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": 1,
   "metadata": {},
   "outputs": [],
   "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)"
   ]
  },
  {
   "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": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "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": "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": 8,
   "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": 8,
     "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": 9,
   "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",
    "    return [create_tiling_grid(low, high, bins, offsets) for bins, offsets in tiling_specs]\n",
    "\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": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "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": 14,
   "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))  # apply along each dimension\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(encoded_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": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "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": 18,
   "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) = 0.06666666666666667\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",
    "        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",
    "        \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": 19,
   "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": 20,
   "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": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 10000/10000 | Max Average Score: -242.47"
     ]
    }
   ],
   "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": 22,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'pd' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-22-5b07e52f7013>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mrolling_mean\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0mrolling_mean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplot_scores\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mscores\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-22-5b07e52f7013>\u001b[0m in \u001b[0;36mplot_scores\u001b[0;34m(scores, rolling_window)\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0;34m\"\"\"Plot scores and optional rolling mean using specified window.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mscores\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Scores\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0mrolling_mean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSeries\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mscores\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrolling\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrolling_window\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrolling_mean\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mrolling_mean\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'pd' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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)"
   ]
  },
  {
   "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}