TD_Methods.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reinforcement Learning using Temporal-Difference Methods\n",
    "\n",
    "In this notebook, I have written an implementation of many Temporal-Difference (TD) methods for solving Markov Decision Process (MDPs).\n",
    "\n",
    "For ilustrate, and testing the differents algorithms I have solved the [CliffWalking](https://github.com/openai/gym/blob/master/gym/envs/toy_text/cliffwalking.py) environment."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CliffWalking Environmet\n",
    "    \n",
    "    This is a simple implementation of the Gridworld Cliff\n",
    "    reinforcement learning task.\n",
    "    Adapted from Example 6.6 (page 106) from Reinforcement Learning: An Introduction\n",
    "    by Sutton and Barto:\n",
    "    http://incompleteideas.net/book/bookdraft2018jan1.pdf\n",
    "    With inspiration from:\n",
    "    https://github.com/dennybritz/reinforcement-learning/blob/master/lib/envs/cliff_walking.py\n",
    "    The board is a 4x12 matrix, with (using Numpy matrix indexing):\n",
    "        [3, 0] as the start at bottom-left\n",
    "        [3, 11] as the goal at bottom-right\n",
    "        [3, 1..10] as the cliff at bottom-center\n",
    "    Each time step incurs -1 reward, and stepping into the cliff incurs -100 reward\n",
    "    and a reset to the start. An episode terminates when the agent reaches the goal.\n",
    "    \n",
    "+info: [CliffWalking](https://github.com/openai/gym/blob/master/gym/envs/toy_text/cliffwalking.py)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 0: Explore CliffWalkingEnv\n",
    "\n",
    "Creating an instance of the [CliffWalking](https://github.com/openai/gym/blob/master/gym/envs/toy_text/cliffwalking.py) environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gym\n",
    "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 $\\mathcal{A} =\\{0, 1, 2, 3\\}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": [
    "If we observe the environment, we could know what is the optimal state-value function. This function is visualized below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcce64ba668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from plot_utils import plot_values\n",
    "%matplotlib inline\n",
    "\n",
    "#<-Define the optimal state-value function->#\n",
    "V_opt = np.zeros((4,12))\n",
    "V_opt[0] = -np.arange(3, 15)[::-1]\n",
    "V_opt[1] = -np.arange(3, 15)[::-1] + 1\n",
    "V_opt[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 Prediction: State Values\n",
    "\n",
    "In this section, I have coded an implementation of TD prediction (for estimating the state-value function).\n",
    "\n",
    "We will begin by investigating a policy where the agent moves:\n",
    "- `RIGHT` in states `0` through `10`, inclusive,  \n",
    "- `DOWN` in states `11`, `23`, and `35`, and\n",
    "- `UP` in states `12` through `22`, inclusive, states `24` through `34`, inclusive, and state `36`.\n",
    "\n",
    "The policy is specified and printed below.  Note that states where the agent does not choose an action have been marked with `-1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  2.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  2.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  2.]\n",
      " [ 0. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.]]\n"
     ]
    }
   ],
   "source": [
    "policy = np.hstack([1*np.ones(11), 2, 0, np.zeros(10), 2, 0, np.zeros(10), 2, 0, -1*np.ones(11)])\n",
    "print(\"\\nPolicy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\")\n",
    "print(policy.reshape(4,12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcce64ba550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "V_true = np.zeros((4,12))\n",
    "for i in range(3):\n",
    "    V_true[0:12][i] = -np.arange(3, 15)[::-1] - i\n",
    "V_true[1][11] = -2\n",
    "V_true[2][11] = -1\n",
    "V_true[3][0] = -17\n",
    "\n",
    "plot_values(V_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithm for TD prediction has five 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",
    "- `policy`: This is a 1D numpy array with `policy.shape` equal to the number of states (`env.nS`).  `policy[s]` returns the action that the agent chooses when in state `s`.\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",
    "- `V`: This is a dictionary where `V[s]` is the estimated value of state `s`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict, deque\n",
    "import sys\n",
    "\n",
    "def td_prediction(env, num_episodes, policy, alpha, gamma=1.0):\n",
    "    ###################\n",
    "    # TD(0) Algorithm #\n",
    "    ###################\n",
    "    \n",
    "    ##<--Initialize empty dictionaries of floats-->##\n",
    "    V = defaultdict(float)\n",
    "    ##<--Loop over episodes-->##\n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        if i_episode % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}\".format(i_episode, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "        state = env.reset()\n",
    "        while True:\n",
    "            #<--Choose action A-->#\n",
    "            action = policy[state]\n",
    "            #<--Observe state and reward for the action-->#\n",
    "            next_state, reward, done, info = env.step(action)\n",
    "            #<--Update values-->#\n",
    "            V[state] = V[state] + (alpha * (reward + (gamma * V[next_state]) - V[state]))            \n",
    "            state = next_state\n",
    "            #<--If terminal state is reached, finish episode-->#\n",
    "            if done:\n",
    "                break        \n",
    "    return V "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cell below tests the implementation and visualize the estimated state-value function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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 0x7fcce64ba0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import check_test\n",
    "\n",
    "#<-Evaluate the policy and reshape the state-value function->#\n",
    "V_pred = td_prediction(env, 5000, policy, .01)\n",
    "\n",
    "#<-Please do not change the code below this line->#\n",
