVCmyZKWqa0VNpUbuRV1zkTZVK0WpVblNIyWV3SRKooTGbdNQxxaulzQyUDtByfJhFgwL5mOXZXdmeoH9lmIDu+zOnIF5HglpJGbnvFqd4cf5n5lzSrVarRYAEBFtRQ8AQPMQBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEDqmMyTd+/ZH4889lT4CjTApeOmFdfHxicendBzJxWFkZOjsaV/+0UNBUAxSqXShJ9r+QiAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEgdRQ9A6+maVY5//seN0TWrXPQoTe/bm16IP/+Lvy96DFqIKEyTpb0L49Of2hAREYMHhuLJzz9T7EBNamnvwvjDRx+Km1csjc5Ou9+F/OY97VEqlexP5+B9N/0sH02Ted1XxYb162LD+nVxz9rVRY/TtOZ1XxXr7/uoIEzQ0t4e+9N5eN9NP+9MCrN7z/545LGnolb0IE3ophXXx8YnHi16DFqQKFCYkZOjsaV/e9FjNKVSqVT0CLQoy0cAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQBSR9EDAO9WqVTi6LETERFxYnik4GloJaIATWjrT16P2z/8UEREVKu1gqehlYgCNKFqtRrHTzhCoPGcUwAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoUKhSqegJuJSdvfvYn97bZH4tHXWbAi6gd/G1sfm7Xyp6DC5h5fLMfGx/Orczf08XIgoUZsaMzlh+w+Kix+AyYX+aHpaPAEiOFCjM7j3745HHnopa0YPAZe6mFdfHxicendBzRYHCjJwcjS3924seAy57pUmcgbd8BEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAp1UioVPUFz8muB5tZR9ACXo97F18bm736p6DGaUrk8s+gRgPMQhWlSqVTi2PHhmN11RcyY0RnLb1hc9EhN7dTYeJwYHil6jKa1tHdhfPpTGyIiYvDAUDz5+WeKHYiWYflommz9yeux5uO/5x+6CfrGd34QDzz0maLHaFrzuq+KDevXxYb16+KetauLHocW4khhmlSr1XjzzcPx4Cc+G+3tWnshBw8dieGRk0WPAZxFFKZRpVqN/v/+n6LHALho/ksLQBIFAJLlI+CyNWPN8mibUy56jIYb27EvKr84eFE/KwrAZat87y3Rcd3VRY/RcCe+8uJFR8HyEQBJFABIogBAEgUAkigAkEQBgCQKANOtVjv95xLkewoA06Dn4PHoOjkWEREzxyqxevsb8e+3Lsq/f6O7K45fMaOo8SZMFAAmqWO8Eu3VWjzwws645shwRETc9dpgzD/y/y+d/+Dmn+Xjl983PwavmhUREf9xS0/sWHR1nOpoj1pbc92PUBQAJqpWi1U7BuO+F3fGjXsOR9foeLRXJ7ZMdOfr+/Px2v5dcaqjLb7+oWXxw76eGFgwt14TT5ooAFxAeXQ8lhw4Gp/ctC36BoZi5lhlaq83VonyWCU+8fyOWNu/K15asSCe+/Cy2H/lrMJv8C4KAOfRXqnGo9/8cazt3xWliJjuf7IXDp2I+3+0Mz7+XwPxZxvujJdWLig0DD59BHAOK3YNxe9/fWv82tZd0RbTH4R3lCJi1qnx+KOvvRwfe2Ug5r1V3G19HSkAnKVUq8Wq7fvi8WdfiTkjYw3bbtfoeDz+bH9sW3x1fO7hD8aRAi777UgB4Cyrtu+Lz3715YYG4Uw37RqKJ778UiFHDKIAcIYVu4bi8WdfifIUTyZPRSkibt41FJ/52stRavCX4EQB4G3tlWrcu+XnhR0hnO19e4/EB3YMNvTb0aIAEKc/dvoHz/XHulcGih4ldY2Oxx9/dUus2fZGw7YpCgARseTA0Vjbvyvam+ySRVecqsT6zT+L8qnxhmxPFABqtfjkpm11+8jpVPUNHIoP7tjXkGUkUQBa3qodg9E3MNS0UShFxO88vyM6x6t135YoAC2tY7wS9724c8qXrqi3BUPD8as/3l337YgC0NLaq7W4cc/hose4oBmVaizfe6Tu2xEFoKU98MLO6BptzEncqfrIq3tj0YFjdd2GKAAt7ZojwxO+/HXRrjo+WvdPIYkCAEkUgJbVc/B43PXaYNFjTMr9P9pZ14+migLQsrpOjr3rFprN7vrBt+r6+qIAQBIFAJIoAJBEAYAkCkDLqkVEtVkveHQO1VJ9BxYFoGX9/Npfin+9bXHRY0zK03f3RdQxDKIAtKzx9rY4OaO96DEm5Xi5s66vLwpAy7s0LnLx9px1Xu4SBaCl/dNHlsfwzI6ix5iQH9xyXQxcM7eu2xAFoKUNzSnHyRnNH4VaRByaW45TnfVd7hIFoKWNdrbHM+tuKnqMCzp2RWd85aMr6r4dUQBaW6kUL65cED9deGXRk5zXc2uW1f0kc4QoAMSR2eX43h1LmvaE896ru+I/+3qi1lb/L1WIAkBEbO7rib3dXUWP8S61iHhp5YIYmF/fE8zvEAWAiBiaW47PPbyqqcJQKUV8744l8Xcfu7lh2xQFgLcNzJ8Tf33frU2zjHTgylnxhftvj9EGfjpKFADeUSrFq73d8Z27egu/JtLRKzrji/f+cow34DzCmUQB4AwjMzvjb37j1vj++xcXFoaRGe2x8cE74oW+nrpe5+i9NP83NgAabKyzPf7y/tvj8OxyfGjbG7Ho4PGGbLcWEVtunB/f+sDSeGnlgoZs82yiAPAexjra4+m7++L7718cf/oPL0bPoRN13d7pk8q98cVfvyVGCrzshuUjgPMYuGZO/MnDq+LZNcui0laa9pPQtYjYPW92PH13X/zVb91WaBAiHCkAnF+pFAML5sbf3t0X31h9Q/zuv2yP23YeiO5jo1N+6dd6roxNdyyJzX09cXhOeRqGnTpRAJiASntbDF7dFU9uuDNWDhyK+YeH47d/+NOYf2Q4IiJmjY5FZ+XcxxHDMztirP304sy/3XZdbFvcHVuXXRNvzZ7ZkPknShQAJmnHku7YsaQ7XuhbGKXa6RDc/fJALD5wLCIiOivVuHH3ULzaOy9/ZtOvLIlfzJ8TUTp9c59qW3Ou3osCwEUa6/i/y1h/c/UN+bitWovuoyPx5pWzihhrSpozVQCXsGpb6ZIMQoQoAHAGUQAgiQIASRQASKIAQBIFAJLvKQCXrergWzFeLXqKxqsdO3nRPysKwGXr+BeeL3qES47lIwCSKACQJh2FBt8ZDlrS2W8z7zumYjK7T6lWq034nhGnTo3FwO59FzESMBnl8sxY1DM/IrzvmLoz96cLmVQUALi8OacAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFANL/ArTxVCVKsiWXAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "frame = env.render(mode='rgb_array')\n",
