Tile_Coding.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tile Coding\n",
    "---\n",
    "\n",
    "Tile coding is an innovative way of discretizing a continuous space that enables better generalization compared to a single grid-based approach. The fundamental idea is to create several overlapping grids or _tilings_; then for any given sample value, you need only check which tiles it lies in. You can then encode the original continuous value by a vector of integer indices or bits that identifies each activated tile.\n",
    "\n",
    "### 1. Import the Necessary Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting pyvirtualdisplay\n",
      "  Downloading https://files.pythonhosted.org/packages/c0/dd/3b0e5318929b949af38a3f7c2653f1528e4c26b1e3251ae7c7696d4599a9/PyVirtualDisplay-1.3-py2.py3-none-any.whl\n",
      "Collecting EasyProcess (from pyvirtualdisplay)\n",
      "  Downloading https://files.pythonhosted.org/packages/48/3c/75573613641c90c6d094059ac28adb748560d99bd27ee6f80cce398f404e/EasyProcess-0.3-py2.py3-none-any.whl\n",
      "Installing collected packages: EasyProcess, pyvirtualdisplay\n",
      "Successfully installed EasyProcess-0.3 pyvirtualdisplay-1.3\n"
     ]
    }
   ],
   "source": [
    "# Import common libraries\n",
    "import sys\n",
    "import gym\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Set plotting options\n",
    "%matplotlib inline\n",
    "plt.style.use('ggplot')\n",
    "np.set_printoptions(precision=3, linewidth=120)\n",
    "\n",
    "!python -m pip install pyvirtualdisplay\n",
    "from pyvirtualdisplay import Display\n",
    "display = Display(visible=0, size=(1400, 900))\n",
    "display.start()\n",
    "\n",
    "is_ipython = 'inline' in plt.get_backend()\n",
    "if is_ipython:\n",
    "    from IPython import display\n",
    "\n",
    "plt.ion()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Specify the Environment, and Explore the State and Action Spaces\n",
    "\n",
    "We'll use [OpenAI Gym](https://gym.openai.com/) environments to test and develop our algorithms. These simulate a variety of classic as well as contemporary reinforcement learning tasks.  Let's begin with an environment that has a continuous state space, but a discrete action space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[33mWARN: gym.spaces.Box autodetected dtype as <class 'numpy.float32'>. Please provide explicit dtype.\u001b[0m\n",
      "State space: Box(6,)\n",
      "- low: [ -1.     -1.     -1.     -1.    -12.566 -28.274]\n",
      "- high: [  1.      1.      1.      1.     12.566  28.274]\n",
      "Action space: Discrete(3)\n"
     ]
    }
   ],
   "source": [
    "# Create an environment\n",
    "env = gym.make('Acrobot-v1')\n",
    "env.seed(505);\n",
    "\n",
    "# Explore state (observation) space\n",
    "print(\"State space:\", env.observation_space)\n",
    "print(\"- low:\", env.observation_space.low)\n",
    "print(\"- high:\", env.observation_space.high)\n",
    "\n",
    "# Explore action space\n",
    "print(\"Action space:\", env.action_space)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score:  500\n"
     ]
    },
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "state = env.reset()\n",
    "img = plt.imshow(env.render(mode='rgb_array'))\n",
    "for t in range(1000):\n",
    "    action = env.action_space.sample()\n",
    "    img.set_data(env.render(mode='rgb_array')) \n",
    "    plt.axis('off')\n",
    "    display.display(plt.gcf())\n",
    "    display.clear_output(wait=True)\n",
    "    state, reward, done, _ = env.step(action)\n",
    "    if done:\n",
    "        print('Score: ', t+1)\n",
    "        break\n",
    "        \n",
    "env.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the state space is multi-dimensional, with most dimensions ranging from -1 to 1 (positions of the two joints), while the final two dimensions have a larger range. How do we discretize such a space using tiles?\n",
    "\n",
    "### 3. Tiling\n",
    "\n",
    "Let's first design a way to create a single tiling for a given state space. This is very similar to a uniform grid! The only difference is that you should include an offset for each dimension that shifts the split points.\n",
