Sarsa_gridworld_example_6.5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grid array NxM. Goal: get from start cell to goal cell (on column with strong wind, neighboring are strong too), each step yields reward of -1, undiscounted.\n",
    "\n",
    "Actions: go to any of 4 or 8 neighboring cells or stay at your cell. Do ablation to compare with just 4 moves.\n",
    "\n",
    "In the middle: wind, blows you up either 1 cell or 2 cells (column property).\n",
    "\n",
    "eps-greedy Sarsa, eps=0.1, alpha=0.5, Q0=0. 80000 timesteps should be enough. Assume that wind is stochastic and can deviate by 1 from mean value in the column (even if this mean value is 0 - it can occur on any column in fact. also it can blow you downwards)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is not intended to be an accurate Sutton-Barto 2018 Example 6.5 reproduction, there are some differences\n",
    "\n",
    "(e.g. timing of when the environment is 'done' and wind application is different)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from tqdm import tqdm_notebook as tqdm, tnrange as trange\n",
    "plt.style.use('dark_background')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def eps_greedy_policy(state, eps, q):\n",
    "    n_actions = q.shape[-1]\n",
    "    if np.random.binomial(n=1, p=eps):\n",
    "        action_i = np.random.randint(n_actions)\n",
    "    else:\n",
    "        action_values = q[[[i] for i in state]]\n",
    "        action_i = np.argmax(action_values)\n",
    "    return action_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def apply_action(state, action_i):\n",
    "    '''Actions: 0 up, 1 right, 2 down, 3 left\n",
    "    Possibly 4 up+right, 5 right+down, 6 down+left, 7 left+up\n",
    "    Possibly 8 do nothing\n",
    "    '''\n",
    "    next_state = state.copy()\n",
    "    if action_i == 0:\n",
    "        next_state[0] -= 1\n",
    "    elif action_i == 1:\n",
    "        next_state[1] += 1\n",
    "    elif action_i == 2:\n",
    "        next_state[0] += 1\n",
    "    elif action_i == 3:\n",
    "        next_state[1] -= 1\n",
    "    elif action_i == 4:\n",
    "        next_state[0] -= 1\n",
    "        next_state[1] += 1\n",
    "    elif action_i == 5:\n",
    "        next_state[0] += 1\n",
    "        next_state[1] += 1\n",
    "    elif action_i == 6:\n",
    "        next_state[0] += 1\n",
    "        next_state[1] -= 1\n",
    "    elif action_i == 7:\n",
    "        next_state[0] -= 1\n",
    "        next_state[1] -= 1\n",
    "    elif action_i == 8:\n",
    "        pass\n",
    "    else:\n",
    "        raise Exception\n",
    "    return next_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def apply_wind(state, column_winds):\n",
    "    wind_strength = column_winds[state[1]]\n",
    "    next_state = state.copy()\n",
    "    next_state[0] -= wind_strength\n",
    "    return next_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def bound_state(state, n, m):\n",
    "    next_state = state.copy()\n",
    "    if next_state[0] < 0:\n",
    "        next_state[0] = 0\n",
    "    if next_state[0] >= n:\n",
    "        next_state[0] = n-1\n",
    "    if next_state[1] < 0:\n",
    "        next_state[1] = 0\n",
    "    if next_state[1] >= m:\n",
    "        next_state[1] = m-1\n",
    "    return next_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def step(state, action_i, apply_wind, n, m, goal_cell):\n",
    "    next_state = apply_action(state, action_i)\n",
    "    next_state = bound_state(next_state, n, m)\n",
    "    next_state = apply_wind(next_state)\n",
    "    next_state = bound_state(next_state, n, m)\n",
    "    \n",
    "    if np.allclose(next_state, goal_cell):\n",
    "        return -1, next_state, True\n",
    "    return -1, next_state, False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def draw_playback(experiences, n, m, goal_cell):\n",
    "    playback = np.zeros((n, m))\n",
    "    for i, exp in enumerate(experiences):\n",
    "        state = exp[0]\n",
    "        playback[state[0], state[1]] = i+1\n",
    "    playback[goal_cell[0], goal_cell[1]] = i+2\n",
    "    return playback"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def train_sarsa(n, m, n_actions, eps, alpha, gamma, start_cell, goal_cell, column_winds, episodes, apply_wind=apply_wind,\n",
    "                expected_sarsa=False):\n",
    "    '''Maybe turn eps decay into param later\n",
    "    '''\n",
    "    q = np.zeros([n, m, n_actions])\n",
    "    experiences = []\n",
    "    episode_lens = []\n",
    "    for episode_i in trange(episodes):\n",
    "        cur_eps = eps * (episodes-episode_i) / episodes  # decay\n",
    "        done = False\n",
    "        state = start_cell\n",
    "        action_i = eps_greedy_policy(state, cur_eps, q)\n",
    "        episode_step = 0\n",
    "        while not done:\n",
    "            reward, next_state, done = step(state, action_i, lambda state: apply_wind(state, column_winds), n, m, goal_cell)\n",
    "            prev_state = state\n",
    "            prev_action_i = action_i\n",
    "            next_action_i = eps_greedy_policy(next_state, cur_eps, q)\n",
    "            # now we have: prev_state, prev_action_i, reward, next_state, next_action_i\n",
    "            experiences.append((prev_state, prev_action_i, reward, next_state))\n",
    "            if not expected_sarsa:\n",
