policy_iter_value_iter.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install gym==0.21.0\n",
    "# !pip install pyglet==1.5.27\n",
    "import gym\n",
    "import random\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Confused Agent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Creating Confused Agent\n",
    "\"\"\"\n",
    "def confused_agent(env_name):\n",
    "    env = gym.make(env_name)\n",
    "    obs = env.reset()\n",
    "    done = False\n",
    "    total_reward = 0\n",
    "    while not done:\n",
    "        action = env.action_space.sample()\n",
    "        obs, reward, done, info = env.step(action)\n",
    "        total_reward += reward\n",
    "        # env.render()\n",
    "        #when we reach goal, we reset the environment\n",
    "        if done:\n",
    "            obs = env.reset()\n",
    "    env.close()\n",
    "    return total_reward\n",
    "\n",
    "#we run the agent 100 times\n",
    "confused_agent_total_rewards = []\n",
    "for i in range(100):\n",
    "    confused_agent_total_rewards.append(confused_agent(\"CliffWalking-v0\"))\n",
    "    \n",
    "plt.plot(confused_agent_total_rewards)\n",
    "plt.title(\"Confused Agent\")\n",
    "plt.xlabel(\"Episode\")\n",
    "plt.ylabel(\"Total Reward\")\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analysis:\n",
    "Random rewards across the iterations"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Value Iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def policy_to_arrows(policy):\n",
    "    arrows = []\n",
    "    for action in policy:\n",
    "        if action == 0:\n",
    "            arrows.append(\"↑\")\n",
    "        elif action == 1:\n",
    "            arrows.append(\"→\")\n",
    "        elif action == 2:\n",
    "            arrows.append(\"↓\")\n",
    "        elif action == 3:\n",
    "            arrows.append(\"←\")\n",
    "    return np.array(arrows).reshape(4,12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions of the optimal policy:\n",
      "[['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↓']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '→' '→']]\n",
      "-----------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions of the optimal policy:\n",
      "[['↑' '↑' '↑' '↑' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['↑' '↑' '↑' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['↑' '↑' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '→' '→']]\n",
      "-----------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions of the optimal policy:\n",
      "[['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '→' '→']]\n",
      "-----------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions of the optimal policy:\n",
      "[['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '→' '→']]\n",
      "-----------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions of the optimal policy:\n",
      "[['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '→' '→']]\n",
      "-----------------------------\n"
     ]
    }
   ],
   "source": [
    "class ValueIterationAgent:\n",
    "    \"\"\"\n",
    "    Value Iteration Agent\n",
    "    \"\"\"\n",
    "    def __init__(self, env_name, discount_factor=0.5, theta=1e-8):\n",
    "        self.env = gym.make(env_name)\n",
    "        self.discount_factor = discount_factor\n",
    "        self.theta = theta\n",
    "        #value function to calculate the value of a given state\n",
    "        self.V = np.zeros(self.env.nS)\n",
    "        #policy to map every state to an action\n",
    "        self.policy = np.random.randint(0, self.env.nA, size=(self.env.nS))\n",