    "\n",
    "For instance, if `low = [-1.0, -5.0]`, `high = [1.0, 5.0]`, `bins = (10, 10)`, and `offsets = (-0.1, 0.5)`, then return a list of 2 NumPy arrays (2 dimensions) each containing the following split points (9 split points per dimension):\n",
    "\n",
    "```\n",
    "[array([-0.9, -0.7, -0.5, -0.3, -0.1,  0.1,  0.3,  0.5,  0.7]),\n",
    " array([-3.5, -2.5, -1.5, -0.5,  0.5,  1.5,  2.5,  3.5,  4.5])]\n",
    "```\n",
    "\n",
    "Notice how the split points for the first dimension are offset by `-0.1`, and for the second dimension are offset by `+0.5`. This might mean that some of our tiles, especially along the perimeter, are partially outside the valid state space, but that is unavoidable and harmless."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\n",
      "    [-1.0, 1.0] / 10 + (-0.1) => [-0.9 -0.7 -0.5 -0.3 -0.1  0.1  0.3  0.5  0.7]\n",
      "    [-5.0, 5.0] / 10 + (0.5) => [-3.5 -2.5 -1.5 -0.5  0.5  1.5  2.5  3.5  4.5]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[array([-0.9, -0.7, -0.5, -0.3, -0.1,  0.1,  0.3,  0.5,  0.7]),\n",
       " array([-3.5, -2.5, -1.5, -0.5,  0.5,  1.5,  2.5,  3.5,  4.5])]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def create_tiling_grid(low, high, bins=(10, 10), offsets=(0.0, 0.0)):\n",
    "    \"\"\"Define a uniformly-spaced grid that can be used for tile-coding a space.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    low : array_like\n",
    "        Lower bounds for each dimension of the continuous space.\n",
    "    high : array_like\n",
    "        Upper bounds for each dimension of the continuous space.\n",
    "    bins : tuple\n",
    "        Number of bins or tiles along each corresponding dimension.\n",
    "    offsets : tuple\n",
    "        Split points for each dimension should be offset by these values.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    grid : list of array_like\n",
    "        A list of arrays containing split points for each dimension.\n",
    "    \"\"\"\n",
    "    grid = [np.linspace(low[dim], high[dim], bins[dim]+1)[1:-1] + offsets[dim] for dim in range(len(bins))]\n",
    "    print(\"Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\")\n",
    "    for l, h, b, o, splits in zip(low, high, bins, offsets, grid):\n",
    "        print(\"    [{}, {}] / {} + ({}) => {}\".format(l, h, b, o, splits))\n",
    "    return grid\n",
    "\n",
    "\n",
    "low = [-1.0, -5.0]\n",
    "high = [1.0, 5.0]\n",
    "create_tiling_grid(low, high, bins=(10, 10), offsets=(-0.1, 0.5))  # [test]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can now use this function to define a set of tilings that are a little offset from each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\n",
      "    [-1.0, 1.0] / 10 + (-0.066) => [-0.866 -0.666 -0.466 -0.266 -0.066  0.134  0.334  0.534  0.734]\n",
      "    [-5.0, 5.0] / 10 + (-0.33) => [-4.33 -3.33 -2.33 -1.33 -0.33  0.67  1.67  2.67  3.67]\n",
      "Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\n",
      "    [-1.0, 1.0] / 10 + (0.0) => [-0.8 -0.6 -0.4 -0.2  0.   0.2  0.4  0.6  0.8]\n",
      "    [-5.0, 5.0] / 10 + (0.0) => [-4. -3. -2. -1.  0.  1.  2.  3.  4.]\n",
      "Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\n",
      "    [-1.0, 1.0] / 10 + (0.066) => [-0.734 -0.534 -0.334 -0.134  0.066  0.266  0.466  0.666  0.866]\n",
      "    [-5.0, 5.0] / 10 + (0.33) => [-3.67 -2.67 -1.67 -0.67  0.33  1.33  2.33  3.33  4.33]\n"
     ]
    }
   ],
   "source": [
    "def create_tilings(low, high, tiling_specs):\n",
    "    \"\"\"Define multiple tilings using the provided specifications.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    low : array_like\n",
    "        Lower bounds for each dimension of the continuous space.\n",
    "    high : array_like\n",
    "        Upper bounds for each dimension of the continuous space.\n",
    "    tiling_specs : list of tuples\n",
    "        A sequence of (bins, offsets) to be passed to create_tiling_grid().\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    tilings : list\n",
