Temporal_Difference.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Temporal difference cheat sheet**\n",
    "\n",
    "Action in next state = Use epsilon greedy policy for next state's action Q values<br>\n",
    "\n",
    "In temporal difference, value for Q updated after every step of every end to end event<br>\n",
    "\n",
    "Qnew = Qcurrent + alpha(target - current)\n",
    "target = reward + gamma * QnextStateAction\n",
    "\n",
    "Selecting Qnext is different for different methods -\n",
    "\n",
    "**1. Sarsa**<br>\n",
    "QnextStateAction = Epsilon greedy action\n",
    "\n",
    "**2. Q learning**<br>\n",
    "QnextStateAction = max(Qs)\n",
    "\n",
    "**3. Expected sarsa**<br>\n",
    "QnextStateAction = Expected value\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Temporal-Difference Methods\n",
    "\n",
    "In this notebook, you will write your own implementations of many Temporal-Difference (TD) methods.\n",
    "\n",
    "While we have provided some starter code, you are welcome to erase these hints and write your code from scratch.\n",
    "\n",
    "---\n",
    "\n",
    "### Part 0: Explore CliffWalkingEnv\n",
    "\n",
    "We begin by importing the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import gym\n",
    "import numpy as np\n",
    "import random\n",
    "import math\n",
    "from collections import defaultdict, deque\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import check_test\n",
    "from plot_utils import plot_values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the code cell below to create an instance of the [CliffWalking](https://github.com/openai/gym/blob/master/gym/envs/toy_text/cliffwalking.py) environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make('CliffWalking-v0')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The agent moves through a $4\\times 12$ gridworld, with states numbered as follows:\n",
    "```\n",
    "[[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11],\n",
    " [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23],\n",
    " [24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35],\n",
    " [36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47]]\n",
    "```\n",
    "At the start of any episode, state `36` is the initial state.  State `47` is the only terminal state, and the cliff corresponds to states `37` through `46`.\n",
    "\n",
    "The agent has 4 potential actions:\n",
    "```\n",
    "UP = 0\n",
    "RIGHT = 1\n",
    "DOWN = 2\n",
    "LEFT = 3\n",
    "```\n",
    "\n",
    "Thus, $\\mathcal{S}^+=\\{0, 1, \\ldots, 47\\}$, and $\\mathcal{A} =\\{0, 1, 2, 3\\}$.  Verify this by running the code cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discrete(4)\n",
      "Discrete(48)\n"
     ]
    }
   ],
   "source": [
    "print(env.action_space)\n",
    "print(env.observation_space)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this mini-project, we will build towards finding the optimal policy for the CliffWalking environment.  The optimal state-value function is visualized below.  Please take the time now to make sure that you understand _why_ this is the optimal state-value function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff78d1bb3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define the optimal state-value function\n",
    "V_opt = np.zeros((4,12))\n",
    "V_opt[0:13][0] = -np.arange(3, 15)[::-1]\n",
    "V_opt[0:13][1] = -np.arange(3, 15)[::-1] + 1\n",
    "V_opt[0:13][2] = -np.arange(3, 15)[::-1] + 2\n",
    "V_opt[3][0] = -13\n",
    "\n",
    "plot_values(V_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1: TD Control: Sarsa\n",
    "\n",
    "In this section, you will write your own implementation of the Sarsa control algorithm.\n",
    "\n",
    "Your algorithm has four arguments:\n",
    "- `env`: This is an instance of an OpenAI Gym environment.\n",
    "- `num_episodes`: This is the number of episodes that are generated through agent-environment interaction.\n",
    "- `alpha`: This is the step-size parameter for the update step.\n",
    "- `gamma`: This is the discount rate.  It must be a value between 0 and 1, inclusive (default value: `1`).\n",
    "\n",
    "The algorithm returns as output:\n",
    "- `Q`: This is a dictionary (of one-dimensional arrays) where `Q[s][a]` is the estimated action value corresponding to state `s` and action `a`.\n",
    "\n",
    "Please complete the function in the code cell below.\n",
    "\n",
    "(_Feel free to define additional functions to help you to organize your code._)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_Q_sarsa(alpha, gamma, Q, state, action, reward, next_state=None, next_action=None):\n",
