Policy_Evaluation.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "03631e9b",
   "metadata": {},
   "source": [
    "# Setup\n",
    "\n",
    "Dependencies:\n",
    "- System: python3\n",
    "- Python: jupyter, numpy, matplotlib, seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "a0894254",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sn\n",
    "from matplotlib.colors import LinearSegmentedColormap\n",
    "\n",
    "W = LinearSegmentedColormap.from_list('w', [\"w\", \"w\"], N=256)\n",
    "\n",
    "ACTIONS = {\n",
    "    0: [1, 0],   # north\n",
    "    1: [-1, 0],  # south\n",
    "    2: [0, -1],  # west\n",
    "    3: [0, 1],   # east\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "29eb375f",
   "metadata": {},
   "outputs": [],
   "source": [
    "class GridWorld:\n",
    "    def __init__(self, size=4):\n",
    "        \"\"\"\n",
    "        A gridworld environment with absorbing states at [0, 0] and [size - 1, size - 1].\n",
    "        Args:\n",
    "            size (int): the dimension of the grid in each direction\n",
    "            cell_reward (float): the reward return after extiting any non absorbing state\n",
    "        \"\"\"\n",
    "        self.state_value = np.zeros((size, size))\n",
    "        return\n",
    "\n",
    "    def reset(self):\n",
    "        self.state_value = np.zeros((size, size))\n",
    "        return\n",
    "\n",
    "    def step(self, state, action):\n",
    "        # is terminal state?\n",
    "        size = len(self.state_value) - 1\n",
    "        if (state == (0, 0)) or (state == (size, size)):\n",
    "            return state, 0\n",
    "\n",
    "        s_1 = (state[0] + action[0], state[1] + action[1])\n",
    "        reward = -1\n",
    "        # out of bounds north-south\n",
    "        if s_1[0] < 0 or s_1[0] >= len(self.state_value):\n",
    "            s_1 = state\n",
    "        # out of bounds east-west\n",
    "        elif s_1[1] < 0 or s_1[1] >= len(self.state_value):\n",
    "            s_1 = state\n",
    "\n",
    "        return s_1, reward\n",
    "\n",
    "    def render(self, title=None):\n",
    "        \"\"\"\n",
    "        Displays the current value table of mini gridworld environment\n",
    "        \"\"\"\n",
    "        size = len(self.state_value) if len(self.state_value) < 20 else 20\n",
    "        fig, ax = plt.subplots(figsize=(size, size))\n",
    "        if title is not None:\n",
    "            ax.set_title(title)\n",
    "        sn.heatmap(self.state_value, annot=True, fmt=\".2f\", cmap=W,\n",
    "                   linewidths=1, linecolor=\"black\", cbar=False)\n",
    "        plt.show()\n",
    "        return fig, ax\n",
    "\n",
    "    def bellman_expectation(self, state, probs, discount):\n",
    "        \"\"\"\n",
    "        Makes a one step lookahead and applies the bellman expectation equation to the state self.state_value[state]\n",
    "        Args:\n",
    "            state (Tuple[int, int]): the x, y indices that define the address on the value table\n",
    "            probs (List[float]): transition probabilities for each action\n",
    "            in_place (bool): if False, the value table is updated after all the new values have been calculated.\n",
    "                             if True the state [i, j] will new already new values for the states [< i, < j]\n",
    "        Returns:\n",
    "            (numpy.ndarrray): the new value for the specified state\n",
    "        \"\"\"\n",
    "        # absorbing state\n",
    "        value = 0\n",
    "        for c, action in ACTIONS.items():\n",
    "            s_1, reward = self.step(state, action)\n",
    "            value += probs[c] * (reward + discount * self.state_value[s_1])\n",
    "        return value\n",
    "\n",
    "\n",
    "def policy_evaluation(env, policy=None, steps=1, discount=1., in_place=False):\n",
    "    \"\"\"\n",
    "    Args:\n",
    "        policy (numpy.array): a numpy 3-D numpy array, where the first two dimensions identify a state and the third dimension identifies the actions.\n",
    "                              The array stores the probability of taking each action.\n",
    "        steps (int): the number of iterations of the algorithm\n",
    "        discount (float): discount factor for the bellman equations\n",
    "        in_place (bool): if False, the value table is updated after all the new values have been calculated.\n",
    "             if True the state [i, j] will new already new values for the states [< i, < j]\n",
    "    \"\"\"\n",
    "    if policy is None:\n",
    "        # uniform random policy\n",
    "        policy = np.ones((*env.state_value.shape, len(ACTIONS))) * 0.25\n",
    "\n",
    "    for k in range(steps):\n",
    "        # cache old values if not in place\n",
    "        values = env.state_value if in_place else np.empty_like(\n",
    "            env.state_value)\n",
    "        for i in range(len(env.state_value)):\n",
    "            for j in range(len(env.state_value[i])):\n",
    "                # apply bellman expectation equation to each state\n",
    "                state = (i, j)\n",
    "                value = env.bellman_expectation(state, policy[i, j], discount)\n",
    "                values[i, j] = value * discount\n",
    "        # set the new value table\n",
    "        env.state_value = values\n",
    "    return env.state_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "89649a9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "env = GridWorld(4)\n",
    "env.render();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edf23abb",
   "metadata": {},
   "source": [
    "### Running k iterations of Policy Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "cef5a28e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.state_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "8396a23e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 3\n",
    "env = GridWorld(4)\n",
    "env.state_value = policy_evaluation(env, policy=None, steps=k, discount=1., in_place=False)\n",
    "env.render();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "754e9297",
   "metadata": {},
   "source": [
    "## Larger maze"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "f1777eb4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 1000\n",