    "        A list of tilings (grids), each produced by create_tiling_grid().\n",
    "    \"\"\"\n",
    "    # TODO: Implement this\n",
    "    return [create_tiling_grid(low, high, bins, offsets) for bins, offsets in tiling_specs]\n",
    "\n",
    "\n",
    "# Tiling specs: [(<bins>, <offsets>), ...]\n",
    "tiling_specs = [((10, 10), (-0.066, -0.33)),\n",
    "                ((10, 10), (0.0, 0.0)),\n",
    "                ((10, 10), (0.066, 0.33))]\n",
    "tilings = create_tilings(low, high, tiling_specs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It may be hard to gauge whether you are getting desired results or not. So let's try to visualize these tilings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f090616d278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.lines import Line2D\n",
    "\n",
    "def visualize_tilings(tilings):\n",
    "    \"\"\"Plot each tiling as a grid.\"\"\"\n",
    "    prop_cycle = plt.rcParams['axes.prop_cycle']\n",
    "    colors = prop_cycle.by_key()['color']\n",
    "    linestyles = ['-', '--', ':']\n",
    "    legend_lines = []\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(10, 10))\n",
    "    for i, grid in enumerate(tilings):\n",
    "        for x in grid[0]:\n",
    "            l = ax.axvline(x=x, color=colors[i % len(colors)], linestyle=linestyles[i % len(linestyles)], label=i)\n",
    "        for y in grid[1]:\n",
    "            l = ax.axhline(y=y, color=colors[i % len(colors)], linestyle=linestyles[i % len(linestyles)])\n",
    "        legend_lines.append(l)\n",
    "    ax.grid('off')\n",
    "    ax.legend(legend_lines, [\"Tiling #{}\".format(t) for t in range(len(legend_lines))], facecolor='white', framealpha=0.9)\n",
    "    ax.set_title(\"Tilings\")\n",
    "    return ax  # return Axis object to draw on later, if needed\n",
    "\n",
    "\n",
    "visualize_tilings(tilings);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! Now that we have a way to generate these tilings, we can next write our encoding function that will convert any given continuous state value to a discrete vector.\n",
    "\n",
    "### 4. Tile Encoding\n",
    "\n",
    "Implement the following to produce a vector that contains the indices for each tile that the input state value belongs to. The shape of the vector can be the same as the arrangment of tiles you have, or it can be ultimately flattened for convenience.\n",
    "\n",
    "You can use the same `discretize()` function here from grid-based discretization, and simply call it for each tiling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Samples:\n",
      "[(-1.2, -5.1), (-0.75, 3.25), (-0.5, 0.0), (0.25, -1.9), (0.15, -1.75), (0.75, 2.5), (0.7, -3.7), (1.0, 5.0)]\n",
      "\n",
      "Encoded samples:\n",
      "[[(0, 0), (0, 0), (0, 0)], [(1, 8), (1, 8), (0, 7)], [(2, 5), (2, 5), (2, 4)], [(6, 3), (6, 3), (5, 2)], [(6, 3), (5, 3), (5, 2)], [(9, 7), (8, 7), (8, 7)], [(8, 1), (8, 1), (8, 0)], [(9, 9), (9, 9), (9, 9)]]\n"
     ]
    }
   ],
   "source": [
    "def discretize(sample, grid):\n",
    "    \"\"\"Discretize a sample as per given grid.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    sample : array_like\n",
    "        A single sample from the (original) continuous space.\n",
    "    grid : list of array_like\n",
    "        A list of arrays containing split points for each dimension.\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    discretized_sample : array_like\n",
    "        A sequence of integers with the same number of dimensions as sample.\n",
    "    \"\"\"\n",
    "    return tuple(int(np.digitize(s,g)) for s,g in zip(sample, grid))\n",
    "\n",
    "\n",
    "def tile_encode(sample, tilings, flatten=False):\n",
    "    \"\"\"Encode given sample using tile-coding.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    sample : array_like\n",
    "        A single sample from the (original) continuous space.\n",
    "    tilings : list\n",
    "        A list of tilings (grids), each produced by create_tiling_grid().\n",
    "    flatten : bool\n",