    "\n",
    "    def run(self):\n",
    "        #we run the agent in the environment\n",
    "        obs = self.env.reset()\n",
    "        done = False\n",
    "        total_reward = 0\n",
    "        steps = 0\n",
    "        while not done and steps < 100:\n",
    "            action = self.policy[obs]\n",
    "            obs, reward, done, info = self.env.step(action)\n",
    "            total_reward += reward\n",
    "            #self.env.render()\n",
    "            #when we reach goal, we reset the environment\n",
    "            if done:\n",
    "                obs = self.env.reset()\n",
    "            steps += 1\n",
    "        self.env.close()\n",
    "        return total_reward\n",
    "    \n",
    "    def perform_value_iteration(self):\n",
    "        rewards = []\n",
    "        for i in range(100):\n",
    "            delta = 0\n",
    "            for s in range(self.env.nS):\n",
    "                v = self.V[s]\n",
    "                self.V[s] = np.max([sum([p*(r + self.discount_factor*self.V[s_] + 1*_) for p, s_, r, _ in self.env.P[s][a]]) for a in range(self.env.nA)])\n",
    "                delta = max(delta, abs(v - self.V[s]))\n",
    "            #update the policy based on the updated value function\n",
    "            for s in range(self.env.nS):\n",
    "                self.policy[s] = np.argmax([sum([p*(r + self.discount_factor*self.V[s_] + 1*_) for p, s_, r, _ in self.env.P[s][a]]) for a in range(self.env.nA)])\n",
    "            #calculate the rewards for the updated policy\n",
    "            rewards.append(self.run())\n",
    "            if delta < self.theta:\n",
    "                break\n",
    "        return self.policy, self.V, rewards\n",
    "\n",
    "\n",
    "for discount in [0, 0.1, 0.5, 0.75, 1]:\n",
    "    agent = ValueIterationAgent(\"CliffWalking-v0\", discount_factor=discount)\n",
    "    policy, V, rewards = agent.perform_value_iteration()\n",
    "    plt.plot(rewards, label=f\"discount factor: {discount}\")\n",
    "    plt.title(\"Value Iteration\")\n",
    "    plt.xlabel(\"Iterations\")\n",
    "    plt.ylabel(\"Total Reward\")\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    print(\"Directions of the optimal policy:\")\n",
    "    print(policy_to_arrows(policy))\n",
    "    print(\"-----------------------------\")\n",
    "\n",
    "        "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analysis:\n",
    "We can clearly see that from $\\alpha=0$ to $\\alpha=0.1$, the policy is changing as seen in the arrow directions, showing that there is learning happening. However, the rewards remain the same.\n",
    "\n",
    "From $\\alpha=0.5$ to $\\alpha=1$, the rewards and the policy remains the same. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Policy Iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def policy_to_arrows(policy):\n",
    "    arrows = []\n",
    "    for action in policy:\n",
    "        if action == 0:\n",
    "            arrows.append(\"↑\")\n",
    "        elif action == 1:\n",
    "            arrows.append(\"→\")\n",
    "        elif action == 2:\n",
    "            arrows.append(\"↓\")\n",
    "        elif action == 3:\n",
    "            arrows.append(\"←\")\n",