    "                next_q = q[next_state[0], next_state[1], next_action_i]\n",
    "            else:\n",
    "                next_q = (1-cur_eps) * q[next_state[0], next_state[1], next_action_i] + \\\n",
    "                         (cur_eps / n_actions) * q[next_state[0], next_state[1]].sum()\n",
    "            q[prev_state[0], prev_state[1], prev_action_i] += \\\n",
    "                alpha * (reward + gamma * next_q - q[prev_state[0], prev_state[1], prev_action_i])\n",
    "            state = next_state\n",
    "            action_i = next_action_i\n",
    "            episode_step += 1\n",
    "        episode_lens.append(episode_step + 1)\n",
    "    return q, episode_lens, experiences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def play_policy(policy, q, start_cell, goal_cell, n, m, apply_wind, column_winds):\n",
    "    n_actions = q.shape[-1]\n",
    "    experiences = []\n",
    "    done = False\n",
    "    state = start_cell\n",
    "    while not done:\n",
    "        action_i = policy(state, q)\n",
    "        reward, next_state, done = step(state, action_i, lambda state: apply_wind(state, column_winds), n, m, goal_cell)\n",
    "        experiences.append((state, action_i, reward, next_state))\n",
    "        state = next_state\n",
    "        if done:\n",
    "            break\n",
    "    return experiences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def play_greedy(q, start_cell, goal_cell, n, m, apply_wind, column_winds):\n",
    "    policy = lambda state, q: eps_greedy_policy(state, 0, q)\n",
    "    return play_policy(policy, q, start_cell, goal_cell, n, m, apply_wind, column_winds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def train_show(**train_params):\n",
    "    q, episode_lens, experiences = train_sarsa(**train_params)\n",
    "    \n",
    "    print(f'Played {len(experiences)} timesteps in {train_params[\"episodes\"]} episodes')\n",
    "    plt.figure(figsize=(12, 3))\n",
    "    plt.title('Episode lengths')\n",
    "    img = plt.semilogy(episode_lens)\n",
    "    \n",
    "    plt.figure(figsize=(6, 5))\n",
    "    plt.title('State values wrt greedy policy')  # well, almost greedy. because eps was decayed!\n",
    "    img = plt.imshow(q.max(axis=2))\n",
    "\n",
    "    # will enter infinite loop if greedy policy doesn't achieve the goal\n",
    "    experiences = play_greedy(q, train_params['start_cell'],\n",
    "                              train_params['goal_cell'], train_params['n'], train_params['m'],\n",
    "                              apply_wind, train_params['column_winds'])\n",
    "    plt.figure(figsize=(6, 5))\n",
    "    plt.title('Greedy policy rollout')\n",
    "    img = plt.imshow(draw_playback(experiences, train_params['n'], train_params['m'], train_params['goal_cell']))\n",
    "    \n",
    "    return q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial SARSA setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1e4a411d02514e1880d868a24b3ca229"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Played 24237 timesteps in 1000 episodes\n"
     ]
    },
    {
     "data": {
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Q7Jg8RKQurzCaGSQTERER+RqfD5Jt6kyyKkg2WcwXszlEREREdAnw+SBZHCdZ5B8SrLht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\nADCSDAAAI8kAADCSDAAAI8kAADABntsSKR92pEwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NHTtWAwcO1OTJkzVgwID2yAYAaIXf4h4yZIj27dungoIC1dfXKzU1VRMmTGiPbACAVvgt\n7ri4OBUWFvpuFxUVKS4ursV6ycnJysrKUlZWlmLO6QAXGwaAbyi/xe1ytfzEEGNaXoA9JSVFXq9X\nXq9XVcdqz046AEALfou7qKhICQkJvtvx8fEqLi4OaigAQNv8FndWVpYuvPBCnX/++QoNDdWkSZO0\nbt269sgGAGiF3w8BbGxs1H333aeNGzfK7Xbr5ZdfVl5eXntkAwC0IqBPb92wYYM2bNgQ7CwAgADw\nzkkAsAzFDQCWobgBwDIUNwBYhuIGAMtQ3ABgGYobACxDcQOAZShuALAMxQ0AlqG4AcAyAV2r5MwZ\nqbEpOFMHmiCyk6PbP6m+W6TTEdTkbnlNdSc0dHI+R3Rho9MRJEl1vZw/Zvoi1ukEX/JUO78vQnuf\ncDqCQkJafs5Bm+sGMQcAIAgobgCwDMUNAJahuAHAMhQ3AFiG4gYAy1DcAGAZihsALENxA4BlKG4A\nsAzFDQCWobgBwDJ+i3vx4sU6cuSIdu/e3R55AAB++C3upUuXasyYMe2RBQAQAL/FvW3bNpWXl7dH\nFgBAADjHDQCWOWsfpJCcnKwZM2ZIkmLOiT5b0wIATnHWjrhTUlLk9Xrl9XpVdazmbE0LADgFp0oA\nwDJ+i3vlypXasWOH+vfvr8LCQt15553tkQsA0Aa/57hvueWW9sgBAAgQp0oAwDIUNwBYhuIGAMtQ\n3ABgGYobACxDcQOAZShuALAMxQ0AlqG4AcAyFDcAWIbiBgDLnLXrcTfT0KjGioqgTB0od4jL0e2f\n5Ooa6XQENUZ0jN/PnQ83OB1BNfHB+ZY/U9mPvuh0BF3wj2lOR5AkNX3hdjqCekV97nQEedxNAa/b\nMX6iAQABo7gBwDIUNwBYhuIGAMtQ3ABgGYobACxDcQOAZShuALAMxQ0AlqG4AcAyFDcAWIbiBgDL\nUNwAYBm/xR0fH68tW7YoLy9Pubm5mjlzZnvkAgC0we81LhsaGvTAAw8oJydHUVFR+te//qXNmzcr\nPz+/PfIBAE7h94j78OHDysnJkSTV1tYqPz9fcXFxQQ8GAGjdGV1VPjExUYMHD1ZmZmaLZcnJyZox\nY4YkKaZHl7OTDgDQQsBPTnbu3Flr167V7NmzVVNT02J5SkqKvF6vvF6vqsqqz2pIAMBXAipuj8ej\ntWvXasWKFUpLSwt2JgDAaQRU3IsXL1Z+fr6ee+65YOcBAPjht7iHDRum22+/XaNGjVJOTo5ycnI0\nduzY9sgGAGiF3ycnMzIy5HJ1jE9MBwDwzkkAsA7FDQCWobgBwDIUNwBYhuIGAMtQ3ABgGYobACxD\ncQOAZShuALAMxQ0AlqG4AcAyZ/RBCgELD5On3/lBmTpQjV07O7r9kxojgrOLz0Sn0hNOR5Ak1cV1\ncjqCDIcqPv8evcTpCJKkvuvvcjqC+kRVOR1BoSGNAa/LtzEAWIbiBgDLUNwAYBmKGwAsQ3EDgGUo\nbgCwDMUNAJahuAHAMhQ3AFiG4gYAy1DcAGAZihsALOO3uMPDw5WZmakPP/xQubm5mjdvXjvEAgC0\nxe+l606cOKFRo0aprq5OHo9H27dv14YNG5SZmdke+QAApwjoVEldXZ0kKTQ0VKGhoTLGBDUUAKBt\nARV3SEiIcnJyVFpaqs2bN2vnzp3BzgUAaENAxd3U1KTBgwcrPj5eQ4YM0SWXXNJineTkZGVlZSkr\nK0sx3TrGhxgAwDfRGb2qpKqqSu+++67GjBnTYllKSoq8Xq+8Xq+qyuvOWkAAQHN+i7t79+6KiYmR\nJHXq1EnXXHON9uzZE/RgAIDW+X1VSe/evbVs2TK53W6FhIRo9erVevvtt9sjGwCgFX6Le/fu3UpK\nSmqPLACAAPDOSQCwDMUNAJahuAHAMhQ3AFiG4gYAy1DcAGAZihsALENxA4BlKG4AsAzFDQCWobgB\nwDJ+r1XyXznxhRoKDgRl6kB5/nOuo9s/yXUi1ukIOh4X5XQESVJTcL7bzsi/5r3odAScIjTqC6cj\nKCGiwukICgtpCHhdjrgBwDIUNwBYhuIGAMtQ3ABgGYobACxDcQOAZShuALAMxQ0AlqG4AcAyFDcA\nWIbiBgDLUNwAYBmKGwAsE3Bxh4SEKDs7W2+++WYw8wAA/Ai4uGfNmqX8/PxgZgEABCCg4o6Li9O4\nceO0aNGiYOcBAPgRUHEvWLBADz30kJqamtpcJzk5WVlZWcrKylJMjy5nLSAAoDm/xT1u3DiVlpYq\nOzv7tOulpKTI6/XK6/Wqqqz6rAUEADTnt7iHDRum8ePHq6CgQKmpqRo1apSWL1/eHtkAAK3wW9yP\nPPKIEhIS1LdvX02aNElbtmzRlClT2iMbAKAVvI4bACxzRp+7nZ6ervT09GBlAQAEgCNuALAMxQ0A\nlqG4AcAyFDcAWIbiBgDLUNwAYBmKGwAsQ3EDgGUobgCwDMUNAJahuAHAMmd0rZKAhbgUEh4elKkD\nFhbq7Pb/X1NUmNMRZNwupyNIkt7//UKnI6AD2viDvzgdQRvr+jsdQeGuhoDX5YgbACxDcQOAZShu\nALAMxQ0AlqG4AcAyFDcAWIbiBgDLUNwAYBmKGwAsQ3EDgGUobgCwDMUNAJYJ6CJTBQUFqqmpUWNj\noxoaGuT1eoOdCwDQhoCvDjhy5EgdO3YsmFkAAAHgVAkAWCag4jbGaNOmTfrggw+UnJwc7EwAgNMI\n6FTJsGHDVFJSoh49emjz5s3as2ePtm3b1myd5ORkzZgxQ5IU073L2U8KAJAU4BF3SUmJJKmsrExp\naWkaMmRIi3VSUlLk9Xrl9XpVdbT67KYEAPj4Le7IyEhFRUX5/v2jH/1Iubm5QQ8GAGid31Ml5557\nrtLS0r5c2ePRypUrtXHjxqAHAwC0zm9xFxQU6Hvf+157ZAEABICXAwKAZShuALAMxQ0AlqG4AcAy\nFDcAWIbiBgDLUNwAYBmKGwAsQ3EDgGUobgCwDMUNAJYJ+KPLzojbLVeMs9fkNuFhjm7/JONyOR1B\n7y5KcToC0Ka+oVFOR1C/sFKnIyg8pD7gdTniBgDLUNwAYBmKGwAsQ3EDgGUobgCwDMUNAJahuAHA\nMhQ3AFiG4gYAy1DcAGAZihsALENxA4BlKG4AsExAxR0TE6NXX31V+fn5ysvL09ChQ4OdCwDQhoAu\n6/r888/rnXfe0cSJExUaGqrIyMhg5wIAtMFvcUdHR2v48OG64447JEn19fWqqqoKdi4AQBv8nirp\n16+fysrKtGTJEmVnZyslJaXVI+7k5GRlZWUpKytLMd2cvzA6AHxT+S1uj8ejpKQkvfjii0pKSlJd\nXZ0efvjhFuulpKTI6/XK6/Wqqrw2KGEBAAEUd1FRkYqKirRz505J0po1a5SUlBT0YACA1vkt7iNH\njqiwsFAXXXSRJGn06NHKy8sLejAAQOsCelXJz3/+c61YsUJhYWHav3+/pk2bFuxcAIA2BFTcu3bt\nktfrDXYWAEAAeOckAFiG4gYAy1DcAGAZihsALENxA4BlKG4AsAzFDQCWobgBwDIUNwBYhuIGAMtQ\n3ABgGZckc7YnLS0t1YEDB/7rr+/evbuOHj16FhPZi33xFfbFV9gXX/mm7IvExET17Nkz4PVNRxtZ\nWVmOZ+gog33BvmBfsC9OHZwqAQDLUNwAYBm3pHlOh2hNdna20xE6DPbFV9gXX2FffOXbti+C8uQk\nACB4OFUCAJahuAHAMh2uuK+99lrt2bNHe/fu1Zw5c5yO45j4+Hht2bJFeXl5ys3N1cyZM52O5LiQ\nkBBlZ2frzTffdDqKo2JiYvTqq68qPz9feXl5Gjp0qNORHDN79mzl5uZq9+7dWrlypcLDw52O1G4c\nf03iyRESEmL27dtn+vbta0JDQ82HH35oBgwY4HguJ0avXr3M4MGDjSQTFRVlPvnkk2/tvjg5fvGL\nX5gVK1aYN9980/EsTo6lS5ea6dOnG0kmNDTUxMTEOJ7JidGnTx+zf/9+06lTJyPJrFq1ykydOtXx\nXO0xOtQR95AhQ7Rv3z4VFBSovr5eqampmjBhgtOxHHH48GHl5ORIkmpra5Wfn6+4uDiHUzknLi5O\n48aN06JFi5yO4qjo6GgNHz5cixcvliTV19erqqrK4VTO8Xg8ioiIkNvtVmRkpIqLi52O1C46VHHH\nxcWpsLDQd7uoqOhbXVYnJSYmavDgwcrMzHQ6imMWLFighx56SE1NTU5HcVS/fv1UVlamJUuWKDs7\nWykpKYqMjHQ6liOKi4v17LPP6uDBgyopKVFVVZU2b97sdKx20aGK2+VytbjPGONAko6jc+fOWrt2\nrWbPnq2amhqn4zhi3LhxKi0t/da9Vrc1Ho9HSUlJevHFF5WUlKS6ujo9/PDDTsdyRGxsrCZMmKC+\nffuqT58+6ty5s2699VanY7WLDlXcRUVFSkhI8N2Oj4//1vzp0xqPx6O1a9dqxYoVSktLczqOY4YN\nG6bx48eroKBAqampGjVqlJYvX+50LEcUFRWpqKhIO3fulCStWbNGSUlJDqdyxjXXXKOCggIdPXpU\nDQ0Neu2113TFFVc4HavdOH6i/eRwu93m3//+tzn//PN9T04OHDjQ8VxOjWXLlpnnnnvO8RwdaYwY\nMeJb/+Tke++9Zy666CIjycydO9f87ne/czyTE2PIkCEmNzfXREREGOnLJ23vu+8+x3O103A8QLMx\nduxY88knn5h9+/aZRx55xPE8To1hw4YZY4zZtWuXycnJMTk5OWbs2LGO53J6UNwyl112mcnKyjK7\ndu0yaWlpJjY21vFMTo158+aZ/Px8s3v3bvPKK6+YsLAwxzO1x+At7wBgmQ51jhsA4B/FDQCWobgB\nwDIUNwBYhuIGAMtQ3ABgGYobACzzf3tSbjm0yrVQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SUr3yyithiAUA6E3AuwNeunRJEydOVFtbm9xut/70pz9p586dOnjwYDjyAQCuEdRUSVtb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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q = train_show(n=7, m=10, n_actions=4,\n",
    "               eps=0.1, alpha=0.5, gamma=1, start_cell=np.array([3, 0]), goal_cell=np.array([3, 7]),\n",
    "               column_winds=np.array((0, 0, 0, 1, 1, 1, 2, 2, 1, 0)), episodes=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "States visited by policy are visualized with cold colors at the beginning and warm colors in the end."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Values of many states are 0 because eps-greedy policy never went in there to explore!\n",
    "Mostly because of the wind."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Expected SARSA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f2aec19d5dda4c11a0e2dc35c7a80beb"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Played 24670 timesteps in 1000 episodes\n"
     ]
    },
    {
     "data": {
      "image/png": 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gWZ5Jlrd7U6mtT03jW26GWstV94iIiIj8id8HyZZSWZAsWzhEo7WWa0c1iEOjNjfV+LiI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\nICQZAABiUh/8sDH01xIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ZihsALENxA4Bl/j/G93Ckqn4/5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SUr3yyithiAUA6E3AuwNeunRJEydOVFtbm9xut/70pz9p586dOnjwYDjyAQCuEdRUSVtb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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q = train_show(n=7, m=10, n_actions=4,\n",
    "               eps=0.1, alpha=0.5, gamma=1, start_cell=np.array([3, 0]), goal_cell=np.array([3, 7]),\n",
    "               column_winds=np.array((0, 0, 0, 1, 1, 1, 2, 2, 1, 0)), episodes=1000, expected_sarsa=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks really similar. Let's compare with SARSA on a finer scale. We'll only trask episode lens because rewards are constant and undiscounted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "outer_iters = 10\n",