    "        If true, flatten the resulting binary arrays into a single long vector.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    encoded_sample : list or array_like\n",
    "        A list of binary vectors, one for each tiling, or flattened into one.\n",
    "    \"\"\"\n",
    "    encoded_sample = [discretize(sample, grid) for grid in tilings]\n",
    "    return np.concatenate(encode_sample) if flatten else encoded_sample\n",
    "\n",
    "\n",
    "# Test with some sample values\n",
    "samples = [(-1.2 , -5.1 ),\n",
    "           (-0.75,  3.25),\n",
    "           (-0.5 ,  0.0 ),\n",
    "           ( 0.25, -1.9 ),\n",
    "           ( 0.15, -1.75),\n",
    "           ( 0.75,  2.5 ),\n",
    "           ( 0.7 , -3.7 ),\n",
    "           ( 1.0 ,  5.0 )]\n",
    "encoded_samples = [tile_encode(sample, tilings) for sample in samples]\n",
    "print(\"\\nSamples:\", repr(samples), sep=\"\\n\")\n",
    "print(\"\\nEncoded samples:\", repr(encoded_samples), sep=\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we did not flatten the encoding above, which is why each sample's representation is a pair of indices for each tiling. This makes it easy to visualize it using the tilings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0905f6cfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Rectangle\n",
    "\n",
    "def visualize_encoded_samples(samples, encoded_samples, tilings, low=None, high=None):\n",
    "    \"\"\"Visualize samples by activating the respective tiles.\"\"\"\n",
    "    samples = np.array(samples)  # for ease of indexing\n",
    "\n",
    "    # Show tiling grids\n",
    "    ax = visualize_tilings(tilings)\n",
    "    \n",
    "    # If bounds (low, high) are specified, use them to set axis limits\n",
    "    if low is not None and high is not None:\n",
    "        ax.set_xlim(low[0], high[0])\n",
    "        ax.set_ylim(low[1], high[1])\n",
    "    else:\n",
    "        # Pre-render (invisible) samples to automatically set reasonable axis limits, and use them as (low, high)\n",
    "        ax.plot(samples[:, 0], samples[:, 1], 'o', alpha=0.0)\n",
    "        low = [ax.get_xlim()[0], ax.get_ylim()[0]]\n",
    "        high = [ax.get_xlim()[1], ax.get_ylim()[1]]\n",
    "\n",
    "    # Map each encoded sample (which is really a list of indices) to the corresponding tiles it belongs to\n",
    "    tilings_extended = [np.hstack((np.array([low]).T, grid, np.array([high]).T)) for grid in tilings]  # add low and high ends\n",
    "    tile_centers = [(grid_extended[:, 1:] + grid_extended[:, :-1]) / 2 for grid_extended in tilings_extended]  # compute center of each tile\n",
    "    tile_toplefts = [grid_extended[:, :-1] for grid_extended in tilings_extended]  # compute topleft of each tile\n",
    "    tile_bottomrights = [grid_extended[:, 1:] for grid_extended in tilings_extended]  # compute bottomright of each tile\n",
    "\n",
    "    prop_cycle = plt.rcParams['axes.prop_cycle']\n",
    "    colors = prop_cycle.by_key()['color']\n",
    "    for sample, encoded_sample in zip(samples, encoded_samples):\n",
    "        for i, tile in enumerate(encoded_sample):\n",
    "            # Shade the entire tile with a rectangle\n",
    "            topleft = tile_toplefts[i][0][tile[0]], tile_toplefts[i][1][tile[1]]\n",
    "            bottomright = tile_bottomrights[i][0][tile[0]], tile_bottomrights[i][1][tile[1]]\n",
    "            ax.add_patch(Rectangle(topleft, bottomright[0] - topleft[0], bottomright[1] - topleft[1],\n",
    "                                   color=colors[i], alpha=0.33))\n",
    "\n",
    "            # In case sample is outside tile bounds, it may not have been highlighted properly\n",
    "            if any(sample < topleft) or any(sample > bottomright):\n",
    "                # So plot a point in the center of the tile and draw a connecting line\n",
    "                cx, cy = tile_centers[i][0][tile[0]], tile_centers[i][1][tile[1]]\n",
    "                ax.add_line(Line2D([sample[0], cx], [sample[1], cy], color=colors[i]))\n",
    "                ax.plot(cx, cy, 's', color=colors[i])\n",
    "    \n",