    "    return np.array(arrows).reshape(4,12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tW537jho1StOmTdPzzz+vPXv26MMPP1RQUJAkOdutWbNGiYmJWrx4saS/AszMmTP14osv6qefflJkZKTuuusu7d+/P1tdUVFRGjJkiOLj4xUZGem8RHj48OHLjsXmzZvVoUOHbNsiIyO1efNmF0fVNTwEEgDgkgsXM9VozKoiOfaeCZHytv/zV9e5c+c0b948ffDBB7rtttskSTExMapWrdpl90lISFBwcLA6dOggDw8PVa9eXS1btpQk/fzzz/r444+1evVq55d17dq1nfu+/vrrCgkJ0auvviqbzaYGDRro2LFjGjlypMaMGePS733169dP9913nyRpypQpevnll7V161bdcccdqlChgiQpMDBQ/v7+ue5vt9sVGBgoSapQoYKCg4MlSVWrVtXw4cOd7f773/9q1apV+vjjj9WyZUudPXtWc+bM0auvvqq+fftKkurUqaObb75Z0l+XICWpYsWKzj4l6cUXX9TIkSPVq1cvSdILL7ygdevWafbs2Xrttdec7YYOHap77rnH+f7IkSOqX7/+FR/WmJSU5AxnlwQFBSkpKemy++QHZo4AAKXOgQMHlJ6erlatWjm3VahQQfXr17/sPj169NCFCxdUu3ZtPfLII1qyZInzslhcXJzc3d0VERGR677x8fEKDw/P9pydNm3a6Ny5czp69KhLtTdt2tT5Zx8fHzkcDv3+++8u9ZGbzMxMTZw4UWFhYapQoYJ8fX21atUqJSQkOM8hLS3NGSbzIjU1VceOHVObNm2ybW/Tpo3i4+OzbbvhhhuyvW/ZsqX27t2rqlWrXuUZFRxmjgAALvHycNeeCZFFduyCEhISon379mnNmjVavXq1Hn/8cc2YMUPr16+Xl5fXNffv5uaW47JgbguT/z6TYrPZlJWVdc3HnzFjhubMmaPZs2crLCxMPj4+Gjp0qNLT0yUpX87xSnx8fFzeJzg4WMePH8+27fjx49lmrgoCM0cAAJfYbDZ528sUySuvT0CuU6eOPDw8tGXLFue206dP6+eff77ifl5eXuratatefvllxcbGavPmzdq5c6fCwsKUlZWl9evX57pfw4YNtXnz5mzhZ+PGjSpXrpzzUl5AQIASExOdn6empurQoUN5Op9LruXnMTZu3Khu3brpwQcf1HXXXafatWtnG4+6devKy8tL33zzTZ6P7XA4VKVKFW3cuDHHsRo1auRyjX8XHh6eo57Vq1crPDz8mvu+EsIRAKDU8fX11YABAzRixAitXbtWu3btUr9+/a649ic6Olrz5s3Trl27dPDgQX3wwQfy8vJSjRo1VLNmTfXt21cPPfSQli5dqkOHDik2NlYff/yxJOnxxx/XkSNH9N///ld79+7V559/rrFjx2rYsGHOY7Zv317vv/++/ve//2nnzp3q27ev3N1dmwmrUaOGbDabvvrqKyUnJ+vcuXN53rdu3bpavXq1Nm3apPj4eD366KPZZmXKli2rkSNH6plnntF7772nAwcO6LvvvnPekRcYGCgvLy+tXLlSx48fV0pKiqS/Fr6/8MIL+uijj7Rv3z5FRUUpLi5OQ4YMuWI9W7duVYMGDfTbb79dts2QIUO0cuVKzZw5U3v37tW4ceP0/fff64knnsjzeV8VA5ekpKQYSSYlJaWoSwGAAnfhwgWzZ88ec+HChaIuxWVnz541Dz74oPH29jZBQUFm+vTpJiIiwgwZMsTZpkaNGuall14yxhizZMkS06pVK+NwOIyPj4+56aabzJo1a5xtL1y4YJ566ilTuXJlY7fbTWhoqHn33Xedn8fGxpobb7zR2O12ExwcbEaOHGkuXrzo/DwlJcXce++9xuFwmJCQEBMdHW2uu+46M3bsWGcbSWbJkiXZzsPPz8/Mnz/f+X7ChAkmODjY2Gw207dv31zP/fTp00aSWbdunXPbyZMnTbdu3Yyvr68JDAw0zz33nOnTp4/p1q2bs01mZqaZNGmSqVGjhvHw8DDVq1c3U6ZMcX7+9ttvm5CQEOPm5mYiIiKc+4wbN85UrVrVeHh4mOuuu86sWLHCuc+hQ4eMJLNjx45sNa5bt85IMocOHcr1HC75+OOPTb169YzdbjeNGzc2y5Ytu2zbK/19deX722aMC/dFQqmpqfLz81NKSoocDkdRlwMABerPP//UoUOHVKtWLZUtW7aoywGu6Ep/X135/uayGgAAgAXhCAAAwIJwBAAAYEE4AgAAsCAcAQD+EffuoCTIr7+nhCMAwGVdelrz+fPni7gS4J9detq3q8+P+jt+PgQAcFnu7u7y9/d3/raXt7d3np9SDRSmrKwsJScny9vbW2XKXFu8IRwBAK7o0u9Y5cePnwIFyc3NTdWrV7/mAE84AgBckc1mU+XKlRUYGJjrD6UCxYXdbr/iT8TkFeEIAJAn7u7u17yWAygJWJANAABgQTgCAACwIBwBAABYEI4AAAAsCEcAAAAWhCMAAAALwhEAAIAF4QgAAMCCcAQAAGBBOAIAALAgHAEAAFiUqnC0fft2dezYUf7+/qpYsaIGDhyoc+fO5WgXHR2tpk2bqmzZsgoMDNTgwYOLoFoAAFAclZpwdOzYMXXo0EGhoaHasmWLVq5cqd27d6tfv37Z2s2aNUujR49WVFSUdu/erTVr1igyMrJoigYAAMWOzRhjirqI/PDWW2/p+eefV2Jiotzc/sp8O3fuVNOmTbV//36Fhobq9OnTqlq1qr788kvddtttV3Wc1NRU+fn5KSUlRQ6HIz9PAQAAFBBXvr9LzcxRWlqa7Ha7MxhJkpeXlyRpw4YNkqTVq1crKytLv/32mxo2bKhq1aqpZ8+eOnLkSJHUDAAAip9SE47at2+vpKQkzZgxQ+np6Tp9+rSioqIkSYmJiZKkgwcPKisrS1OmTNHs2bP16aef6tSpU+rYsaPS09Nz7TctLU2pqanZXgAAoPQq9uEoKipKNpvtiq+9e/eqcePGiomJ0cyZM+Xt7a3g4GDVqlVLQUFBztmkrKwsXbx4US+//LIiIyN10003aeHChdq/f7/WrVuX6/GnTp0qPz8/5yskJKQwTx8AABSyYr/mKDk5WSdPnrxim9q1a8tutzvfHz9+XD4+PrLZbHI4HFq0aJF69Oih+fPn66GHHtKRI0dUrVo1Z/ugoCBNmjRJjzzySI6+09LSlJaW5nyfmpqqkJAQ1hwBAFCCuLLmqEwh1XTVAgICFBAQ4NI+QUFBkqR3331XZcuWVceOHSVJbdq0kSTt27fPGY5OnTqlEydOqEaNGrn25enpKU9Pz6stHwAAlDDFPhy54tVXX1Xr1q3l6+ur1atXa8SIEZo2bZr8/f0lSfXq1VO3bt00ZMgQvfXWW3I4HBo1apQaNGigW2+9tWiLBwAAxUKxX3Pkiq1bt6pjx44KCwvTW2+9pTfffFNPPvlktjbvvfeeWrVqpS5duigiIkIeHh5auXKlPDw8iqhqAABQnBT7NUfFDc85AgCg5PlXPucIAAAgPxCOAAAALAhHAAAAFoQjAAAAC8IRAACABeEIAADAgnAEAABgQTgCAACwIBwBAABYEI4AAAAsCEcAAAAWhCMAAAALwhEAAIAF4QgAAMCCcAQAAGBBOAIAALAgHAEAAFgQjgAAACwIRwAAABaEIwAAAAvCEQAAgAXhCAAAwIJwBAAAYEE4AgAAsCAcAQAAWBCOAAAALAhHAAAAFoQjAAAAC8IRAACABeEIAADAgnAEAABgQTgCAACwIBwBAABYEI4AAAAsCEcAAAAWhCMAAAALwhEAAIAF4QgAAMCCcAQAAGBBOAIAALAgHAEAAFgQjgAAACwIRwAAABaEIwAAAAvCEQAAgAXhCAAAwIJwBAAAYEE4AgAAsCAcAQAAWBCOAAAALAhHAAAAFoQjAAAAC8IRAACABeEIAADAgnAEAABgQTgCAACwKFXhaPv27erYsaP8/f1VsWJFDRw4UOfOncvWZtu2bbrtttvk7++v8uXLKzIyUj/++GMRVQwAAIqbUhOOjh07pg4dOig0NFRbtmzRypUrtXv3bvXr18/Z5ty5c7rjjjtUvXp1bdmyRRs2bFC5cuUUGRmpixcvFl3xAACg2LAZY0xRF5Ef3nrrLT3//PNKTEyUm9tfmW/nzp1q2rSp9u/fr9DQUH3//fe68cYblZCQoJCQkFzb/JPU1FT5+fkpJSVFDoejQM8JAADkD1e+v0vNzFFaWprsdrszGEmSl5eXJGnDhg2SpPr166tixYqaN2+e0tPTdeHCBc2bN08NGzZUzZo1i6JsAABQzJSacNS+fXslJSVpxowZSk9P1+nTpxUVFSVJSkxMlCSVK1dOsbGx+uCDD+Tl5SVfX1+tXLlSK1asUJkyZXLtNy0tTampqdleAACg9Cr24SgqKko2m+2Kr71796px48aKiYnRzJkz5e3treDgYNWqVUtBQUHO2aQLFy5owIABatOmjb777jtt3LhRTZo0UZcuXXThwoVcjz916lT5+fk5X5cuxwEAgNKp2K85Sk5O1smTJ6/Ypnbt2rLb7c73x48fl4+Pj2w2mxwOhxYtWqQePXpo3rx5evbZZ7OtS0pPT1f58uU1b9489erVK0ffaWlpSktLc75PTU1VSEgIa44AAChBXFlzlPu1pGIkICBAAQEBLu0TFBQkSXr33XdVtmxZdezYUZJ0/vx5ubm5yWazOdteep+VlZVrX56envL09LzK6gEAQElT7C+rueLVV1/V9u3b9fPPP+u1117TE088oalTp8rf31+S1LFjR50+fVqDBw9WfHy8du/erf79+6tMmTK69dZbi7Z4AABQLBT7mSNXbN26VWPHjtW5c+fUoEEDvfnmm+rdu7fz8wYNGujLL7/U+PHjFR4eLjc3NzVv3lwrV65U5cqVi7ByAABQXBT7NUfFDc85AgCg5PlXPucIAAAgPxCOAAAALAhHAAAAFoQjAAAAC8IRAACABeEIAADAgnAEAABgQTgCAACwIBwBAABYEI4AAAAsCEcAAAAWhCMAAAALwhEAAIAF4QgAAMCCcAQAAGBBOAIAALAgHAEAAFgQjgAAACwIRwAAABZl8tJo2LBhee5w1qxZV10MAABAUctTONqxY0e299u3b1dGRobq168vSfr555/l7u6uFi1a5H+FAAAAhShP4WjdunXOP8+aNUvlypVTTEyMypcvL0k6ffq0+vfvr7Zt2xZMlQAAAIXEZowxruxQtWpVff3112rcuHG27bt27dLtt9+uY8eO5WuBxU1qaqr8/PyUkpIih8NR1OUAAIA8cOX72+UF2ampqUpOTs6xPTk5WWfPnnW1OwAAgGLF5XB09913q3///lq8eLGOHj2qo0eP6rPPPtOAAQN0zz33FESNAAAAhSZPa46s5s6dq+HDh+v+++/XxYsX/+qkTBkNGDBAM2bMyPcCAQAACpNLa44yMzO1ceNGhYWFyW6368CBA5KkOnXqyMfHp8CKLE5YcwQAQMnjyve3SzNH7u7uuv322xUfH69atWqpadOm11QoAABAcePymqMmTZro4MGDBVELAABAkXM5HE2aNEnDhw/XV199pcTERKWmpmZ7AQAAlGQuP+fIze3/85TNZnP+2Rgjm82mzMzM/KuuGGLNEQAAJU+BrTmSsj8tGwAAoLRxORxFREQURB0AAADFgsvh6JLz588rISFB6enp2bZzBxsAACjJXA5HycnJ6t+/v1asWJHr56V9zREAACjdXL5bbejQoTpz5oy2bNkiLy8vrVy5UjExMapbt66++OKLgqgRAACg0Lg8c7R27Vp9/vnnuuGGG+Tm5qYaNWqoY8eOcjgcmjp1qrp06VIQdQIAABQKl2eO/vjjDwUGBkqSypcvr+TkZElSWFiYtm/fnr/VAQAAFDKXw1H9+vW1b98+SdJ1112nN998U7/99pvmzp2rypUr53uBAAAAhcnly2pDhgxRYmKiJGns2LG64447tGDBAtntdkVHR+d3fQAAAIXK5Sdk/9358+e1d+9eVa9eXZUqVcqvuootnpANAEDJ48r3t8uX1f7+o7Pe3t66/vrr/xXBCAAAlH4uX1YLDQ1VtWrVFBERoXbt2ikiIkKhoaEFURsAAEChc3nm6MiRI5o6daq8vLw0ffp01atXT9WqVdMDDzygd955pyBqBAAAKDTXvOZo//79mjx5shYsWKCsrKxS/4Rs1hwBAFDyuPL97fJltfPnz2vDhg2KjY1VbGysduzYoQYNGuiJJ55Qu3btrrZmAACAYsHlcOTv76/y5cvrgQceUFRUlNq2bavy5csXRG0AAACFzuVw1LlzZ23YsEGLFi1SUlKSkpKS1K5dO9WrV68g6gMAAChULi/IXrp0qU6cOKGVK1cqPDxcX3/9tdq2bauqVavqgQceKIgaAQAACo3LM0eXhIWFKSMjQ+np6frzzz+1atUqffTRR1qwYEF+1gcAAFCoXJ45mjVrlu666y5VrFhRrVq10sKFC1WvXj199tlnzh+hBQAAKKlcnjlauHChIiIiNHDgQLVt21Z+fn4FURcAAECRcDkcbdu2rSDqAAAAKBZcvqwmSf/73//04IMPKjw8XL/99psk6f3339eGDRvytTgAAIDC5nI4+uyzzxQZGSkvLy/t2LFDaWlpkqSUlBRNmTIl3wsEAAAoTC6Ho0mTJmnu3Ll6++235eHh4dzepk0bbd++PV+LAwAAKGwuh6N9+/bplltuybHdz89PZ86cyY+aAAAAiozL4Sg4OFi//PJLju0bNmxQ7dq186Wo3EyePFmtW7eWt7e3/P39c22TkJCgLl26yNvbW4GBgRoxYoQyMjKytYmNjdX1118vT09PhYaGKjo6usBqBgAAJY/L4eiRRx7RkCFDtGXLFtlsNh07dkwLFizQ8OHDNWjQoIKoUZKUnp6uHj16XPYYmZmZ6tKli9LT07Vp0ybFxMQoOjpaY8aMcbY5dOiQunTpoltvvVVxcXEaOnSoHn74Ya1atarA6gYAACWLzRhjXNnBGKMpU6Zo6tSpOn/+vCTJ09NTw4cP18SJEwukSKvo6GgNHTo0xyW8FStW6M4779SxY8cUFBQkSZo7d65Gjhyp5ORk2e12jRw5UsuWLdOuXbuc+/Xq1UtnzpzRypUr83T81NRU+fn5KSUlRQ6HI9/OyxijCxcz860/AABKMi8Pd9lstnzrz5Xvb5efc2Sz2TR69GiNGDFCv/zyi86dO6dGjRrJ19dXFy5ckJeX11UXfi02b96ssLAwZzCSpMjISA0aNEi7d+9W8+bNtXnzZnXo0CHbfpGRkRo6dOhl+01LS3PekSf9NbgF4cLFTDUawwwWAACStGdCpLztV/0rZ9fkqp5zJEl2u12NGjVSy5Yt5eHhoVmzZqlWrVr5WZtLkpKSsgUjSc73SUlJV2yTmpqqCxcu5Nrv1KlT5efn53yFhIQUQPUAAKC4yHMkS0tL07hx47R69WrZ7XY988wz6t69u+bPn6/Ro0fL3d1dTz31lEsHj4qK0gsvvHDFNvHx8WrQoIFL/eanUaNGadiwYc73qampBRKQvDzctWdCZL73CwBASeTl4V5kx85zOBozZozefPNNdejQQZs2bVKPHj3Uv39/fffdd5o1a5Z69Oghd3fXTuTpp59Wv379