    "episodes = 300"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3a33c0fc417540b7b4d98efe8cc73370"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e8f6735faf6c4c369a33aada3983e18a"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9d153742da244500825d6f3d3a6b3119"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3407e9d11d1f40a786920d16b72ea049"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "457ae0716d7449cd860e695027103a8f"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dd496c61d9e84277b523064630502774"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8010dce502b64baba3c8b0c0a3bf4264"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "592b817860bb493a994ed47dce7d61ed"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "62d12b59ed2240cdad130211b6bcf1d6"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d6c97d16c58847e2af68e64283c85f64"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "usual_episode_lens_sum = np.zeros(episodes)\n",
    "for i in range(outer_iters):\n",
    "    q, episode_lens, experiences = train_sarsa(n=7, m=10, n_actions=4,\n",
    "        eps=0.1, alpha=0.5, gamma=1, start_cell=np.array([3, 0]), goal_cell=np.array([3, 7]),\n",
    "        column_winds=np.array((0, 0, 0, 1, 1, 1, 2, 2, 1, 0)), episodes=episodes, expected_sarsa=False)\n",
    "    usual_episode_lens_sum += np.array(episode_lens)\n",
    "usual_episode_lens_sum /= outer_iters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "578eef26bfb44b00983f1b9a602fc6f8"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "22c7057fad4e4fcba93fdbaae84dfa6d"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7819d66d64cb49dfa0e4aaf8a35a36cc"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dcd902769eb64820989a19f788316c94"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9b603e2edd864a269bd47c427243f2bd"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f0a2886ed6c549e2aae8c98f45af01be"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "582eba52cf1946f1861faeed814842c6"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0cd87cd7fea04210ae7c27339b34bde4"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6b75cb4d2e43439aa9eecc1f7a51d1a6"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bd2e1c8f21e1493c8b65c7eaea652765"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "expected_episode_lens_sum = np.zeros(episodes)\n",
    "for i in range(outer_iters):\n",
    "    q, episode_lens, experiences = train_sarsa(n=7, m=10, n_actions=4,\n",
    "        eps=0.1, alpha=0.5, gamma=1, start_cell=np.array([3, 0]), goal_cell=np.array([3, 7]),\n",
    "        column_winds=np.array((0, 0, 0, 1, 1, 1, 2, 2, 1, 0)), episodes=episodes, expected_sarsa=True)\n",
    "    expected_episode_lens_sum += np.array(episode_lens)\n",
    "expected_episode_lens_sum /= outer_iters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16e09be3e80>]"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FEOL88dKZNt4FlgEnbOvlgAGlTp4B3Bb0lf6EBB5h9dNDCAnQVf645k2Ao7agjwMyAYUQ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\nde8wqMMGOrVy3kVdcCSCAN9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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(usual_episode_lens_sum, color='blue')\n",
    "plt.semilogy(expected_episode_lens_sum, color='orange')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exactly same convergence speed.\n",
    "\n",
    "I will not even implement q-learning here because I expect it to have roughly the same speed of convergence on this problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8 actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "81dcd0f3e32e4501a03ca5a7dac45b7a"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Played 47812 timesteps in 4000 episodes\n"
     ]
    },
    {
     "data": {
      "image/png": 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HOuw1eazDxVz3saMwbulibYUtE187GS379sQtTz/q8HznEUMRl1xT07pGL1mE\n3lPHqx7w2npgX7ffHxC8FHBsyKo4tvNIMFuUpb7vvEMRXEwBFzLCPkjesPRFnCw4gn8/9woAYMe/\nNuDsyUJN63AZEKcpGYR1YdttVPtcypq5DZI9f9W1Gl8l3dZNbdZEYRPuT9K2g2xiagqG3HMnxj+7\nRHrN1q/ZWx2GZmHWu68rvq5XyCJQo36a2/V6OiFEVo1BzbI0eYMXzEHmnNvQtEsnxfcOe2AesubO\nRMN2rd2u156aE6OtlVMu+KrT3Ho3wBztGpQa3bQya1WtRnUk1K7ldpnONw2R/u/cCm5PbzTIttym\ntWyBcc88hqy5M5F8VQPE106WLrbsLyKbde2M1gP6av0IDmz5uEVZ8Kk36BFRpQpqNb4K0XGxuPG+\nuzF12XPQ6XRStx+XdShcuKU2d71DI2fM4w/h7n+963YZad9WEbwkpqagamIC6l57tc8D5ioiYLP/\nfamhNxhQx5fjZAiISYxHYp3y/Ob2uc59nWDKF+UX/95djOl0OtS99mq/ladqYoLmVKhXEsbIwRf2\nQXL+T3vwWMaN+OrNVZh7TSesW/QYLJdLMfeaTqrX4Zx/WEuOTecr96y58rfD1XAb7Hn4sRmMRtz1\n0Srp71mrlqFqksxgG48n6bIR/WX9ZSuyb5teoSW5QZvrfFrvrW++jHmfrAZQHoTavnO525JVqsZY\nl9EwSl2p7HLcBT4Dbp8us7z/+isv+nI9Zq95S/XyRplZAm1uuOt2l3U17doJt7+7HA3L+vAWX7iA\n+z7/GIu+2gAAGPno/Q7LRyfEqS6Ls07Dh2DWqmW4ukcXlNoGR+oNGP/sY7jro1WIqFIFgHUf7nrL\nCNz+7nI07tTOYR3Nu3dRvHBz1wVGK2n/UHHWXLj5Qzy47d+447030GfqeJ+2q+bi2lf2vy81MmZN\nxez339TcNSqULPpqIxZuKp8p02FMQTBbkm3b9rIhudstI3HHe2+gUYe2finPg9v+jYWbP/TLuiqa\nLxeo5edyRsnBFvZBsj84tyTbZ1zwxJ+tBsLpyGY/a52nFiG5E7o5yrV/qhDAhBeewANfrreu1+lA\nMHrJAw5/2wZXzXznNbfb12LJzq9ln3d3UJr08tMOfy/YuE7VtpbmZiOlmbWP+CM/fI5re/ewbks6\nmSifTaYue071lNFqg5EGbVt57MIwbfkLDp/PeVBgoAfUqSXX0pqYUtvxCaf9tt51jq22kTIt52o1\naGu9eIqMiYGwm7Clfmvr87YuDlUTE6Q7PPG1kh3WkZDi+LciL3/mox57AI/t+FLat02RZizNzUaX\n0cOlZW556hE88v3nsu+v1fjJmmBJAAAgAElEQVQqxXX3nDTWOnGQu5O5QrnVZGxRy/b7Ur182ZgN\nXzJmjFr8AB7b8ZXX7/eVc19T+0HNi3/8Aktzs1XdeWuV0QdLc7MRHe/9xaLNws0f+ZwxJrlRAwBA\nXC1tXZS63jwCS3Ozg57+bmluNgbOnuHzeoYvWoD569dIfz+esw0jHrkXd37wjtu7oQBw/YQx0kUG\nUycGX9hPS+0PvqTL8WtLjVO81rJf+a3uOetWuH2rpy4J5dsQaHF9N8TWqI5GHduhVUZvh5ebd0uX\nnea6fuuW6tavQkSVSNnn3SXhb94t3eHv6l5MFuCQ1s92W9JDk4vSlNG1GjdE+qhh0t/NuqfLLufM\nOSe3nMYd2zl8PrkLpB7jRnucMOH6iTc73BL2Vd/pE1GtRnkav/qtPE89HhEp/13b2E4iaiZg6D11\nPJqkdwQA9Jk+UbqNW3LpUnlOY71easXpM22C9N6YeGvw0HnEjQ7rVNt109tuC22zMmCOipI+n+3C\ntYvdvnNd/96Kd2zk7i51Gj4EU197VgoG3A0OatBa/i6MUsaWa3p1R9MuHWVfSx95I/pMn4jxzz0O\no0zOdn/epncoU+8eaNK5g8NzbW/IgDmqivR3dHwc7lz3jnQHo6LJDchMaS7f5c2e7RhSPc23TC9N\nu3ZCYqrdBaqG3bVlv15o1LGd5wXd6F2Wmch2F86ZLX+9Vq0G9PX4naY0bYxOdl3Eek4a69W27HUc\nNsjhGGyKNKP94EykNG3sca6BPtMnSf/3x00FY0QEBs6eoXjetBdfKxm9fbz7dKXhtNR+oDRJhxp+\nbUl2c8ZO8hDszHjzZc3bmL78BYx5/CGXZUYtvt+nOtFKawDij1YX2za9Sb0WFVsNd330LoYunCtl\nk0jW0CdTrfhayYiOj5Pdx7LumoVb33L9zvVGA6pUq4ao2GrInHMbpi9/QfX25FqhbPtLcqOG6Hfb\nFI8D65zz8na7ZaT0/+j4OJf+2HE1a8BgNKJNllOuchkZs6Zh6mvPIvmqBuh/2xSk2QVl9t+n8wQ/\n9lKdAhfZHOMBYLt7oLWvqMFoQGzN6lLXEcDaZ952sQDA7Zl48itLpf9XTUzw2H1q/HOPY8qrz8q+\nNvTeu9D/tim4pld3dB0zvGxfqyq9fsd7b3j6OG4p/a7HP7sEU5c95/a9wxct0Nyi7SyiSqRsIFKl\nWlXFKeWl71VmQGZU2ftiEuJhjIhQlXnGW1NecZz8yr7xJjo+TrFuDUYjxj79qKbjhBz784rBaESk\nU7A8a5X71lclNz/xEG59+xW3y9z5wTuyA7ajYqs5tOSao6IcGsSqVKvmderN6LhYxCSqaLVXcW7z\n1PqfPvJG9Jw0FtdPcMyUJbe/TnjhCWTMmubXxhE5/jgHVxS25fuBL9OI+jPFiy8nbLVBrZpRzyaz\nGXM/XOl1WbTqOVn9lX/7IVl4+NvNPm/Tduga65QNwRNzdJTDrfHHtn+p6f1avuP7tnyMh7/djMad\n2su+LtdKe+N9d+PRHz6XWvrUtD4AQNsbBuChbzZJt8Kl8pbtL7Z85LYg67r+jncgbAbPn+3wt8mu\nv//D3252mVCm/ZBMTHrpKU39f+VuYdouJLRmSFGdKsvHJiHbOAelwalKWvTsjge2rseSncpdC9Tc\n0u0xbjQe3PZvPPL956r2ifZDsty+HlGlCkY/tgiP/rDF47rU6Dh8MB7+djOSr2rg1fvV7ufuLNn5\nNR798QuX5x/9YQtufuJh2fcszt4KQP64OvLR+zFr1et46JtNeOK/32g+VvjCdqGY0rQxHv52Mx7+\ndrNsP2OlCyJvtwdYL8wWO9VjtepJDhd6gRYVWw2PfP+5NZVjmcd2fImFmz8CYP3NPPrD57jpoXu8\nWv/D332Gh7ZtQq3GHrLaeLjTXL91Szz0zSZcU9YNUI6tC4tzV5YlO7/GYqd9ylbHgewW3yazPx7+\ndrNf0m1WBAbJQaamb6tqPqxCbZDhTWqga/tcr/k9WjRX2VUBABrJzBhomw5Wi+TGDdH15hEuQSHg\nvmW7Soz87US17Puiqn6P3a15e7bvslGHtmhVlrbNdtFmsGshSUxNcXsL0hgRgVGLrQPqajdx7ANr\na6G5XFwMoDwYkcv8IdcXsPVAz/mTHVpFnQy99y4szc1Gp+FDFJep3bSR1EKt1xs0pTl0btlV6noV\nVa0aBs6egeRGDdF97Chc1b4NWjll5ug7fSLMUVHInHOb4oBH57sCqrtJARg451bZ1sisuTPdDrAE\ngGbdOkv/N3noAgMA/W6d5Pb1XpPGSvucs4gqVTBwzq2a+qc2KbsQdDfBTMfhgwHAod5r1E9Dj3Gj\nXS4UnLtnmaOirGXy0CCi9Lq7LC9XX98VLXp2lX1NLtvRbStexdLcbAy4w/H3kj7yRtnjUY9xo93u\nJ7Kvle3j9hcdE154wiXTRKOO6gfo1Wt5jezdGWeKF/VRkegxbrRXkwg17ap+ID5Q3jrbZfQw9J1R\nvi9XK+tK2HnEUABA6wGOx6dajRtqOkbXrF/P5Tn744unu6R1WlgDzfqtW0JvMGDAHTNQReVsv0Bw\n8jDbZu219V8Pdf4bfk1eqXQd870Iksc985jD32/dPg9tszJwbZ/rYbFYcOKPw5pO9r7wV/7PPlMn\neF4oxNlapae/8aLri3bH5mnLn0diagp2frxBdj32FxkGmWDL/raiKTISOp1O9uDvj76A9szRUVLZ\nhj2gnP+6z9QJ2PGhdSCq3qD3mItYbzRKLePO+5NSbue0a69G2rVXu3zGXZvKW1L73TYFdVu2QLMu\nnXDyzyPIXvex67Z9OF70nHiL7B2jLqOG4WTBn/h25RqZd3nHU25ppYtyc1QUek8dh54Tb0HR38fw\nw/v+y2ww/IH52P7BJ7j5ifIuYjNXLkN0XCzyd/3ssOz1E8Zg4zMvSX/3nTEJPcaPRmHBX8j+wPV7\n8cXEF55UvWyVatWkbD29Jo91KPfQe+8CAIfMTAajEVl3zUKvKeNwfxf5C065gWR6md+nOSoKU157\nFo9nep5B1N12dn6y0eU1VXcoI8zIumsWek66BQ9089y9yt6UV57xmLFK7phkjopCv1sn49dt3zk8\nP3ThXNl13PWR+1SOWnlq0dWXtTSLUguu7tEFvSaPRWyN6nj/Xvk7F6RdJYvQrjzX9e+NpbnZuKq9\nawunVt7mttS2Dd+DzF+//g4r77oPAHD0UD6O/va7z+u897N/eVwmJjE+ZGeSOvTfXRW+TbWTz9hu\nwd2x+k3ZZe1b/OJlgqOHtm3CDXfdbl1XZCTu2fQBOpW16vmLXJ9CTX3VNSzq0FroVIda0v7JsQ0O\nVfpufL2oVupWZftMXcfcVJZloPwzPrB1veL6Jr/6jOJr3ug56RbpQsKbbmz2ednVsA3e8zSI1HaH\nQKlvsf3dsrkfrZK98Fyam41eZQPUvKX5NnjZG9x1JzFXkenrrLCh6ml1sDQ3G/Wuu9btHRyvuft8\nZa8FqtuFu9/WrJXe9Yn21cQXn5IGHj7w5XqXyY5s3cOExSL9XowRwc0QcqVhkHwFURvAvn3HAlXL\nyfXv81dLrLBY8Pq02Xht8iysue8RfPH62z6tT83o51pXNURkTOAGv3ii0+lkR6zrdDokN2yAgzv+\ng3fnlafQW3X3/S7L+pO7AR+2E5EpMlJKtaWmjuNry6dEswURpkhzwCcH8GYkvP0JUm4ft89ikpBa\nWxpY5O+LLlswU3LhouzrWibdkONpoFGf6RNdloutWV1xX2nWpZOUOUJuUJ9z+kFP7EfW26+vZoN6\nsssnpdWB3miQzagDwCGbil8oHP/s76bUbnwVGnVoi+r16roE+nJ5zH1huxC0z9Rh33XG9roxIkJT\nXRjNEdbBWwrBcoehWegw1H2/c2+4m6XSXxPbKP2G3K3f2wxW/iizrctZbI3qLtmNbGMUKqKBLFwx\nSA5Dv3z1jarlZPOQ+nG60v/9uAPnCk/h4rl/8MuX6srkqxY9u1fIduTEJCbI3lrtPm40ouNikdKs\nMXZtLh+wsvuzrarWa3/L3l/GP2ed8tr+5KuGL3mL/UW6q6BlenjbABmFriD2J++7//WulAvd3ycn\nW4BTUtaH21n/26b4tH5vW6LtL5id62fqsufQpHMH2VzNvgxqtqXgS23eFPM+fd+lK0vVpETcs3Ed\nhiy4U7EleNGXyq3ggPvJbny1YMNaDJxza8DWD0BqXbXP3jHy0fvKX7brw+6pLuyNXvwAFm76QDEF\nY1Rs1cBMXe3mN+uPSZHaZGVg3ierZdMU6rzMVOFOoLtT2r5fS6mF0/MFCIPkK4itVatZt3TF24I+\nb0PFgdGbq+eSi5e8KU5AeDM4zqZZ186o30o+J7RSCidbKrIoDQMu/EWphURNHumYhHi0yugjDR4B\nrIOQQoWWHOS2XVapJcs564XtAtLiY0uy829FmhbYYtGcW1xN3fsl5aTMKsY+45razx8BQtOunVCj\ngXW8Qt1rHAex2dLHaZn+3dNEPM4atm2FKtWqSnVrf/yLqFIFPSeNdZv31p/54eXI7eP2A9+8zcNv\nm4Jdqe+43hCY4Uzu9hkts5IqsaVwrF7PdQxMIAaxBXpad+cZe8n/OHDvCiIg0KhDW0x++WlsfX1F\nYLah4sfoTe7I4ovyt5eDYcg9d3r9Xvu8ss7UHoTPnzmDgr3/A2DNChHI1q5h98/36f03Pxm6A0T0\nGgJC6eSs8BaDwj7ta0uyS1Bgt32ts1ROfOFJrLnffUpCb/O62pMLvOTuIPjjdvyUV57B6aPHfV6P\nzRi7QXuemCLNLjl27Y9/Ix+9T8pakbfzv6rX68sgZZeLKg/7uD/z8LusNwCBmdyAQek1P+y7tmOw\nXCpN+wsCfwW3AW9J1tlakksD8n0Qg+Qrjq3vYGJqbZwtPOX39asJkuPd9Ak9sD1H9vlQakkOFLUH\n+fvTy0ehe8q0APiU+Q+1GrnP0+mt16bcjuP5f+D+rZ8GZP2e6HQ6xRPU1T26yC5vIzfISSkdmUuf\nZI0n19SrHafmtpXD25N0DQ/psfwSJKs88Sc4TzFeZl6rroBOB6PJBJ1eJ+UKVuKcG1uNxDqpst9j\nzQbq+3TLdjUQ1rsIiXVSFftJ25P7HrW2Zjusz6nuPX0XgQrS/DpTLOzOK272e1+67tjo3ATJ9r+N\nGiq+W3XbC2xLsq3MQgj/drdg1w0Jg+QrSIXM/qUiSK6mMIjG3fvDOUh2dyIL9O06LZNwaGEpLVXs\nV1sRdHq9Yr3aTxAgLe8hOFU8QTvtz1parwHlWea8vfVr9tAn3B+BhrvWPntyo+wPbM+RBvPZ0ugd\n+u8uNGzj3+mgF276QPZ5S2mp6nU45yEGrHfr5qxdgdia1fF33m/lzysdF/38+3XeP/UeglVfg1ml\n35A/uj7Ib085R7BfWpLL1iHX+GD/21CdJcXD1+uPiwnhphnEoSXZzRqcKQ7aLtuPA3neCfQ5zd8Y\nJF9J7H4LcbWSUawwQt6nTQTols7lshPmlUzpIO9zXzgfvhMtEzZoIYTA5UuhGSTLv8H9NONKffyd\nfw++9tW0Zf5IUtEnXI6nsQhKn69GvTRUTUp0mCZaidp6te1bnz71PL5duQZ6owGWy64n81fG34ql\nudmq1ilbHg0nXS1BclJdmal5hZBt2a6oE79LS7KHYFVNsdwGYQoXff5uSbYdw+yzlDh/Vn+Ms7Ed\na6smJcAcFYVL589Lr8Ul1/B5/c780ZLsLuOHXkoBJzSdBzzNsFvZAtlA4sC9K1T9Vteiw403+H/F\nAQqSLRpTRVVGSq0vbg/+AT5W+aNlUY4oLUVJcfDuDugNetUtnoDnwE+pnpyD5IRU