    "    # Finally, plot original samples\n",
    "    ax.plot(samples[:, 0], samples[:, 1], 'o', color='r')\n",
    "\n",
    "    ax.margins(x=0, y=0)  # remove unnecessary margins\n",
    "    ax.set_title(\"Tile-encoded samples\")\n",
    "    return ax\n",
    "\n",
    "visualize_encoded_samples(samples, encoded_samples, tilings);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspect the results and make sure you understand how the corresponding tiles are being chosen. Note that some samples may have one or more tiles in common.\n",
    "\n",
    "### 5. Q-Table with Tile Coding\n",
    "\n",
    "The next step is to design a special Q-table that is able to utilize this tile coding scheme. It should have the same kind of interface as a regular table, i.e. given a `<state, action>` pair, it should return a `<value>`. Similarly, it should also allow you to update the `<value>` for a given `<state, action>` pair (note that this should update all the tiles that `<state>` belongs to).\n",
    "\n",
    "The `<state>` supplied here is assumed to be from the original continuous state space, and `<action>` is discrete (and integer index). The Q-table should internally convert the `<state>` to its tile-coded representation when required."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\n",
      "    [-1.0, 1.0] / 10 + (-0.066) => [-0.866 -0.666 -0.466 -0.266 -0.066  0.134  0.334  0.534  0.734]\n",
      "    [-5.0, 5.0] / 10 + (-0.33) => [-4.33 -3.33 -2.33 -1.33 -0.33  0.67  1.67  2.67  3.67]\n",
      "Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\n",
      "    [-1.0, 1.0] / 10 + (0.0) => [-0.8 -0.6 -0.4 -0.2  0.   0.2  0.4  0.6  0.8]\n",
      "    [-5.0, 5.0] / 10 + (0.0) => [-4. -3. -2. -1.  0.  1.  2.  3.  4.]\n",
      "Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\n",
      "    [-1.0, 1.0] / 10 + (0.066) => [-0.734 -0.534 -0.334 -0.134  0.066  0.266  0.466  0.666  0.866]\n",
      "    [-5.0, 5.0] / 10 + (0.33) => [-3.67 -2.67 -1.67 -0.67  0.33  1.33  2.33  3.33  4.33]\n",
      "QTable(): size = (10, 10, 2)\n",
      "QTable(): size = (10, 10, 2)\n",
      "QTable(): size = (10, 10, 2)\n",
      "TiledQTable(): no. of internal tables =  3\n",
      "[GET]    Q((0.25, -1.9), 0) = 0.0\n",
      "[UPDATE] Q((0.15, -1.75), 0) = 1.0\n",
      "[GET]    Q((0.25, -1.9), 0) = 0.6666666666666666\n"
     ]
    }
   ],
   "source": [
    "class QTable:\n",
    "    \"\"\"Simple Q-table.\"\"\"\n",
    "\n",
    "    def __init__(self, state_size, action_size):\n",
    "        \"\"\"Initialize Q-table.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        state_size : tuple\n",
    "            Number of discrete values along each dimension of state space.\n",
    "        action_size : int\n",
    "            Number of discrete actions in action space.\n",
    "        \"\"\"\n",
    "        self.state_size = state_size\n",
    "        self.action_size = action_size\n",
    "\n",
    "        # TODO: Create Q-table, initialize all Q-values to zero\n",
    "        # Note: If state_size = (9, 9), action_size = 2, q_table.shape should be (9, 9, 2)\n",
    "        self.q_table = np.zeros(shape=(self.state_size + (self.action_size,)))\n",
    "        \n",
    "        print(\"QTable(): size =\", self.q_table.shape)\n",
    "\n",
    "\n",
    "class TiledQTable:\n",
    "    \"\"\"Composite Q-table with an internal tile coding scheme.\"\"\"\n",
    "    \n",
    "    def __init__(self, low, high, tiling_specs, action_size):\n",
    "        \"\"\"Create tilings and initialize internal Q-table(s).\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        low : array_like\n",
    "            Lower bounds for each dimension of state space.\n",
    "        high : array_like\n",
    "            Upper bounds for each dimension of state space.\n",
    "        tiling_specs : list of tuples\n",
    "            A sequence of (bins, offsets) to be passed to create_tilings() along with low, high.\n",
    "        action_size : int\n",
    "            Number of discrete actions in action space.\n",
    "        \"\"\"\n",
    "        self.tilings = create_tilings(low, high, tiling_specs)\n",