rtgmr3fABQcHa+vWrdm2HT9+3PnZpf+9tM3axuFwXPZyoKenpzw9PfNUw7Ww2WxFNn0IAAD+X56/jT/55BO99957uuuuu7Rr1y41bdpUGRkZ+vHHH696wVRAQIACAgKuat+/Cw8P1+TJk/X7778rMDBQkrR69Wo5HA41atTI2Wb58uXZ9lu9erXCw8PzpQYAAFDy5XnN0dGjR9WiRQtJUpMmTeTp6amnnnoqX1eSX0lCQoLi4uKUkJCgzMxMxcXFKS4uTufOnZMk3X777WrUqJF69+6tH3/8UatWrdJzzz2nwYMHO2d+HnvsMR08eFDPPPOM9u7dq9dff10ff/yxy5cDAQBA6ZXnmaPMzEzZ7fb/37FMGfn6+hZIUbkZM2aMYmJinO+bN28uSVq3bp3atWsnd3d3ffXVVxo0aJDCw8Pl4+Ojvn37asKECc59atWqpWXLlumpp57SnDlzVK1aNb3zzjuKjGStDwAA+Euen3Pk5uamTp06OWdhvvzyS7Vv314+Pj7Z2i1evDj/qyxGCuo5RwAAoOAUyHOO+vbtm+39gw8+eHXVAQAAFGN5Dkfz588vyDoAAACKhat+CCQAAEBpRDgCAACwIBwBAABYEI4AAAAsCEcAAAAWebpb7Ysvvshzh3fddddVFwMAAFDU8hSOunfvnqfObDabMjMzr6UeAACAIpWncJSVlVXQdQAAABQLrDkCAACwyPMTsq3++OMPrV+/XgkJCUpPT8/22ZNPPpkvhQEAABQFl8PRjh071LlzZ50/f15//PGHKlSooBMnTsjb21uBgYGEIwAAUKK5fFntqaeeUteuXXX69Gl5eXnpu+++06+//qoWLVroxRdfLIgaAQAACo3L4SguLk5PP/203Nzc5O7urrS0NIWEhGj69Ol69tlnC6JGAACAQuNyOPLw8JCb21+7BQYGKiEhQZLk5+enI0eO5G91AAAAhczlNUfNmzfXtm3bVLduXUVERGjMmDE6ceKE3n//fTVp0qQgagQAACg0Ls8cTZkyRZUrV5YkTZ48WeXLl9egQYOUnJysN998M98LBAAAKEw2Y4wp6iJKktTUVPn5+SklJUUOh6OoywEAAHngyve3yzNH7du315kzZ3I9aPv27V3tDgAAoFhxORzFxsbmePCjJP3555/63//+ly9FAQAAFJU8L8j+6aefnH/es2ePkpKSnO8zMzO1cuVKVa1aNX+rAwAAKGR5DkfNmjWTzWaTzWbL9fKZl5eXXnnllXwtDgAAoLDlORwdOnRIxhjVrl1bW7duVUBAgPMzu92uwMBAubu7F0iRAAAAhSXP4ahGjRqSpKysrAIrBgAAoKi5/BBISTpw4IBmz56t+Ph4SVKjRo00ZMgQ1alTJ1+LAwAAKGwu3622atUqNWrUSFu3blXTpk3VtGlTbdmyRY0bN9bq1asLokYAAIBC4/JDIJs3b67IyEhNmzYt2/aoqCh9/fXX2r59e74WWNzwEEgAAEqeAn0IZHx8vAYMGJBj+0MPPaQ9e/a42h0AAECx4nI4CggIUFxcXI7tcXFxCgwMzI+aAAAAikyeF2RPmDBBw4cP1yOPPKKBAwfq4MGDat26tSRp48aNeuGFFzRs2LACKxQAAKAw5HnNkbu7uxITExUQEKDZs2dr5syZOnbsmCSpSpUqGjFihJ588knZbLYCLbioseYIAICSx5Xv7zyHIzc3NyUlJWW7dHb27FlJUrly5a6h3JKFcAQAQMnjyve3S885+vus0L8pFAEAgH8Hl8JRvXr1/vGy2alTp66pIAAAgKLkUjgaP368/Pz8CqoWAACAIudSOOrVqxe36wMAgFItz885Ku13oQEAAEguhCMXf2UEAACgRMrzZbWsrKyCrAMAAKBYcPnnQwAAAEozwhEAAIAF4QgAAMCCcAQAAGBBOAIAALAgHAEAAFgQjgAAACwIRwAAABaEIwAAAAvCEQAAgAXhCAAAwIJwBAAAYEE4AgAAsCAcAQAAWBCOAAAALAhHAAAAFiUmHE2ePFmtW7eWt7e3/P39c22TkJCgLl26yNvbW4GBgRoxYoQyMjKcny9evFgdO3ZUQECAHA6HwsPDtWrVqkI6AwAAUBKUmHCUnp6uHj16aNCgQbl+npmZqS5duig9PV2bNm1STEyMoqOjNWbMGGebb7/9Vh07dtTy5cv1ww8/6NZbb1XXrl21Y8eOwjoNAABQzNmMMaaoi3BFdHS0hg4dqjNnzmTbvmLFCt155506duyYgoKCJElz587VyJEjlZycLLvdnmt/jRs31r333pstRF1Jamqq/Pz8lJKSIofDcU3nAgAACocr398lZubon2zevFlhYWHOYCRJkZGRSk1N1e7du3PdJysrS2fPnlWFChUu229aWppSU1OzvQAAQOlVasJRUlJStmAkyfk+KSkp131efPFFnTt3Tj179rxsv1OnTpWfn5/zFRISkn9FAwCAYqdIw1FUVJRsNtsVX3v37i2QY3/44YcaP368Pv74YwUGBl623ahRo5SSkuJ8HTlypEDqAQAAxUOZojz4008/rX79+l2xTe3atfPUV3BwsLZu3Zpt2/Hjx52fWS1atEgPP/ywPvnkE3Xo0OGK/Xp6esrT0zNPNQAAgJKvSMNRQECAAgIC8qWv8PBwTZ48Wb///rtzJmj16tVyOBxq1KiRs93ChQv10EMPadGiRerSpUu+HBsAAJQeRRqOXJGQkKBTp04pISFBmZmZiouLkySFhobK19dXt99+uxo1aqTevXtr+vTpSkpK0nPPPafBgwc7Z34+/PBD9e3bV3PmzFGrVq2ca5G8vLzk5+dXVKcGAACKkRJzK3+/fv0UExOTY/u6devUrl07SdKvv/6qQYMGKTY2Vj4+Purbt6+mTZumMmX+yoDt2rXT+vXrc/TRt29fRUdH56kObuUHAKDkceX7u8SEo+KCcAQAQMnzr3zOEQAAQH4gHAEAAFgQjgAAACwIRwAAABaEIwAAAAvCEQAAgAXhCAAAwIJwBAAAYEE4AgAAsCAcAQAAWBCOAAAALAhHAAAAFoQjAAAAC8IRAACABeEIAADAgnAEAABgQTgCAACwIBwBAABYEI4AAAAsCEcAAAAWhCMAAAALwhEAAIAF4QgAAMCCcAQAAGBBOAIAALAgHAEAAFgQjgAAACwIRwAAABaEIwAAAAvCEQAAgAXhCAAAwIJwBAAAYEE4AgAAsCAcAQAAWBCOAAAALAhHAAAAFoQjAAAAC8IRAACABeEIAADAgnAEAABgQTgCAACwIBwBAABYEI4AAAAsCEcAAAAWhCMAAAALwhEAAIAF4QgAAMCCcAQAAGBBOAIAALAgHAEAAFgQjgAAACwIRwAAABaEIwAAAAvCEQAAgAXhCAAAwIJwBAAAYFFiwtHkyZPVunVreXt7y9/fP9c2CQkJ6tKli7y9vRUYGKgRI0YoIyMj17YbN25UmTJl1KxZs4IrGgAAlDglJhylp6erR48eGjRoUK6fZ2ZmqkuXLkpPT9emTZsUExOj6OhojRkzJkfbM2fOqE+fPrrtttsKumwAAFDC2IwxpqiLcEV0dLSGDh2qM2fOZNu+YsUK3XnnnTp27JiCgoIkSXPnztXIkSOVnJwsu93ubNurVy/VrVtX7u7uWrp0qeLi4vJ8/NTUVPn5+SklJUUOhyM/TgkAABQwV76/S8zM0T/ZvHmzwsLCnMFIkiIjI5Wamqrdu3c7t82fP18HDx7U2LFj89RvWlqaUlNTs70AAEDpVWrCUVJSUrZgJMn5PikpSZK0f/9+RUVF6YMPPlCZMmXy1O/UqVPl5+fnfIWEhORv4QAAoFgp0nAUFRUlm812xdfevXvz5ViZmZm6//77NX78eNWrVy/P+40aNUopKSnO15EjR/KlHgAAUDzlbfqkgDz99NPq16/fFdvUrl07T30FBwdr69at2bYdP37c+dnZs2f1/fffa8eOHXriiSckSVlZWTLGqEyZMvr666/Vvn37HP16enrK09MzTzUAAICSr0jDUUBAgAICAvKlr/DwcE2ePFm///67AgMDJUmrV6+Ww+FQo0aN5OHhoZ07d2bb5/XXX9fatWv16aefqlatWvlSBwAAKNmKNBy5IiEhQadOnVJCQoIyMzOdd5iFhobK19dXt99+uxo1aqTevXtr+vTpSkpK0nPPPafBgwc7Z36aNGmSrc/AwECVLVs2x3YAAPDvVWLC0ZgxYxQTE+N837x5c0nSunXr1K5dO7m7u+urr77SoEGDFB4eLh8fH/Xt21cTJkwoqpIBAEAJVOKec1TUeM4RAAAlz7/yOUcAAAD5gXAEAABgQTgCAACwIBwBAABYEI4AAAAsCEcAAAAWhCMAAAALwhEAAIAF4QgAAMCCcAQAAGBBOAIAALAgHAEAAFgQjgAAACwIRwAAABaEIwAAAAvCEQAAgAXhCAAAwIJwBAAAYEE4AgAAsCAcAQAAWBCOAAAALAhHAAAAFoQjAAAAC8IRAACABeEIAADAgnAEAABgQTgCAACwIBwBAABYEI4AAAAsCEcAAAAWhCMAAAALwhEAAIAF4QgAAMCCcAQAAGBBOAIAALAgHAEAAFgQjgAAACwIRwAAABaEIwAAAAvCEQAAgAXhCAAAwIJwBAAAYEE4AgAAsChT1AWUNMYYSVJqamoRVwIAAPLq0vf2pe/xKyEcuejs2bOSpJCQkCKuBAAAuOrs2bPy8/O7YhubyUuEglNWVpaOHTumcuXKyWaz5WvfqampCgkJ0ZEjR+RwOPK1b/w/xrlwMM6Fg3EuPIx14SiocTbG6OzZs6pSpYrc3K68qoiZIxe5ubmpWrVqBXoMh8PBv3iFgHEuHIxz4WCcCw9jXTgKYpz/acboEhZkAwAAWBCOAAAALAhHxYinp6fGjh0rT0/Poi6lVGOcCwfjXDgY58LDWBeO4jDOLMgGAACwYOYIAADAgnAEAABgQTgCAACwIBwBAABYEI4K2WuvvaaaNWuqbNmyatWqlbZu3XrF9p988okaNGigsmXLKiwsTMuXLy+kSks2V8b57bffVtu2bVW+fHmVL19eHTp0+Md/LviLq3+fL1m0aJFsNpu6d+9esAWWEq6O85kzZzR48GBVrlxZnp6eqlevHv/tyANXx3n27NmqX7++vLy8FBISoqeeekp//vlnIVVbMn377bfq2rWrqlSpIpvNpqVLl/7jPrGxsbr++uvl6emp0NBQRUdHF3idMig0ixYtMna73bz77rtm9+7d5pFHHjH+/v7m+PHjubbfuHGjcXd3N9OnTzd79uwxzz33nPHw8DA7d+4s5MpLFlfH+f777zevvfaa2bFjh4mPjzf9+vUzfn5+5ujRo4Vcecni6jhfcujQIVO1alXTtm1b061bt8IptgRzdZzT0tLMDTfcYDp37mw2bNhgDh06ZGJjY01cXFwhV16yuDrOCxYsMJ6enmbBggXm0KFDZtWqVaZy5crmqaeeKuTKS5bly5eb0aNHm8WLFxtJZsmSJVdsf/DgQePt7W2GDRtm9uzZY1555RXj7u5uVq5cWaB1Eo4KUcuWLc3gwYOd7zMzM02VKlXM1KlTc23fs2dP06VLl2zbWrVqZR599NECrbOkc3Wc/y4jI8OUK1fOxMTEFFSJpcLVjHNGRoZp3bq1eeedd0zfvn0JR3ng6ji/8cYbpnbt2iY9Pb2wSiwVXB3nwYMHm/bt22fbNmzYMNOmTZsCrbM0yUs4euaZZ0zjxo2zbbv33ntNZGRkAVZmDJfVCkl6erp++OEHdejQwbnNzc1NHTp00ObNm3PdZ/PmzdnaS1JkZORl2+Pqxvnvzp8/r4sXL6pChQoFVWaJd7XjPGHCBAUGBmrAgAGFUWaJdzXj/MUXXyg8PFyDBw9WUFCQmjRpoilTpigzM7Owyi5xrmacW7durR9++MF56e3gwYNavny5OnfuXCg1/1sU1fcgPzxbSE6cOKHMzEwFBQVl2x4UFKS9e/fmuk9SUlKu7ZOSkgqszpLuasb570aOHKkqVark+BcS/+9qxnnDhg2aN2+e4uLiCqHC0uFqxvngwYNau3atHnjgAS1fvly//PKLHn/8cV28eFFjx44tjLJLnKsZ5/vvv18nTpzQzTffLGOMMjIy9Nhjj+nZZ58tjJL/NS73PZiamqoLFy7Iy8urQI7LzBFgMW3aNC1atEhLlixR2bJli7qcUuPs2bPq3bu33n77bVWqVKmoyynVsrKyFBgYqLfeekstWrTQvffeq9GjR2vu3LlFXVqpEhsbqylTpuj111/X9u3btXjxYi1btkwTJ04s6tKQD5g5KiSVKlWSu7u7jh8/nm378ePHFRwcnOs+wcHBLrXH1Y3zJS+++KKmTZumNWvWqGnTpgVZZonn6jgfOHBAhw8fVteuXZ3bsrKyJEllypTRvn37VKdOnYItugS6mr/PlStXloeHh9zd3Z3bGjZsqKSkJKWnp8tutxdozSXR1Yzz888/r969e+vhhx+WJIWFhemPP/7QwIEDNXr0aLm5MfeQHy73PehwOAps1khi5qjQ2O12tWjRQt98841zW1ZWlr755huFh4fnuk94eHi29pK0evXqy7bH1Y2zJE2fPl0TJ07UypUrdcMNNxRGqSWaq+PcoEED7dy5U3Fxcc7XXXfdpVtvvVVxcXEKCQkpzPJLjKv5+9ymTRv98ssvzvApST///LMqV65MMLqMqxnn8+fP5whAlwKp4SdL802RfQ8W6HJvZLNo0SLj6elpoqOjzZ49e8zAgQONv7+/SUpKMsYY07t3bxMVFeVsv3HjRlOmTBnz4osvmvj4eDN27Fhu5c8DV8d52rRpxm63m08//dQkJiY6X2fPni2qUygRXB3nv+NutbxxdZwTEhJMuXLlzBNPPGH27dtnvvrqKxMYGGgmTZpUVKdQIrg6zmPHjjXlypUzCxcuNAcPHjRff/21qVOnjunZs2dRnUKJcPbsWbNjxw6zY8cOI8nMmjXL7Nixw/z666/GGGOioqJM7969ne0v3co/YsQIEx8fb1577TVu5S+NXnnlFVO9enVjt9tNy5YtzXfffef8LCIiwvTt2zdb+48//tjUq1fP2O1207hxY7Ns2bJCrrhkcmWca9SoYSTleI0dO7bwCy9hXP37bEU4yjtXx3nTpk2mVatWxtPT09SuXdtMnjzZZGRkFHLVJY8r43zx4kUzbtw4U6dOHVO2bFkTEhJiHn/8cXP69OnCL7wEWbduXa7/vb00tn379jURERE59mnWrJmx2+2mdu3aZv78+QVep80Y5v8AAAAuYc0RAACABeEIAADAgnAEAABgQTgCAACwIBwBAABYEI4AAAAsCEcAAAAWhCMAyIOaNWtq9uzZRV0GgEJAOAJQ7PTr10/du3eXJLVr105Dhw4ttGNHR0fL398/x/Zt27Zp4MCBhVYHgKJTpqgLAIDCcK2/SB8QEJCP1QAozpg5AlBs9evXT+vXr9ecOXNks9lks9l0+PBhSdKuXbvUqVMn+fr6KigoSL1799aJEyec+7Zr105PPPGEhg4dqkqVKikyMlKSNGvWLIWFhcnHx0chISF6/PHHde7cOUlSbGys+vfvr5SUFOfxxo0bJynnZbWEhAR169ZNvr6+cjgc6tmzp44fP+78fNy4cWrWrJnef/991axZU35+furVq5fOnj3rbPPpp58qLCxMXl5eqlixojp06KA//vijgEYTQF4RjgAUW3PmzFF4eLgeeeQRJSYmKjExUSEhITpz5ozat2+v5s2b6/vvv9fKlSt1/Phx9ezZM9v+MTExstvt2rhxo+bOnStJcnNz08svv6zdu3crJiZGa9eu1TPPPCNJat26tWbPni2Hw+E83vDhw3PUlZWVpW7duunUqVNav369Vq9erYMHD+ree+/N1u7AgQNaunSpvvrqK3311Vdav369pk2bJklKTEzUfffdp4ceekjx8fGKjY3VPffcI37uEih6XFYDUGz5+fnJbrfL29tbwcHBzu2vvvqqmjdvrilTpji3vfvuuwoJCdHPP/+sevXqSZLq1q2r6dOnZ+vTun6pZs2amjRpkh577DG9/vrrstvt8vPzk81my3a8v/vmm2+0c+dOHTp0SCEhIZKk9957T40bN9a2bdt04403SvorREVHR6tcuXKSpN69e+ubb77R5MmTlZiYqIyMDN1zzz2qUaOGJCksLOwaRgtAfmHmCECJ8+OPP2rdunXy9fV1vho0aCDpr9maS1q0aJFj3zVr1ui2225T1apVVa5cOfXu3VsnT57U+fPn83z8+Ph4hYSEOIORJDVq1Ej+/v6Kj493bqtZs6YzGElS5cqV9fvvv0uSrrvuOt12220KCwtTjx499Pbbb+v06dN5HwQABYZwBKDEOXfunLp27aq4uLhsr/379+uWW25xtvPx8cm23+HDh3XnnXeqadOm+uyzz/TDDz/otddek/TXgu385uHhke29zWZTVlaWJMnd3V2rV6/WihUr1KhRI73yyiuqX7++Dh06lO91AHAN4QhAsWa325WZmZlt2/XXX6/du3erZs2aCg0Nzfb6eyCy+uGHH5SVlaWZM2fqpptuUr169XTs2LF/PN7fNWzYUEeOHNGRI0ec2/bs2aMzZ86oUaNGeT43m82mNm3aaPz48dqxY4fsdruWLFmS5/0BFAzCEYBirWbNmtqyZYsOHz6sEydOKCsrS4MHD9apU6d03333adu2bTpw4IBWrVql/v37XzHYhIaG6uLFi3rllVd08OBBvf/++86F2tbjnTt3Tt98841OnDiR6+W2Dh06KCwsTA888IC2b9+urVu3qk+fPoqIiNANN9yQp/PasmWLpkyZou+//14JCQlavHixkpOT1bBhQ9cGCEC+IxwBKNaGDx8ud3d3NWrUSAEBAUpISFCVKlW0ceNGZWZm6vbbb1dYWJiGDh0qf39/ubld/j9r1113nWbNmqUXXnhBTZo00YIFCzR16tRsbVq3bq3HHntM9957rwICAnIs6Jb+mvH5/PPPVb58ed1yyy3q0KGDateurY8++ijP5+VwOPTtt9+qc+fOqlevnp577jnNnDlTnTp1yvvgACgQNsN9owAAAE7MHAEAAFgQjgAAACwIRwAAABaEIwAAAAvCEQAAgAXhCAAAwIJwBAAAYEE4AgAAsCAcAQAAWBCOAAAALAhHAAAAFoQjAAAAi/8D3GwnucaajO4AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions of the optimal policy:\n",
      "[['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↓']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '→' '→']]\n",
      "-----------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions of the optimal policy:\n",
      "[['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '→' '→']]\n",
      "-----------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions of the optimal policy:\n",
      "[['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '→' '→']]\n",
      "-----------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions of the optimal policy:\n",
      "[['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '→' '→']]\n",
      "-----------------------------\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Directions of the optimal policy:\n",
      "[['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '→' '↓']\n",
      " ['↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '↑' '→' '→']]\n",
      "-----------------------------\n"
     ]
    }
   ],
   "source": [
    "class PolicyIterationAgent:\n",
    "    \"\"\"\n",
    "    Learns optimal policy by maximizing the long-term reward.\n",
    "    We map every possible action to every possible state.\n",
    "    \"\"\"\n",
    "    def __init__(self, env_name, discount_factor=0, theta=1e-8):\n",
    "        self.env = gym.make(env_name)\n",
    "        self.discount_factor = discount_factor\n",
    "        self.theta = theta\n",
    "        #value function to calculate the value of a given state\n",
    "        self.V = np.zeros(self.env.nS)\n",
    "        #policy to map every state to an action\n",
    "        self.policy = np.random.randint(0, self.env.nA, size=(self.env.nS))\n",