    "    \"\"\"Returns updated Q-value for the most recent experience.\"\"\"\n",
    "    current = Q[state][action]  # estimate in Q-table (for current state, action pair)\n",
    "    # get value of state, action pair at next time step\n",
    "    Qsa_next = Q[next_state][next_action] if next_state is not None else 0    \n",
    "    target = reward + (gamma * Qsa_next)               # construct TD target\n",
    "    new_value = current + (alpha * (target - current)) # get updated value\n",
    "    return new_value\n",
    "\n",
    "def epsilon_greedy(Q, state, nA, eps):\n",
    "    \"\"\"Selects epsilon-greedy action for supplied state.\n",
    "    \n",
    "    Params\n",
    "    ======\n",
    "        Q (dictionary): action-value function\n",
    "        state (int): current state\n",
    "        nA (int): number actions in the environment\n",
    "        eps (float): epsilon\n",
    "    \"\"\"\n",
    "    if random.random() > eps: # select greedy action with probability epsilon\n",
    "        return np.argmax(Q[state])\n",
    "    else:                     # otherwise, select an action randomly\n",
    "        return random.choice(np.arange(env.action_space.n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sarsa(env, num_episodes, alpha, gamma=1.0, plot_every=100):\n",
    "    nA = env.action_space.n                # number of actions\n",
    "    Q = defaultdict(lambda: np.zeros(nA))  # initialize empty dictionary of arrays\n",
    "    \n",
    "    # monitor performance\n",
    "    tmp_scores = deque(maxlen=plot_every)     # deque for keeping track of scores\n",
    "    avg_scores = deque(maxlen=num_episodes)   # average scores over every plot_every episodes\n",
    "    \n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        # monitor progress\n",
    "        if i_episode % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}\".format(i_episode, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()   \n",
    "        score = 0                                             # initialize score\n",
    "        state = env.reset()                                   # start episode\n",
    "        \n",
    "        eps = 1.0 / i_episode                                 # set value of epsilon\n",
    "        action = epsilon_greedy(Q, state, nA, eps)            # epsilon-greedy action selection\n",
    "        \n",
    "        while True:\n",
    "            next_state, reward, done, info = env.step(action) # take action A, observe R, S'\n",
    "            score += reward                                   # add reward to agent's score\n",
    "            if not done:\n",
    "                next_action = epsilon_greedy(Q, next_state, nA, eps) # epsilon-greedy action\n",
    "                Q[state][action] = update_Q_sarsa(alpha, gamma, Q, \\\n",
    "                                                  state, action, reward, next_state, next_action)\n",
    "                \n",
    "                state = next_state     # S <- S'\n",
    "                action = next_action   # A <- A'\n",
    "            if done:\n",
    "                Q[state][action] = update_Q_sarsa(alpha, gamma, Q, \\\n",
    "                                                  state, action, reward)\n",
    "                tmp_scores.append(score)    # append score\n",
    "                break\n",
    "        if (i_episode % plot_every == 0):\n",
    "            avg_scores.append(np.mean(tmp_scores))\n",
    "\n",
    "    # plot performance\n",
    "    plt.plot(np.linspace(0,num_episodes,len(avg_scores),endpoint=False), np.asarray(avg_scores))\n",
    "    plt.xlabel('Episode Number')\n",
    "    plt.ylabel('Average Reward (Over Next %d Episodes)' % plot_every)\n",
    "    plt.show()\n",
    "    # print best 100-episode performance\n",
    "    print(('Best Average Reward over %d Episodes: ' % plot_every), np.max(avg_scores))    \n",
    "    return Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the next code cell to visualize the **_estimated_** optimal policy and the corresponding state-value function.  \n",
    "\n",
    "If the code cell returns **PASSED**, then you have implemented the function correctly!  Feel free to change the `num_episodes` and `alpha` parameters that are supplied to the function.  However, if you'd like to ensure the accuracy of the unit test, please do not change the value of `gamma` from the default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 5000/5000"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7b9cf4940>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Average Reward over 100 Episodes:  -13.0\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "**<span style=\"color: green;\">PASSED</span>**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Estimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 0  1  1  2  1  1  1  3  2  2  1  2]\n",