    "        self.state_sizes = [tuple(len(splits)+1 for splits in tiling_grid) for tiling_grid in self.tilings]\n",
    "        self.action_size = action_size\n",
    "        self.q_tables = [QTable(state_size, self.action_size) for state_size in self.state_sizes]\n",
    "        print(\"TiledQTable(): no. of internal tables = \", len(self.q_tables))\n",
    "    \n",
    "    def get(self, state, action):\n",
    "        \"\"\"Get Q-value for given <state, action> pair.\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        state : array_like\n",
    "            Vector representing the state in the original continuous space.\n",
    "        action : int\n",
    "            Index of desired action.\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        value : float\n",
    "            Q-value of given <state, action> pair, averaged from all internal Q-tables.\n",
    "        \"\"\"\n",
    "        # TODO: Encode state to get tile indices\n",
    "        encoded_state = tile_encode(state, self.tilings)\n",
    "        \n",
    "        # TODO: Retrieve q-value for each tiling, and return their average\n",
    "        value = 0.0\n",
    "        for idx, q_table in zip(encoded_state, self.q_tables):\n",
    "            value += q_table.q_table[tuple(idx+(action,))]\n",
    "        value /= len(self.q_tables)\n",
    "        return value\n",
    "\n",
    "    def update(self, state, action, value, alpha=0.1):\n",
    "        \"\"\"Soft-update Q-value for given <state, action> pair to value.\n",
    "        \n",
    "        Instead of overwriting Q(state, action) with value, perform soft-update:\n",
    "            Q(state, action) = alpha * value + (1.0 - alpha) * Q(state, action)\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        state : array_like\n",
    "            Vector representing the state in the original continuous space.\n",
    "        action : int\n",
    "            Index of desired action.\n",
    "        value : float\n",
    "            Desired Q-value for <state, action> pair.\n",
    "        alpha : float\n",
    "            Update factor to perform soft-update, in [0.0, 1.0] range.\n",
    "        \"\"\"\n",
    "        # TODO: Encode state to get tile indices\n",
    "        encoded_state = tile_encode(state, self.tilings)\n",
    "        # TODO: Update q-value for each tiling by update factor alpha\n",
    "        for idx, q_table in zip(encoded_state, self.q_tables):\n",
    "            value_ = q_table.q_table[tuple(idx + (action,))]  # current value\n",
    "            q_table.q_table[tuple(idx + (action,))] = alpha * value + (1.0 - alpha) * value\n",
    "\n",
    "\n",
    "# Test with a sample Q-table\n",
    "tq = TiledQTable(low, high, tiling_specs, 2)\n",
    "s1 = 3; s2 = 4; a = 0; q = 1.0\n",
    "print(\"[GET]    Q({}, {}) = {}\".format(samples[s1], a, tq.get(samples[s1], a)))  # check value at sample = s1, action = a\n",
    "print(\"[UPDATE] Q({}, {}) = {}\".format(samples[s2], a, q)); tq.update(samples[s2], a, q)  # update value for sample with some common tile(s)\n",
    "print(\"[GET]    Q({}, {}) = {}\".format(samples[s1], a, tq.get(samples[s1], a)))  # check value again, should be slightly updated"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you update the q-value for a particular state (say, `(0.25, -1.91)`) and action (say, `0`), then you should notice the q-value of a nearby state (e.g. `(0.15, -1.75)` and same action) has changed as well! This is how tile-coding is able to generalize values across the state space better than a single uniform grid."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. Implement a Q-Learning Agent using Tile-Coding\n",
    "\n",
    "Now it's your turn to apply this discretization technique to design and test a complete learning agent! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "class QLearningAgent:\n",
    "    \"\"\"Q-Learning agent that can act on a continuous state space by discretizing it.\"\"\"\n",
    "\n",
    "    def __init__(self, env, tq, alpha=0.02, gamma=0.99,\n",