    "\n",
    "    def policy_evaluation(self):\n",
    "        \"\"\"\n",
    "        Evaluates the value function for a given policy\n",
    "        \"\"\"\n",
    "        for _ in range(100):\n",
    "            delta = 0\n",
    "            for state in range(self.env.nS):\n",
    "                v = self.V[state]\n",
    "                action = self.policy[state]\n",
    "                #we calculate the value of a given state\n",
    "                self.V[state] = sum([prob * (reward + self.discount_factor * self.V[next_state]+ done * 1) for prob, next_state, reward, done in self.env.P[state][action]])\n",
    "                delta = max(delta, abs(v - self.V[state]))\n",
    "            if delta < self.theta:\n",
    "                break\n",
    "\n",
    "    def policy_improvement(self):\n",
    "        \"\"\"\n",
    "        Improves the policy by calculating the best action for a given state\n",
    "        \"\"\"\n",
    "        policy_stable = True\n",
    "        for state in range(self.env.nS):\n",
    "            old_action = self.policy[state]\n",
    "            #we calculate the best action for a given state\n",
    "            self.policy[state] = np.argmax([sum([prob * (reward + self.discount_factor * self.V[next_state]+ done * 1) for prob, next_state, reward, done in self.env.P[state][action]]) for action in range(self.env.nA)])\n",
    "            if old_action != self.policy[state]:\n",
    "                policy_stable = False\n",
    "        return policy_stable\n",
    "    \n",
    "    def run(self):\n",
    "        obs = self.env.reset()\n",
    "        done = False\n",
    "        total_reward = 0\n",
    "        iterations = 0\n",
    "        while not done and iterations < 100:\n",
    "            action = self.policy[obs]\n",
    "            obs, reward, done, info = self.env.step(action)\n",
    "            total_reward += reward \n",
    "            iterations += 1\n",
    "        if done: \n",
    "            total_reward += 1\n",
    "        return total_reward\n",
    "    \n",
    "    def perform_policy_iteration(self):\n",
    "        policy_stable = False\n",
    "        rewards = []\n",
    "        while not policy_stable:\n",
    "            self.policy_evaluation()\n",
    "            policy_stable = self.policy_improvement()\n",
    "            rewards.append(self.run())\n",
    "        return self.policy, self.V, rewards\n",
    "    \n",
    "for discount in [0, 0.1, 0.5, 0.75, 1]:\n",
    "    agent = PolicyIterationAgent(\"CliffWalking-v0\", discount_factor=discount)\n",
    "    policy, V, rewards = agent.perform_policy_iteration()\n",
    "    plt.plot(rewards, label=f\"discount factor: {discount}\")\n",
    "    plt.title(\"Policy Iteration\")\n",
    "    plt.xlabel(\"Iterations\")\n",
    "    plt.ylabel(\"Total Reward\")\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    print(\"Directions of the optimal policy:\")\n",
    "    print(policy_to_arrows(policy))\n",
    "    print(\"-----------------------------\")\n",
    "\n",
    "    \n",
    "\n"
   ]
  },
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   "source": [
    "### Analysis:\n",
    "We can clearly see that for $\\alpha=0$, there are few states exhibiting change in direction. However, the overall policy remains same. The rewards graph supports the same.  \n",
    "\n",
    "From $\\alpha=0.1$ to $\\alpha=1$, the rewards and the policy keep improving. A slight lesser number of iterations are taken to reach the best policy from $\\alpha=0.5$ to $\\alpha=0.75$. "
   ]
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