+S4GWsm1dqvR\nYaj737zS52g/JBMPfr1R1QWb2hO/7S6FKGu1kwuQK5qWu21yAWiwB0g5172nYMbX7hZKLdU6g96/\ndVH2OezvrDh/Nr/cBSlbR79bJ+OO9x3zvivlgXemJYDUfLGuke1iRVhK/XrXotJNchZArIkriYbf\nyPIZc7zaRKDOEcE++VQEpVZGNYHJQ70CcMGDwPWZExYR1KBIrzdoOtB7nNlKqSXZKeiKUtESG0ie\n9iW/9OtU2YpoNFkHnFp87AbmqfVXy7FDy7J6uZRjGo9T7loBveFc956DZM/bd5ubWKklOcB9bQHX\nlGz+6G5hn9JSTZ9yOdqOK/qA1pXOviVZeamysqhZYdmyDJIlfm9Gql+/Pu69917ExsZi+HDvU2mR\nds27paNxx3aqlr1w9pxX22DScu+Nekx+chB3t+jPHD+BxNQU/HOqKCBliq8lP/mHryyW4LYa6gx6\nDJzt2qdUcXkPgZ9ccDnr3dddZv/yx8yZgdSoY1uf1zH+OXX9NdsNGgDA9xZki8UCvcEgZZJwpqVl\nT0tLsseLVxXb9fdt6/u/+MRx/Z4G7vncJ1mpi5jBvy0mMutyTkNp0NDdouPwwejlNAX8oz9sUdWd\nyBMt36ler/N/15QyyY0aose40QC0X4h6CtznrH0bX7z2VkCyZFW2BjFV396bb76Jo0ePIjc31+H5\nfv36Yf/+/Th48CDmz7emksrPz8fkyZP9X9Ig+HGt56mOQ43adGF/7PnFuw2E4A4eqIOQvyXVkenj\nCPf9Cl+ZcBveu+dBaZCTnFA86AR7+m+9Xo9WA/qqXt7TiU+u73a9ltegduOrNJetsqvdpJGm5X29\nYFIKbL0JQLX8VuQCUPu3ByKvrlYB726h1EXMU3Duhxb01gP6OJVFfZA8/IH5LjNv5ny6Cfu++9Hn\ncjm0cHvYnQLZ3cI+xaKwWDSdmz1NzGI0mbzu8qVaCJ635KhqSV6xYgVeeuklrFy5UnpOr9fj5Zdf\nRp8+fVBQUICcnBysX78e+/btC1hhK9rJw38Guwghx+dpXv3UspJoF3DaJuOoqG37my1tl9xt5aK/\nj+Knja4zmYW6oLckazwxecpd6zZjC7nla2uq0iAjb9ZbrXqS6mVlW9vsTuyqgrYAH3LkymAwGlHv\numvx++6fXfrlN+7UHkV/H4VOr0fJpUtSf3ElSr8jnV4vGx/aJtkxR0chtXkTKd+7s5iEeNRqfBUO\nlqUElbt4cW78sL+bY4o0o0nnjvj70G848cdht58BAE4cLsCnTz6HxNQUNNvcWXq+7Q0DPL7XmZYM\nNq0y+qDkkvLYjIbt28BoNqNW44b468AhAPIpKD2JSYjH2ZOFqpfX0irvjZjEeETHxuLob78HdDsV\nQVWQ/N133yEtzfEk0r59e+Tl5SE/Px8AsGbNGgwaNEh1kDxlyhRMnToVAJCUpP7AVaECEFQd+d9B\nzS0xziwWS9BaMQbcPj0o23WmlOLJHX/0aQsE24k7FFuEvRUKLclaBGpSlJJLlzyOJA+UMydOhkRw\nf+b4yYCs15s0ZLYgTtX6ZVrb7DNB2AeQMRrW61cyp6jImGjMWrUMz9w0DueLzji8Nu31512WLy1R\nHjStdCGidPerWVdrADp4gXXMy7zW3WTvgo145F4075aO+9L74cKZMy6vAzLZLeyO3zc9tBCty+4U\nzb2mk2L5bfZ+8wMA60RN9hM0jVos3wXOHS3nEVs9KOl80xB0vmmI5jI4S0iphb8OHlK9fKDPhQs2\nrEOVqjGqvptQ53Wf5JSUFBw+XH4FV1BQgA4dOiAhIQGLFy9Gq1atsGDBAjz++OOy71++fDmWL18O\nAMjJkZ9gItgC0fD42cvLMfGFJ71+/3fvrcP6p17AU7u/97ksd1/XxS/r8Zeiv48iLrlmwNZvMgdu\n5jp/qAxB8oM9BsJSWgqT2Yxu40ah+y0jZZdT6iNnKS2tkIsV50E//rJh6UvImjvT7TIrZi9AXs4u\nmCLN6H/bFL/MPOfJg9dnorSkBJEx0dIFyunjx2E0RVgHE+qsM6TpTUYYjEYs2LA24GWy2ftNYI4x\nAZ/NTKbF0L5/tX2QHqkw5XygLxbdtabHJCTgwpmzvq1fKU+yTq/qdrnRZJINkpumdwQAmKtEugmS\nlbNbqL57WGb9k9aLgwtnzuLB67NQpVqM9QWnSUwsJZetg3R1Oty7+SMAwO97cvHeggfR/ZaR6DJ6\nOMz237WbGOGR3oOkAb+Wy6UQENDp9I6DgIXAgNuno9WAvvhi2dvY+fEGANaxIs6zPbqj9a5KoI/B\nVarGKL4mlTVE7+w68zpIlvtShBAoLCzEjBnqB8yEtAB8iWpmUHP7fotFU65P92Wp+Fvi7vqq+Vo3\nnvS7NbT7ylfIZDA+sr+lV1ig3B1J6bMIiwAqoEG/z9TxAVnvpX/Oe1ym8MhfuHDmDC6cqbjv9OwJ\na2vt+dOOAUfx5QsovnDB4bnKPHK9VUYfNCkLsJTGIvgyo509uTt+9sdM2ewXzsvLdDuqnuZ+VkQt\n3I3HuLpHF3zzjueuCO4o3ZFJadYYKc0ae3y/LQ2g/Xdiv/8ZIiKQ0rQxYmW68V3Xr7fD360z+wOw\ndrWw5RMHgIFzbvVYDvsGCOtvUz4wt3f+9BlExVZD0d/HUFhwRGqp7Tej/DxiMBplt1909BiKjh7z\nuA0A+KfoNADgXGEhCv/8C4D2c2GdFs1hLqvjJukdHcrUuGN7AECLnt2lmKZqYvkdJvtlnQdLqqlb\nd+Te37SLtXW59cB+iEmIx9dvvevTNgLN6yC5oKAAdeqUV2hqaiqOHDmiaR2ZmZnIyspCbGyst8UI\nqNyt25A55zaf1vHr19/h6uu7Sn8X/qmtjpz9d/1mANYfVnRcaNWb/W0sJW6zYwT4wtLXbi4B52Wj\n0y9ff4eTBUfQd/pE/5bHie2Wpf3fQ+6ZK7us7RZ76eXLDi1AFZUdpd2ggX5f5995v6Fg736PyxX9\ndVT6//YPP0XHYYP8XhZ7WkegC4sFF//5B9+8837ALxx3bf5C1XKXzp+HOUq+NdaefbcYpRH6wx6Y\nr65wXrAPtuwnFVG68JBrSR69ZJHfyuMuS0H6yBvx7ao1Pq3f15n1bANeb7zvbuk5+zIbTUbc+cE7\nsu91nrRFKXNT19E3+VRGJYd/3YcGra+TfvNHDuThwpmzaD2wn8ft527d5tO2SzXOGxBbo7o0GUqV\nqjEOZTKUzXxZo34autZyLau7+vO1buXeb4q0dj9r0OY6VKuedOUGyTk5OWjUqBHq1auHP//8EyNH\njsTo0aM1rWPjxo3YuHFjyHa3OPF/BZh7TSdpNqjDe/fjuRETAED1DFEbnnnJIUg+V3gKx/L/8DhQ\nSMmf+w8AAB7o2l/ze32Z1cqT50dPwv/l7nV4rk1mf5cTgnOrlj1/p0ty7g/l7ed/c+bdiEmIx4iH\nF2p6X9HRY3ik9yB0HjHU4SShxFMaH3f9u37e8hU+f3m5pvL5qvDPvzz2OSstcQ6S/XP7+UD2Tiyb\neodf1qWVln52h3/d51W/vBvvn+e2r+Jbs+7Gr9u878Zwb0drK92WV9VNoBBoax94DGOfflTTe5Ra\nOavVcB3j8u27a2GuUgUdbrwB/xSdlj1+6o0GPLXLfZ1qnbbc00Wh3L7RakBf3PzEQwCAT598Xgp0\nm3bthCmvPONYHj+kqXM/7bHnIPmble8jfdQw2deMZUGy/YBvHXTSccA+a8yZEyfx0PWZHrdXUV6f\nNtvh7//7+Vfcl64+Y45q0ndU/l0Vn1c+TzqzlJZiQbse/i0TSVQFyatXr0aPHj2QlJSEw4cPY9Gi\nRXjrrbcwc+ZMfP755zAYDHjrrbewd+9ezysLM85B4aXzFxARVUVh6cpLruuGXF+04ovBm4XNW8Ji\ncZuCzeP7VQaGV2IOaucWEX91qakM/bcDyRLkgZH+5k23FNvtfucGh9qNXe8YCSFwsWwKYqVAV00+\n5wZtrpN9PiYhXvZ5b8ZYKAXccuWLq+l+KuVrenX3uD2jm6npazfxnOKw9PJl6A0GtMl0vfBo2a8X\nzp446bCeNlkZ0mds0bOb9DynQi5XfPGi9P/U5k0d6tb2/7otmgMITrfJcKIqSFZqId68eTM2b97s\n9cZDvbuFTd7O/+Kq9m2w699bpOdyPt0kJct35x+n0cWXL13C0UP5Hg9uctyNQlbj9925LgfzvJyf\ncFW71j6tFwD+OXXa5bnTx0+4PLf/++2K68j55N/oO2OSz2VRXL/K78zZuVNFOOmm/62SX7/+zvp+\nlal59nz+leZthLoD2TsdJoE49J+f0Lxbus/rzd/1s8/rCGX7vv3RbUvyP6dOVWBpAu9cofbP06Kn\nfAAoN2jo3MlTKCkLPE4fO655WzadRwzVtLy74/xxhdRlf+4vT5v2++7y/fzsSe1ZQnztLmjr/63k\n0vnzOH30OPR6vWw3ErlBrvZ35Oy7+5yROV+Eg33f/Yguo4Y5zF0gLBap+2Jq8yYOdetcz9+v/rDC\nyhqOdPC6J6T/5OTkoF07dTPFBYNOp0NElSq4dP68w3NGcwTMUVEwRZpx9oQ1EDJFmmEwGqHT63Hx\n3DmUXLyEiCqRiEmIx/kzZ3Hx7DkYTCbE16qJC2fPISLSmhNRbzDgckkxTGYz/ik6jeILF2E0mSCE\nQGRMNCylpTh/+oxPV40GkwkGowHFFy46PBcdFwuDyYh/ThXBFBlpnbpTp4Ner4cQQGlxMQwREbhc\nfMn62XR6lF6+DGOECZeLS1B84YLLgCGbqokJ1kwDQqC0pEQapKDEHBWFqLhquHjuH0RGR0uDJ0qK\nrS3QJrO5bMphHYRFQAjrbFxCWFtizxw/iajYajh3stClrnQ6HQwmEyJjomGMiIDeoIdOb5Dep9MB\nVapWlfJUWiwWlFy8JA2KMprNiIg0o/jCRcTWqA6dQQ9RasHFc+dgNEdAbzBAp7OVS+D00WNSi2dc\nzRpSHZrMZpSWXJY+g76sVaXwzyOVYvCeFnqDAdWSEmEwmVB84QLOFZ5CbM0a0Ol0KC0thSgthSnS\njJJLxdDp9TCarPtXSXExdDrAVPb7uFC2f106fwGRVaNx7uSVFSTKMUWaUTUpEaLUAmGx4FzRaZjM\nETBFRuKMD4FeqKpWPRhyllkAAAmISURBVAnQ6WA0GWG5XCqlGTOYTFIWAiGkRB2AENJvCDqddNda\nWAQEBEouXEREVBSEsKCwwDoWJL52Mv45dVqx21dkTDSiYqtJ0wmXllhbSe3/D0DabklxMYwRJuig\nQ0lxMfQ6HQxl4zIsZS2spSUl0JuM1vcKIZX31F9/KbZeW8ugczleVk1MgNEcIR1n9AaDVCE6g15a\nv6W0FAaTUdqWjeXyZeiNxvI6RHk9WsrumFlKLYiIjHSoW8vly9a+rUKg+MJF6Rh57lQRLp49h/ja\nydaBjDodLKWXHY7RNjq9TvreALtMN2XlO3vihMO5KZwYIyJwubjY4TlzdBRiEhJcMnDYZxURENK+\nTdqojTsZJBMRERFR2FAbd1beXEBERERERAHidXYLf6gsfZKJiIiIKLwEtSV548aNmDZtGk6fdt9P\nlYiIiIioIrG7BRERERGREwbJREREREROQqJPcqNGjYIy615SUhJOnAjP3IzeYH1pxzrThvWlDetL\nG9aXNqwvbVhf2gSzvtLS1M96LML1kZOTE/QyVKYH64t1xvoKrQfri/XF+gqdB+vryqsvdrcgIiIi\nInLCIJmIiIiIyIkBwIPBLkQw/fTTT8EuQqXC+tKOdaYN60sb1pc2rC9tWF/asL60CfX6ColpqYmI\niIiIQgm7WxAREREROQnbILlfv37Yv38/Dh48iPnz5we7OCEjPz8fP//8M3bt2iWl5YuPj8eWLVtw\n4MABbNmyBXFxcdLyzz//PA4ePIg9e/agVatWwSp2hXnzzTdx9OhR5ObmSs95Uz9jx47FgQMHcODA\nAYwdO7ZCP0NFkquvRYsWoaCgALt27cKuXbuQkZEhvbZgwQIcPHgQ+/fvR9++faXnw+X3mpqaiq++\n+gp79+7FL7/8gttvvx0A9zElSvXFfUye2WzGjh07sHv3bvzyyy948MEHAQD16tXD9u3bceDAAaxZ\nswYmkwkAEBERgTVr1uDgwYPYvn27Q9ospXq8kijV19tvv43ffvtN2r9atmwpvSecf482er0eP/30\nEzZs2ACg8u9fQU+xUdEPvV4v8vLyRP369YXJZBK7d+8WzZo1C3q5QuGRn58vEhMTHZ574oknxPz5\n8wUAMX/+fPH4448LACIjI0Ns2rRJABAdOnQQ27dvD3r5A/3o2rWraNWqlcjNzfW6fuLj48WhQ4dE\nfHy8iIuLE4cOHRJxcXFB/2wVVV+LFi0Sc+fOdVm2WbNmYvfu3SIiIkLUq1dP5OXlCb1eH1a/1+Tk\nZNGqVSsBQMTExIj//e9/olmzZtzHNNYX9zHlR3R0tAAgjEaj2L59u+jQoYNYu3atGDFihAAgXn31\nVTF9+nQBQMyYMUO8+uqrAoAYMWKEWLNmjdt6DPZnq6j6evvtt8WNN97osmy4/x5tjzlz5oj33ntP\nbNiwQQCo1PtXWLYkt2/fHnl5ecjPz0dJSQnWrFmDQYMGBbtYIWvQoEF45513AADvvPMOBg8eLD2/\ncuVKAMCOHTsQFxeH5OTkoJWzInz33XcoLCx0eE5r/fTr1w9ffPEFTp06haKiInzxxRfo379/xX6Q\nCiJXX0oGDRqENWvWoLi4GL///jvy8vLQvn37sPq9/v3339i1axcA4Ny5c9i3bx9SUlK4jylQqi8l\n3MeAf/75BwBgMplgMpkghEDPnj3x4YcfAnDdv2z73YcffohevXpJz8vV45VIrr6UhPvvEQBSUlIw\ncOBAvPHGG9JzlXn/CssgOSUlBYcPH5b+LigocHtgDSdCCGzZsgX/+c9/MGXKFABAzZo18ffffwOw\nnpRq1KgBgPVoo7V+WG/AzJkzsWfPHrz55ptS1wHWl6O0tDS0atUKO3bs4D6mgn19AdzHlOj1euza\ntQvHjh3DF198gUOHDqGoqAilpaUAHD+7fb2Ulpbi9OnTSExMDOv62rlzJwBg8eLF2LNnD5555hlE\nREQA4P4FAM899xzmzZsHi8UCAEhMTKzU+1dYBsk6nc7lOXdXh+EkPT0dbdq0QUZGBm677TZ07dpV\ncVnWo3tK9RPu9fbqq6+iYcOGuO666/DXX39h6dKlAFhf9qKjo/HRRx9h9uzZOHv2rOJyrDMr5/ri\nPqbMYrGgVatWSE1NRfv27dGsWTOXZWyfnfXlWl9XX3017rnnHjRt2hTt2rVDQkKC1Ic93Otr4MCB\nOHbsmENaN3efvTLUV1gGyQUFBahTp470d2pqKo4cORLEEoWOv/76CwBw/PhxfPzxx2jfvj2OHj0q\ndaNITk7GsWPHALAebbTWT7jX27Fjx2CxWCCEwPLly6XbaKwvK6PRiI8++gjvvfcePv74YwDcx9yR\nqy/uY56dPn0a27ZtQ8eOHREXFweDwQDA8bPb14vBYEBsbCwKCwvDur769+8v3dUpLi7G22+/zf2r\nTHp6Om644Qbk5+djzZo16NmzJ5577rlKv38FvZN3RT8MBoM4dOiQqFevnjRIo3nz5kEvV7AfUVFR\nIiYmRvr/Dz/8IPr16yeefPJJh0FDTzzxhAAgBgwY4DBIYceOHUH/DBXxSEtLcxiIprV+4uPjxW+/\n/Sbi4uJEXFyc+O2330R8fHzQP1dF1VdycrL0/9mzZ4v3339fABDNmzd3GKxx6NAhodfrw+73+s47\n74hnn33W4TnuY9rqi/uY/CMpKUnExsYKACIyMlJ8++23YuDAgWLdunUOA6tmzJghAIhbb73VYWDV\n2rVr3dZjsD9fRdWX/f717LPPiiVLlgiAv0f7R/fu3aWBe5V8/wp+ZQbjkZGRIf73v/+JvLw8sXDh\nwqCXJxQe9evXF7t37xa7d+8Wv/zyi1QvCQkJYuvWreLAgQNi69atDj/ul156SeTl5Ymff/5ZtGnT\nJuifIdCP1atXiyNHjoji4mJx+PBhMXHiRK/qZ8KECeLgwYPi4MGDYvz48UH/XBVZXytXrhQ///yz\n2LNnj/j0008dTjgLFy4UeXl5Yv/+/aJ///7S8+Hye01PTxdCCLFnzx6xa9cusWvXLpGRkcF9TGN9\ncR+Tf1xzzTXip59+Env27BG5ubni/vvvF4D12L9jxw5x8OBBsW7dOhERESEACLPZLNatWycOHjwo\nduzYIerXr++xHq+kh1J9ffnll+Lnn38Wubm5YtWqVVIGDCC8f4/2D/sguTLvX5xxj4iIiIjISVj2\nSSYiIiIicodBMhERERGREwbJREREREROGCQTERERETlhkExERERE5IRBMhERERGREwbJRERERERO\nGCQTERERETn5fyt252CNR4jZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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yFDcAWOb/AVUddY6J3e1DAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VNDY26tNPP9WDDz7YYZnP55PX65XX61VjQ2u3BQQAtBeyuFNSUpSUlCRJiouL04QJE3Tk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\nCXvmWdncVrQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q = train_show(n=7, m=10, n_actions=8,\n",
    "               eps=0.1, alpha=0.5, gamma=1, start_cell=np.array([3, 0]), goal_cell=np.array([3, 7]),\n",
    "               column_winds=np.array((0, 0, 0, 1, 1, 1, 2, 2, 1, 0)), episodes=4000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9 actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1192b802fad54d6785fe9f0af957fffe"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Played 40108 timesteps in 3000 episodes\n"
     ]
    },
    {
     "data": {
      "image/png": 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iIvIevw6S1RiMBiknWW0wkQfeXY26jZKkv5t27YSC/BM4l/+nx8pIRERERO7FIFnBYDBW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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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B48aN0+DBgzVlyhQNGjSoI7IBANrgs7iTkpK0Z88eFRUVqaGhQWlpaZo4cWJHZAMAtMFn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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VNDY26tNPP9WDDz7YYZnP55PX65XX61VjQ2u3BQQAtBeyuFNSUpSUlCRJiouL04QJE3Tk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\nCXvmWdncVrQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q = train_show(n=7, m=10, n_actions=9,\n",
    "               eps=0.1, alpha=0.5, gamma=1, start_cell=np.array([3, 0]), goal_cell=np.array([3, 7]),\n",
    "               column_winds=np.array((0, 0, 0, 1, 1, 1, 2, 2, 1, 0)), episodes=3000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's sometimes learning a policy that's a bit less effective than in the case with 8 actions for some reason. Maybe because I'm still using an eps-greedy policy and sometimes it will just do nothing on a step and be carried away by wind or something."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stochastic wind with 9 actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def apply_stoch_wind(state, column_winds):\n",