      " [ 0  1  1  2  1  2  1  2  1  1  1  2]\n",
      " [ 1  1  1  1  1  1  1  1  1  1  1  2]\n",
      " [ 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7b9cf4320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# obtain the estimated optimal policy and corresponding action-value function\n",
    "Q_sarsa = sarsa(env, 5000, .01)\n",
    "\n",
    "# print the estimated optimal policy\n",
    "policy_sarsa = np.array([np.argmax(Q_sarsa[key]) if key in Q_sarsa else -1 for key in np.arange(48)]).reshape(4,12)\n",
    "check_test.run_check('td_control_check', policy_sarsa)\n",
    "print(\"\\nEstimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\")\n",
    "print(policy_sarsa)\n",
    "\n",
    "# plot the estimated optimal state-value function\n",
    "V_sarsa = ([np.max(Q_sarsa[key]) if key in Q_sarsa else 0 for key in np.arange(48)])\n",
    "plot_values(V_sarsa)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2: TD Control: Q-learning\n",
    "\n",
    "In this section, you will write your own implementation of the Q-learning control algorithm.\n",
    "\n",
    "Your algorithm has four arguments:\n",
    "- `env`: This is an instance of an OpenAI Gym environment.\n",
    "- `num_episodes`: This is the number of episodes that are generated through agent-environment interaction.\n",
    "- `alpha`: This is the step-size parameter for the update step.\n",
    "- `gamma`: This is the discount rate.  It must be a value between 0 and 1, inclusive (default value: `1`).\n",
    "\n",
    "The algorithm returns as output:\n",
    "- `Q`: This is a dictionary (of one-dimensional arrays) where `Q[s][a]` is the estimated action value corresponding to state `s` and action `a`.\n",
    "\n",
    "Please complete the function in the code cell below.\n",
    "\n",
    "(_Feel free to define additional functions to help you to organize your code._)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_Q_sarsamax(alpha, gamma, Q, state, action, reward, next_state=None):\n",
    "    \"\"\"Returns updated Q-value for the most recent experience.\"\"\"\n",
    "    current = Q[state][action]  # estimate in Q-table (for current state, action pair)\n",
    "    Qsa_next = np.max(Q[next_state]) if next_state is not None else 0  # value of next state \n",
    "    target = reward + (gamma * Qsa_next)               # construct TD target\n",
    "    new_value = current + (alpha * (target - current)) # get updated value \n",
    "    return new_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def q_learning(env, num_episodes, alpha, gamma=1.0, plot_every=100):\n",
    "    \"\"\"Q-Learning - TD Control\n",
    "    \n",
    "    Params\n",
    "    ======\n",
    "        num_episodes (int): number of episodes to run the algorithm\n",
    "        alpha (float): learning rate\n",
    "        gamma (float): discount factor\n",
    "        plot_every (int): number of episodes to use when calculating average score\n",
    "    \"\"\"\n",
    "    nA = env.action_space.n                # number of actions\n",
    "    Q = defaultdict(lambda: np.zeros(nA))  # initialize empty dictionary of arrays\n",
    "    \n",
    "    # monitor performance\n",
    "    tmp_scores = deque(maxlen=plot_every)     # deque for keeping track of scores\n",
    "    avg_scores = deque(maxlen=num_episodes)   # average scores over every plot_every episodes\n",
    "    \n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        # monitor progress\n",
    "        if i_episode % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}\".format(i_episode, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "        score = 0                                              # initialize score\n",
    "        state = env.reset()                                    # start episode\n",
    "        eps = 1.0 / i_episode                                  # set value of epsilon\n",
    "        \n",
    "        while True:\n",
    "            action = epsilon_greedy(Q, state, nA, eps)         # epsilon-greedy action selection\n",
    "            next_state, reward, done, info = env.step(action)  # take action A, observe R, S'\n",
    "            score += reward                                    # add reward to agent's score\n",
    "            Q[state][action] = update_Q_sarsamax(alpha, gamma, Q, \\\n",