    "env = GridWorld(7)\n",
    "env.state_value = policy_evaluation(env, policy=None, steps=k, discount=1., in_place=False)\n",
    "env.render();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "226bbd30",
   "metadata": {},
   "source": [
    "## Discount factor $\\gamma = 0.9$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "163d09ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 1\n",
    "env = GridWorld(4)\n",
    "env.state_value = policy_evaluation(env, policy=None, steps=k, discount=0.95, in_place=False)\n",
    "env.render();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ffc9f9d",
   "metadata": {},
   "source": [
    "## Other, non-(0,0) reward location"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "eb234d86",
   "metadata": {},
   "outputs": [],
   "source": [
    "class GridWorld:\n",
    "    def __init__(self, size=4):\n",
    "        \"\"\"\n",
    "        A gridworld environment with absorbing states at [0, 0] and [size - 1, size - 1].\n",
    "        Args:\n",
    "            size (int): the dimension of the grid in each direction\n",
    "            cell_reward (float): the reward return after extiting any non absorbing state\n",
    "        \"\"\"\n",
    "        self.state_value = np.zeros((size, size))\n",
    "        return\n",
    "\n",
    "    def reset(self):\n",
    "        self.state_value = np.zeros((size, size))\n",
    "        return\n",
    "\n",
    "    def step(self, state, action):\n",
    "        # is terminal state?\n",
    "        size = len(self.state_value) - 1\n",
    "        if (state == (0, 0)) or (state == (2,2)):\n",
    "            return state, 0\n",
    "\n",
    "        s_1 = (state[0] + action[0], state[1] + action[1])\n",
    "        reward = -1\n",
    "        # out of bounds north-south\n",
    "        if s_1[0] < 0 or s_1[0] >= len(self.state_value):\n",
    "            s_1 = state\n",
    "        # out of bounds east-west\n",
    "        elif s_1[1] < 0 or s_1[1] >= len(self.state_value):\n",
    "            s_1 = state\n",
    "\n",
    "        return s_1, reward\n",
    "\n",
    "    def render(self, title=None):\n",
    "        \"\"\"\n",
    "        Displays the current value table of mini gridworld environment\n",
    "        \"\"\"\n",
    "        size = len(self.state_value) if len(self.state_value) < 20 else 20\n",
    "        fig, ax = plt.subplots(figsize=(size, size))\n",
    "        if title is not None:\n",
    "            ax.set_title(title)\n",
    "        #ax.grid(which='major', axis='both',\n",
    "        #        linestyle='-', color='k', linewidth=2)\n",
    "        sn.heatmap(self.state_value, annot=True, fmt=\".2f\", cmap=W,\n",
    "                   linewidths=1, linecolor=\"black\", cbar=False)\n",
    "        plt.show()\n",
    "        return fig, ax\n",
    "\n",
    "    def bellman_expectation(self, state, probs, discount):\n",
    "        \"\"\"\n",
    "        Makes a one step lookahead and applies the bellman expectation equation to the state self.state_value[state]\n",
    "        Args:\n",
    "            state (Tuple[int, int]): the x, y indices that define the address on the value table\n",
    "            probs (List[float]): transition probabilities for each action\n",
    "            in_place (bool): if False, the value table is updated after all the new values have been calculated.\n",
    "                             if True the state [i, j] will new already new values for the states [< i, < j]\n",
    "        Returns:\n",
    "            (numpy.ndarrray): the new value for the specified state\n",
    "        \"\"\"\n",
    "        # absorbing state\n",
    "        value = 0\n",
    "        for c, action in ACTIONS.items():\n",
    "            s_1, reward = self.step(state, action)\n",
    "            value += probs[c] * (reward + discount * self.state_value[s_1])\n",
    "        return value\n",
    "\n",
    "\n",
    "def policy_evaluation(env, policy=None, steps=1, discount=1., in_place=False):\n",
    "    \"\"\"\n",
    "    Args:\n",
    "        policy (numpy.array): a numpy 3-D numpy array, where the first two dimensions identify a state and the third dimension identifies the actions.\n",
    "                              The array stores the probability of taking each action.\n",
    "        steps (int): the number of iterations of the algorithm\n",
    "        discount (float): discount factor for the bellman equations\n",
    "        in_place (bool): if False, the value table is updated after all the new values have been calculated.\n",
    "             if True the state [i, j] will new already new values for the states [< i, < j]\n",
    "    \"\"\"\n",
    "    if policy is None:\n",
    "        # uniform random policy\n",
    "        policy = np.ones((*env.state_value.shape, len(ACTIONS))) * 0.25\n",
    "\n",
    "    for k in range(steps):\n",
    "        # cache old values if not in place\n",
    "        values = env.state_value if in_place else np.empty_like(\n",
    "            env.state_value)\n",
    "        for i in range(len(env.state_value)):\n",
    "            for j in range(len(env.state_value[i])):\n",
    "                # apply bellman expectation equation to each state\n",
    "                state = (i, j)\n",
    "                value = env.bellman_expectation(state, policy[i, j], discount)\n",
    "                values[i, j] = value * discount\n",
    "        # set the new value table\n",
    "        env.state_value = values\n",
    "    return env.state_value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8179a6a0",
   "metadata": {},
   "source": [
    "### Running k iterations of Policy Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "abebf71b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 1\n",
    "env = GridWorld(4)\n",
    "env.state_value = policy_evaluation(env, policy=None, steps=k, discount=1., in_place=False)\n",
    "env.render();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f1b042c2",
   "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": "3.10.10 (main, Feb 16 2023, 02:49:39) [Clang 14.0.0 (clang-1400.0.29.202)]"
  },
  "vscode": {
   "interpreter": {
    "hash": "bda33b16be7e844498c7c2d368d72665b4f1d165582b9547ed22a0249a29ca2e"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}