    "                 epsilon=1.0, epsilon_decay_rate=0.9995, min_epsilon=.01, seed=0):\n",
    "        \"\"\"Initialize variables, create grid for discretization.\"\"\"\n",
    "        # Environment info\n",
    "        self.env = env\n",
    "        self.tq = tq \n",
    "        self.state_sizes = tq.state_sizes           # list of state sizes for each tiling\n",
    "        self.action_size = self.env.action_space.n  # 1-dimensional discrete action space\n",
    "        self.seed = np.random.seed(seed)\n",
    "        print(\"Environment:\", self.env)\n",
    "        print(\"State space sizes:\", self.state_sizes)\n",
    "        print(\"Action space size:\", self.action_size)\n",
    "        \n",
    "        # Learning parameters\n",
    "        self.alpha = alpha  # learning rate\n",
    "        self.gamma = gamma  # discount factor\n",
    "        self.epsilon = self.initial_epsilon = epsilon  # initial exploration rate\n",
    "        self.epsilon_decay_rate = epsilon_decay_rate   # how quickly should we decrease epsilon\n",
    "        self.min_epsilon = min_epsilon\n",
    "\n",
    "    def reset_episode(self, state):\n",
    "        \"\"\"Reset variables for a new episode.\"\"\"\n",
    "        # Gradually decrease exploration rate\n",
    "        self.epsilon *= self.epsilon_decay_rate\n",
    "        self.epsilon = max(self.epsilon, self.min_epsilon)\n",
    "        \n",
    "        self.last_state = state\n",
    "        Q_s = [self.tq.get(state, action) for action in range(self.action_size)]\n",
    "        self.last_action = np.argmax(Q_s)\n",
    "        return self.last_action\n",
    "    \n",
    "    def reset_exploration(self, epsilon=None):\n",
    "        \"\"\"Reset exploration rate used when training.\"\"\"\n",
    "        self.epsilon = epsilon if epsilon is not None else self.initial_epsilon\n",
    "\n",
    "    def act(self, state, reward=None, done=None, mode='train'):\n",
    "        \"\"\"Pick next action and update internal Q table (when mode != 'test').\"\"\"\n",
    "        Q_s = [self.tq.get(state, action) for action in range(self.action_size)]\n",
    "        # Pick the best action from Q table\n",
    "        greedy_action = np.argmax(Q_s)\n",
    "        if mode == 'test':\n",
    "            # Test mode: Simply produce an action\n",
    "            action = greedy_action\n",
    "        else:\n",
    "            # Train mode (default): Update Q table, pick next action\n",
    "            # Note: We update the Q table entry for the *last* (state, action) pair with current state, reward\n",
    "            value = reward + self.gamma * max(Q_s)\n",
    "            self.tq.update(self.last_state, self.last_action, value, self.alpha)\n",
    "\n",
    "            # Exploration vs. exploitation\n",
    "            do_exploration = np.random.uniform(0, 1) < self.epsilon\n",
    "            if do_exploration:\n",
    "                # Pick a random action\n",
    "                action = np.random.randint(0, self.action_size)\n",
    "            else:\n",
    "                # Pick the greedy action\n",
    "                action = greedy_action\n",
    "\n",
    "        # Roll over current state, action for next step\n",
    "        self.last_state = state\n",
    "        self.last_action = action\n",
    "        return action"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\n",
      "    [-1.0, 1.0] / 5 + (-0.13333334028720856) => [-0.733 -0.333  0.067  0.467]\n",
      "    [-1.0, 1.0] / 5 + (-0.13333334028720856) => [-0.733 -0.333  0.067  0.467]\n",
      "    [-1.0, 1.0] / 5 + (-0.13333334028720856) => [-0.733 -0.333  0.067  0.467]\n",
      "    [-1.0, 1.0] / 5 + (-0.13333334028720856) => [-0.733 -0.333  0.067  0.467]\n",
      "    [-12.566370964050293, 12.566370964050293] / 5 + (-1.675516128540039) => [-9.215 -4.189  0.838  5.864]\n",
      "    [-28.274333953857422, 28.274333953857422] / 5 + (-3.769911289215088) => [-20.735  -9.425   1.885  13.195]\n",
      "Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\n",
      "    [-1.0, 1.0] / 5 + (0.0) => [-0.6 -0.2  0.2  0.6]\n",
      "    [-1.0, 1.0] / 5 + (0.0) => [-0.6 -0.2  0.2  0.6]\n",