    "                                                 state, action, reward, next_state)        \n",
    "            state = next_state                                 # S <- S'\n",
    "            if done:\n",
    "                tmp_scores.append(score)                       # append score\n",
    "                break\n",
    "        if (i_episode % plot_every == 0):\n",
    "            avg_scores.append(np.mean(tmp_scores))\n",
    "            \n",
    "    # plot performance\n",
    "    plt.plot(np.linspace(0,num_episodes,len(avg_scores),endpoint=False), np.asarray(avg_scores))\n",
    "    plt.xlabel('Episode Number')\n",
    "    plt.ylabel('Average Reward (Over Next %d Episodes)' % plot_every)\n",
    "    plt.show()\n",
    "    # print best 100-episode performance\n",
    "    print(('Best Average Reward over %d Episodes: ' % plot_every), np.max(avg_scores))\n",
    "    return Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the next code cell to visualize the **_estimated_** optimal policy and the corresponding state-value function. \n",
    "\n",
    "If the code cell returns **PASSED**, then you have implemented the function correctly!  Feel free to change the `num_episodes` and `alpha` parameters that are supplied to the function.  However, if you'd like to ensure the accuracy of the unit test, please do not change the value of `gamma` from the default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 5000/5000"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff78adf25f8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Average Reward over 100 Episodes:  -13.0\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "**<span style=\"color: green;\">PASSED</span>**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Estimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 2  1  2  2  0  1  1  1  1  1  2  0]\n",
      " [ 1  1  2  1  1  1  2  1  1  2  0  2]\n",
      " [ 1  1  1  1  1  1  1  1  1  1  1  2]\n",
      " [ 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  0]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff78adf27b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# obtain the estimated optimal policy and corresponding action-value function\n",
    "Q_sarsamax = q_learning(env, 5000, .01)\n",
    "\n",
    "# print the estimated optimal policy\n",
    "policy_sarsamax = np.array([np.argmax(Q_sarsamax[key]) if key in Q_sarsamax else -1 for key in np.arange(48)]).reshape((4,12))\n",
    "check_test.run_check('td_control_check', policy_sarsamax)\n",
    "print(\"\\nEstimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\")\n",
    "print(policy_sarsamax)\n",
    "\n",
    "# plot the estimated optimal state-value function\n",
    "plot_values([np.max(Q_sarsamax[key]) if key in Q_sarsamax else 0 for key in np.arange(48)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3: TD Control: Expected Sarsa\n",
    "\n",
    "In this section, you will write your own implementation of the Expected Sarsa control algorithm.\n",
    "\n",
    "Your algorithm has four arguments:\n",
    "- `env`: This is an instance of an OpenAI Gym environment.\n",
    "- `num_episodes`: This is the number of episodes that are generated through agent-environment interaction.\n",
    "- `alpha`: This is the step-size parameter for the update step.\n",
    "- `gamma`: This is the discount rate.  It must be a value between 0 and 1, inclusive (default value: `1`).\n",
    "\n",
    "The algorithm returns as output:\n",
    "- `Q`: This is a dictionary (of one-dimensional arrays) where `Q[s][a]` is the estimated action value corresponding to state `s` and action `a`.\n",
    "\n",
    "Please complete the function in the code cell below.\n",
    "\n",
    "(_Feel free to define additional functions to help you to organize your code._)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_Q_expsarsa(alpha, gamma, nA, eps, Q, state, action, reward, next_state=None):\n",
    "    \"\"\"Returns updated Q-value for the most recent experience.\"\"\"\n",
    "    current = Q[state][action]         # estimate in Q-table (for current state, action pair)\n",
    "    policy_s = np.ones(nA) * eps / nA  # current policy (for next state S')\n",
    "    policy_s[np.argmax(Q[next_state])] = 1 - eps + (eps / nA) # greedy action\n",
    "    Qsa_next = np.dot(Q[next_state], policy_s)         # get value of state at next time step\n",
    "    target = reward + (gamma * Qsa_next)               # construct target\n",
    "    new_value = current + (alpha * (target - current)) # get updated value \n",
    "    return new_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_sarsa(env, num_episodes, alpha, gamma=1.0, plot_every=100):\n",