    "    wind_strength = column_winds[state[1]]\n",
    "    increment = np.random.randint(-1, 2)\n",
    "    wind_strength += np.random.randint(-1, 2)\n",
    "    next_state = state.copy()\n",
    "    next_state[0] -= wind_strength\n",
    "    return next_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bc73e705e291426da3609de6df28531e"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "q, episode_lens, experiences = train_sarsa(n=7, m=10, n_actions=9,\n",
    "                eps=0.1, alpha=0.5, gamma=1, start_cell=np.array([3, 0]), goal_cell=np.array([3, 7]),\n",
    "                column_winds=np.array((0, 0, 0, 1, 1, 1, 2, 2, 1, 0)), episodes=4000, apply_wind=apply_stoch_wind)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Pm7y8PLN7927z6quvmrCwMMcztcXgT94BwDLt6hw3AMA/ihsALENxA4BlKG4A\nsAzFDQCWobgBwDIUNwBY5v8BJX6JaLUq9k4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 5))\n",
    "plt.title('State values wrt greedy policy')\n",
    "img = plt.imshow(q.max(axis=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks a bit more grim once most of it is explored because of stochasticity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize several runs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gwYO9kQ8AcI2wpkpaWlokSdHR0YqOjpYx4V9+EADQs8IqbrfbraKiItXU1GjXrl06dOhQ\npHMBALoRVnG3t7dr7NixGjp0qDIzM3XXXXd1Wic3N1d+v19+v19JtyT0eFAAwOdu6F0lDQ0N+uST\nT/Tggw92Wubz+eT1euX1etVwvrnHAgIAOgpZ3IMGDVJSUpIkKTY2VpMmTdLx48cjHgwA0LWQ7yoZ\nMmSI8vLyFBUVJbfbrS1btujDDz/sjWwAgC6ELO5jx44pIyOjN7IAAMLAJycBwDIUNwBYhuIGAMtQ\n3ABgGYobACxDcQOAZShuALAMxQ0AlqG4AcAyFDcAWIbiBgDLhLxWyVdy5Yram5oisutwedJSHX3+\nq9o+q3Q6glz/79+djiBJakuIcTqCoj4pdDpCn3Hk0iWnI/QZ5t8uOx1B8oR/ZzHOuAHAMhQ3AFiG\n4gYAy1DcAGAZihsALENxA4BlKG4AsAzFDQCWobgBwDIUNwBYhuIGAMtQ3ABgGYobACwTdnG73W4V\nFhZqx44dkcwDAAgh7OJ+6qmnVFpaGsksAIAwhFXcaWlpysnJ0dtvvx3pPACAEMIq7jfeeEPPPPOM\n2tvbu10nNzdXfr9ffr9fSSkDeiwgAKCjkMWdk5OjmpoaFRZe/84hPp9PXq9XXq9XDbWNPRYQANBR\nyOLOysrStGnTFAgElJ+frwkTJmjDhg29kQ0A0IWQxb1s2TINGzZMw4cP18MPP6zdu3dr7ty5vZEN\nANAF3scNAJa5obu87927V3v37o1UFgBAGDjjBgDLUNwAYBmKGwAsQ3EDgGUobgCwDMUNAJahuAHA\nMhQ3AFiG4gYAy1DcAGAZihsALHND1yqxSdtnlU5HkCRFfePrTkfQlb8UOx1BkhTldAB08N912U5H\nkCRtKP8fpyNo7jCnE0ixh/4j7HU54wYAy1DcAGAZihsALENxA4BlKG4AsAzFDQCWobgBwDIUNwBY\nhuIGAMtQ3ABgGYobACxDcQOAZcK6yFQgEFBTU5OuXLmitrY2eb3eSOcCAHQj7KsDPvDAAzp//nwk\nswAAwsBUCQBYJqziNsboD3/4g/7yl78oNzc30pkAANcR1lRJVlaWqqqqlJKSol27dun48ePat29f\nh3Vyc3O1YMECSVJSyoCeTwoAkBTmGXdVVZUkqba2Vtu3b1dmZmandXw+n7xer7xerxpqG3s2JQAg\nKGRxx8XFKSEhIfj15MmTVVzcN26FBQA3o5BTJbfeequ2b9/++coejzZt2qSPP/444sEAAF0LWdyB\nQED33HNPb2QBAISBtwMCgGUobgCwDMUNAJahuAHAMhQ3AFiG4gYAy1DcAGAZihsALENxA4BlKG4A\nsAzFDQCWCfvWZfhqrpw45XQEoEunvf90OoIkaa6ynI6gsi3fcjqCLo3oH/a6nHEDgGUobgCwDMUN\nAJahuAHAMhQ3AFiG4gYAy1DcAGAZihsALENxA4BlKG4AsAzFDQCWobgBwDIUNwBYJqziTkpK0tat\nW1VaWqqSkhKNGzcu0rkAAN0I67Kub775pj766CPNnDlT0dHRiouLi3QuAEA3QhZ3YmKixo8frx/9\n6EeSpNbWVjU0NEQ6FwCgGyGnSkaMGKHa2lqtW7dOhYWF8vl8XZ5x5+bmyu/3y+/3KyllQETCAgDC\nKG6Px6OMjAytWbNGGRkZamlp0XPPPddpPZ/PJ6/XK6/Xq4baxoiEBQCEUdwVFRWqqKjQoUOHJEnv\nvfeeMjIyIh4MANC1kMVdXV2t8vJyjRw5UpI0ceJElZSURDwYAKBrYb2r5Mknn9TGjRsVExOjM2fO\n6Mc//nGkcwEAuhFWcR89elRerzfSWQAAYeCTkwBgGYobACxDcQOAZShuALAMxQ0AlqG4AcAyFDcA\nWIbiBgDLUNwAYBmKGwAsQ3EDgGVckkxP77SmpkZlZWVfeftBgwaprq6uBxPZi2PxBY7FFzgWX/hX\nORbp6en62te+Fvb6pq8Nv9/veIa+MjgWHAuOBcfi2sFUCQBYhuIGAMtESXrJ6RBdKSwsdDpCn8Gx\n+ALH4gsciy/cbMciIi9OAgAih6kSALAMxQ0AlulzxT1lyhQdP35cJ0+e1LPPPut0HMcMHTpUu3fv\nVklJiYqLi7Vo0SKnIznO7XarsLBQO3bscDqKo5KSkrR161aVlpaqpKRE48aNczqSYxYvXqzi4mId\nO3ZMmzZtUr9+/ZyO1Gscf0/i1eF2u82pU6fM8OHDTXR0tDly5IgZNWqU47mcGIMHDzZjx441kkxC\nQoI5ceLETXssro6f/exnZuPGjWbHjh2OZ3FyvPvuu+axxx4zkkx0dLRJSkpyPJMTIzU11Zw5c8bE\nxsYaSWbz5s1m3rx5jufqjdGnzrgzMzN16tQpBQIBtba2Kj8/X9OnT3c6liPOnTunoqIiSVJzc7NK\nS0uVlpbmcCrnpKWlKScnR2+//bbTURyVmJio8ePHa+3atZKk1tZWNTQ0OJzKOR6PR/3791dUVJTi\n4uJUWVnpdKRe0aeKOy0tTeXl5cHHFRUVN3VZXZWenq6xY8fq4MGDTkdxzBtvvKFnnnlG7e3tTkdx\n1IgRI1RbW6t169apsLBQPp9PcXFxTsdyRGVlpV577TV9+umnqqqqUkNDg3bt2uV0rF7Rp4rb5XJ1\n+p4xxoEkfUd8fLy2bdumxYsXq6mpyek4jsjJyVFNTc1N917drng8HmVkZGjNmjXKyMhQS0uLnnvu\nOadjOWLgwIGaPn26hg8frtTUVMXHx2v27NlOx+oVfaq4KyoqNGzYsODjoUOH3jT/9emKx+PRtm3b\ntHHjRm3fvt3pOI7JysrStGnTFAgElJ+frwkTJmjDhg1Ox3JERUWFKioqdOjQIUnSe++9p4yMDIdT\nOWPSpEkKBAKqq6tTW1ubfvvb3+q+++5zOlavcXyi/eqIiooyp0+fNrfffnvwxcnRo0c7nsupkZeX\nZ1atWuV4jr40srOzb/oXJ//4xz+akSNHGklm+fLl5pe//KXjmZwYmZmZpri42PTv399In79ou3Dh\nQsdz9dJwPECHMXXqVHPixAlz6tQps2zZMsfzODWysrKMMcYcPXrUFBUVmaKiIjN16lTHczk9KG6Z\nMWPGGL/fb44ePWq2b99uBg4c6Hgmp8ZLL71kSktLzbFjx8z69etNTEyM45l6Y/CRdwCwTJ+a4wYA\nhEZxA4BlKG4AsAzFDQCWobgBwDIUNwBYhuIGAMv8L6w/DI8q43GCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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gwXDkAwBcI6ipkpaWFklSdHS0oqOjZYzzj0AEgL4qqOJ2uVwqKipSTU2Ndu3apUOHDoU6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\nRK5CYII=\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(3):\n",
    "    experiences = play_greedy(q, start_cell=np.array([3, 0]), goal_cell=np.array([3, 7]), apply_wind=apply_stoch_wind,\n",
    "                              n=7, m=10, column_winds=np.array((0, 0, 0, 1, 1, 1, 2, 2, 1, 0)))\n",
    "    plt.figure(figsize=(6, 5))\n",
    "    plt.title('Greedy policy rollout')\n",
    "    img = plt.imshow(draw_playback(experiences, n=7, m=10, goal_cell=np.array([3, 7])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seems robust. But this policy run in the env without stochasticity results in an infinite loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}