        "plt.axis('off')\n",
        "plt.imshow(frame)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "-mJuSuvmnawM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1f6a3886-e026-48d7-cf82-c920333cf95f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Observation space shape: [5 5]\n",
            "Number of actions: 4\n"
          ]
        }
      ],
      "source": [
        "print(f\"Observation space shape: {env.observation_space.nvec}\")\n",
        "print(f\"Number of actions: {env.action_space.n}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VI4LgZwfnawN"
      },
      "source": [
        "## Define value table $Q(s, a)$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2Dl-VI9vnawN"
      },
      "source": [
        "#### Create the $Q(s, a)$ table"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "Enbb5n6GnawN"
      },
      "outputs": [],
      "source": [
        "action_values = np.zeros(shape=(5, 5, 4))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L2HpoEzanawN"
      },
      "source": [
        "#### Plot Q(s, a)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "qlEzZ1ZsnawO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 707
        },
        "outputId": "630c61ec-7339-4061-c0c9-916beb12aefc"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x700 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plot_action_values(action_values)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WcCVmpfmnawO"
      },
      "source": [
        "## Define the policy $\\pi(s)$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O5LVZQSGnawO"
      },
      "source": [
        "#### Create the policy $\\pi(s)$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "MlphKjJtnawO"
      },
      "outputs": [],
      "source": [
        "def policy(state, epsilon=0.):\n",
        "    if np.random.random() < epsilon:\n",
        "        return np.random.randint(4)\n",
        "    else:\n",
        "        av = action_values[state]\n",
        "        return np.random.choice(np.flatnonzero(av == av.max()))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qk4HCqGZnawO"
      },
      "source": [
        "#### Test the policy with state (0, 0)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "B_zxUCWAnawO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cb53dfc6-37fb-40be-9499-26cb93d9ce27"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Action taken in state (0,0): 3\n"
          ]
        }
      ],
      "source": [
        "action = policy((0,0))\n",
        "print(f\"Action taken in state (0,0): {action}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RGkcRgLknawO"
      },
      "source": [
        "#### Plot the policy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "scrolled": false,
        "id": "o2wPlGyvnawO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 414
        },
        "outputId": "292d0778-6d54-4cfc-e373-d9b169566657"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 2 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plot_policy(action_values, frame)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SVow816ZnawP"
      },