      "    [-1.0, 1.0] / 5 + (0.0) => [-0.6 -0.2  0.2  0.6]\n",
      "    [-1.0, 1.0] / 5 + (0.0) => [-0.6 -0.2  0.2  0.6]\n",
      "    [-12.566370964050293, 12.566370964050293] / 5 + (0.0) => [-7.54  -2.513  2.513  7.54 ]\n",
      "    [-28.274333953857422, 28.274333953857422] / 5 + (0.0) => [-16.965  -5.655   5.655  16.965]\n",
      "Tiling: [<low>, <high>] / <bins> + (<offset>) => <splits>\n",
      "    [-1.0, 1.0] / 5 + (0.13333334028720856) => [-0.467 -0.067  0.333  0.733]\n",
      "    [-1.0, 1.0] / 5 + (0.13333334028720856) => [-0.467 -0.067  0.333  0.733]\n",
      "    [-1.0, 1.0] / 5 + (0.13333334028720856) => [-0.467 -0.067  0.333  0.733]\n",
      "    [-1.0, 1.0] / 5 + (0.13333334028720856) => [-0.467 -0.067  0.333  0.733]\n",
      "    [-12.566370964050293, 12.566370964050293] / 5 + (1.675516128540039) => [-5.864 -0.838  4.189  9.215]\n",
      "    [-28.274333953857422, 28.274333953857422] / 5 + (3.769911289215088) => [-13.195  -1.885   9.425  20.735]\n",
      "QTable(): size = (5, 5, 5, 5, 5, 5, 3)\n",
      "QTable(): size = (5, 5, 5, 5, 5, 5, 3)\n",
      "QTable(): size = (5, 5, 5, 5, 5, 5, 3)\n",
      "TiledQTable(): no. of internal tables =  3\n",
      "Environment: <TimeLimit<AcrobotEnv<Acrobot-v1>>>\n",
      "State space sizes: [(5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 5), (5, 5, 5, 5, 5, 5)]\n",
      "Action space size: 3\n"
     ]
    }
   ],
   "source": [
    "n_bins = 5\n",
    "bins = tuple([n_bins]*env.observation_space.shape[0])\n",
    "offset_pos = (env.observation_space.high - env.observation_space.low)/(3*n_bins)\n",
    "\n",
    "tiling_specs = [(bins, -offset_pos),\n",
    "                (bins, tuple([0.0]*env.observation_space.shape[0])),\n",
    "                (bins, offset_pos)]\n",
    "\n",
    "tq = TiledQTable(env.observation_space.low, \n",
    "                 env.observation_space.high, \n",
    "                 tiling_specs, \n",
    "                 env.action_space.n)\n",
    "agent = QLearningAgent(env, tq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 10000/10000 | Max Average Score: -162.04"
     ]
    }
   ],
   "source": [
    "def run(agent, env, num_episodes=10000, mode='train'):\n",
    "    \"\"\"Run agent in given reinforcement learning environment and return scores.\"\"\"\n",
    "    scores = []\n",
    "    max_avg_score = -np.inf\n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        # Initialize episode\n",
    "        state = env.reset()\n",
    "        action = agent.reset_episode(state)\n",
    "        total_reward = 0\n",
    "        done = False\n",
    "\n",
    "        # Roll out steps until done\n",
    "        while not done:\n",
    "            state, reward, done, info = env.step(action)\n",
    "            total_reward += reward\n",
    "            action = agent.act(state, reward, done, mode)\n",
    "\n",
    "        # Save final score\n",
    "        scores.append(total_reward)\n",
    "\n",
    "        # Print episode stats\n",
    "        if mode == 'train':\n",
    "            if len(scores) > 100:\n",
    "                avg_score = np.mean(scores[-100:])\n",
    "                if avg_score > max_avg_score:\n",
    "                    max_avg_score = avg_score\n",
    "            if i_episode % 100 == 0:\n",
    "                print(\"\\rEpisode {}/{} | Max Average Score: {}\".format(i_episode, num_episodes, max_avg_score), end=\"\")\n",
    "                sys.stdout.flush()\n",
    "    return scores\n",
    "\n",
    "scores = run(agent, env)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f09044d4a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "def plot_scores(scores, rolling_window=100):\n",
    "    \"\"\"Plot scores and optional rolling mean using specified window.\"\"\"\n",
    "    plt.plot(scores); plt.title(\"Scores\");\n",
    "    rolling_mean = pd.Series(scores).rolling(rolling_window).mean()\n",
    "    plt.plot(rolling_mean);\n",
    "    return rolling_mean\n",
    "\n",
    "rolling_mean = plot_scores(scores)"
   ]
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}