    "    \"\"\"Expected SARSA - TD Control\n",
    "    \n",
    "    Params\n",
    "    ======\n",
    "        num_episodes (int): number of episodes to run the algorithm\n",
    "        alpha (float): step-size parameters for the update step\n",
    "        gamma (float): discount factor\n",
    "        plot_every (int): number of episodes to use when calculating average score\n",
    "    \"\"\"\n",
    "    nA = env.action_space.n                # number of actions\n",
    "    Q = defaultdict(lambda: np.zeros(nA))  # initialize empty dictionary of arrays\n",
    "    \n",
    "    # monitor performance\n",
    "    tmp_scores = deque(maxlen=plot_every)     # deque for keeping track of scores\n",
    "    avg_scores = deque(maxlen=num_episodes)   # average scores over every plot_every episodes\n",
    "    \n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        # monitor progress\n",
    "        if i_episode % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}\".format(i_episode, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "        \n",
    "        score = 0             # initialize score\n",
    "        state = env.reset()   # start episode\n",
    "        eps = 0.005           # set value of epsilon\n",
    "        \n",
    "        while True:\n",
    "            action = epsilon_greedy(Q, state, nA, eps)         # epsilon-greedy action selection\n",
    "            next_state, reward, done, info = env.step(action)  # take action A, observe R, S'\n",
    "            score += reward                                    # add reward to agent's score\n",
    "            # update Q\n",
    "            Q[state][action] = update_Q_expsarsa(alpha, gamma, nA, eps, Q, \\\n",
    "                                                 state, action, reward, next_state)        \n",
    "            state = next_state              # S <- S'\n",
    "            if done:\n",
    "                tmp_scores.append(score)    # append score\n",
    "                break\n",
    "        if (i_episode % plot_every == 0):\n",
    "            avg_scores.append(np.mean(tmp_scores))\n",
    "            \n",
    "    # plot performance\n",
    "    plt.plot(np.linspace(0,num_episodes,len(avg_scores),endpoint=False), np.asarray(avg_scores))\n",
    "    plt.xlabel('Episode Number')\n",
    "    plt.ylabel('Average Reward (Over Next %d Episodes)' % plot_every)\n",
    "    plt.show()\n",
    "    # print best 100-episode performance\n",
    "    print(('Best Average Reward over %d Episodes: ' % plot_every), np.max(avg_scores))\n",
    "    return Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the next code cell to visualize the **_estimated_** optimal policy and the corresponding state-value function.  \n",
    "\n",
    "If the code cell returns **PASSED**, then you have implemented the function correctly!  Feel free to change the `num_episodes` and `alpha` parameters that are supplied to the function.  However, if you'd like to ensure the accuracy of the unit test, please do not change the value of `gamma` from the default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 10000/10000"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff78acecf60>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Average Reward over 100 Episodes:  -13.0\n"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "**<span style=\"color: green;\">PASSED</span>**"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Estimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 0  1  2  2  1  0  1  1  1  1  2  2]\n",
      " [ 1  1  1  1  1  1  1  1  1  1  1  2]\n",
      " [ 1  1  1  1  1  1  1  1  1  1  1  2]\n",
      " [ 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  0]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff78acecf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# obtain the estimated optimal policy and corresponding action-value function\n",
    "Q_expsarsa = expected_sarsa(env, 10000, 1)\n",
    "\n",
    "# print the estimated optimal policy\n",
    "policy_expsarsa = np.array([np.argmax(Q_expsarsa[key]) if key in Q_expsarsa else -1 for key in np.arange(48)]).reshape(4,12)\n",
    "check_test.run_check('td_control_check', policy_expsarsa)\n",
    "print(\"\\nEstimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\")\n",
    "print(policy_expsarsa)\n",
    "\n",
    "# plot the estimated optimal state-value function\n",
    "plot_values([np.max(Q_expsarsa[key]) if key in Q_expsarsa else 0 for key in np.arange(48)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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