      "source": [
        "## Implement the algorithm\n",
        "\n",
        "</br>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "oS6xb3hlnawP"
      },
      "outputs": [],
      "source": [
        "def constant_alpha_mc(policy, action_values, episodes, gamma=0.99, epsilon=0.2, alpha=0.1):\n",
        "\n",
        "    for episode in range(1, episodes+1):\n",
        "        state = env.reset()\n",
        "        done = False\n",
        "        transitions = []\n",
        "\n",
        "        while not done:\n",
        "            action = policy(state, epsilon)\n",
        "            next_state, reward, done, _ = env.step(action)\n",
        "            transitions.append([state, action, reward])\n",
        "            state = next_state\n",
        "\n",
        "        G = 0\n",
        "        for state_t, action_t, reward_t in reversed(transitions):\n",
        "            G = reward_t + gamma * G\n",
        "            action_values[state_t][action_t] += alpha * (G - action_values[state_t][action_t])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "XIObBa_6nawP"
      },
      "outputs": [],
      "source": [
        "constant_alpha_mc(policy, action_values, episodes=1000)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "APkcdvo7nawP"
      },
      "source": [
        "## Show results"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uKwSTqbJnawP"
      },
      "source": [
        "#### Show resulting value table $Q(s, a)$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "di0-Q_cznawP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 707
        },
        "outputId": "9dee29d1-ff6b-4732-fe60-ec93f2869690"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x700 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plot_action_values(action_values)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gbl9SUNKnawP"
      },
      "source": [
        "#### Show resulting policy $\\pi(\\cdot|s)$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "AwZcbTiTnawP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 414
        },
        "outputId": "ab7f8e15-a4aa-48d9-f041-942903d252b8"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plot_policy(action_values, frame)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-F5qY5DgnawP"
      },
      "source": [
        "#### Test the resulting agent"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "8PpECiz5nawP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        },
        "outputId": "7229bac8-bc2f-42ea-f353-708741d466dd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
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              "  Your browser does not support the video tag.\n",
              "</video>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "test_agent(env, policy)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u60cRVCqnawP"
      },
      "source": [
        "## Resources"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dJY7tkIQnawP"
      },
      "source": [
        "[[1] Reinforcement Learning: An Introduction. Ch. 4: Dynamic Programming](https://web.stanford.edu/class/psych209/Readings/SuttonBartoIPRLBook2ndEd.pdf)"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    "colab": {
      "provenance": []
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