    "V_pred_plot = np.reshape([V_pred[key] if key in V_pred else 0 for key in np.arange(48)], (4,12)) \n",
    "plot_values(V_pred_plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2: TD Control: Sarsa\n",
    "\n",
    "In this section, I have coded an implementation of the Sarsa control algorithm.\n",
    "\n",
    "The 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`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_Q(Qsa, Qsa_next, reward, alpha, gamma):\n",
    "    ##############################################################################\n",
    "    # Updates the action-value function estimate using the most recent time step #\n",
    "    ##############################################################################\n",
    "    return Qsa + (alpha * (reward + (gamma * Qsa_next) - Qsa))\n",
    "\n",
    "def epsilon_greedy_probs(env, Q_s, i_episode, eps=None):\n",
    "    ###########################################################################\n",
    "    # Obtains the action probabilities corresponding to epsilon-greedy policy #\n",
    "    ###########################################################################\n",
    "    \n",
    "    epsilon = 1.0 / i_episode\n",
    "    if eps is not None:\n",
    "        epsilon = eps\n",
    "    policy_s = np.ones(env.nA) * epsilon / env.nA\n",
    "    policy_s[np.argmax(Q_s)] = 1 - epsilon + (epsilon / env.nA)\n",
    "    return policy_s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def sarsa(env, num_episodes, alpha, gamma=1.0):\n",
    "    ######################\n",
    "    # SARSA(0) Algorithm #\n",
    "    ######################\n",
    "    \n",
    "    ###<-Initialize action-value function (empty dictionary of arrays)->###\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\n",
    "    ###<-Initialize performance monitor->###\n",
    "    plot_every = 100\n",
    "    tmp_scores = deque(maxlen=plot_every)\n",
    "    scores = deque(maxlen=num_episodes)\n",
    "    ###<-Loop over episodes->###\n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        if i_episode % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}\".format(i_episode, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()   \n",
    "        ##<-Initialize score->##\n",
    "        score = 0\n",
    "        ##<-Begin an episode, observe S->##\n",
    "        state = env.reset()   \n",
    "        ##<-Get epsilon-greedy action probabilities->##\n",
    "        policy_s = epsilon_greedy_probs(env, Q[state], i_episode)\n",
    "        ##<-Pick action A->##\n",
    "        action = np.random.choice(np.arange(env.nA), p=policy_s)\n",
    "        ##<-Limit number of time steps per episode->##\n",
    "        for t_step in np.arange(300):\n",
    "            #<-Take action A, observe R, S'->#\n",
    "            next_state, reward, done, info = env.step(action)\n",
    "            #<-Add reward to score->#\n",
    "            score += reward\n",
    "            if not done:\n",
    "                #Get epsilon-greedy action probabilities\n",
    "                policy_s = epsilon_greedy_probs(env, Q[next_state], i_episode)\n",
    "                #Pick next action A'\n",
    "                next_action = np.random.choice(np.arange(env.nA), p=policy_s)\n",
    "                #Update values\n",
    "                Q[state][action] = update_Q(Q[state][action], Q[next_state][next_action], \n",
    "                                            reward, alpha, gamma)\n",
    "                state = next_state\n",
    "                action = next_action\n",
    "                \n",
    "            if done:\n",
    "                #Update TD estimate of Q\n",
    "                Q[state][action] = update_Q(Q[state][action], 0, reward, alpha, gamma)\n",
    "                #Append score\n",
    "                tmp_scores.append(score)\n",
    "                break\n",
    "                \n",
    "        if (i_episode % plot_every == 0):\n",
    "            scores.append(np.mean(tmp_scores))\n",
    "            \n",
    "    ###<-Plot performance->###\n",
    "    plt.plot(np.linspace(0,num_episodes,len(scores),endpoint=False),np.asarray(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(scores))\n",
    "    return Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cell below tests the implementation and visualize the estimated optimal policy and the corresponding state-value function.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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 0x7fccda64bdd8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Average Reward over 100 Episodes:  -13.0\n",
      "\n",
      "Estimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 1  1  2  1  1  1  1  0  0  3  1  2]\n",
      " [ 1  1  1  1  1  1  2  1  2  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 0x7fccda64b6a0>"
      ]
     },
     "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",
    "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 3: TD Control: Q-learning\n",
    "\n",
    "In this section,I have coded an 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`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def q_learning(env, num_episodes, alpha, gamma=1.0):\n",
    "    ######################\n",
    "    # SARSAMAX Algorithm #\n",
    "    ######################\n",
    "    \n",
    "    ###<-Initialize action-value function (empty dictionary of arrays)->###\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\n",
    "    ###<-Initialize performance monitor->###\n",
    "    plot_every = 100\n",
    "    tmp_scores = deque(maxlen=plot_every)\n",
    "    scores = deque(maxlen=num_episodes)\n",
    "    ###<-Loop over episodes->###\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",
    "        ##<-Initialize score->##\n",
    "        score = 0\n",
    "        ##<-Begin an episode, observe S->##\n",
    "        state = env.reset()\n",
    "        while True:\n",
    "            #<-Get epsilon-greedy action probabilities->#\n",
    "            policy_s = epsilon_greedy_probs(env, Q[state], i_episode)\n",
    "            #<-Pick next action A->#\n",
    "            action = np.random.choice(np.arange(env.nA), p=policy_s)\n",
    "            #<-Take action A, observe R, S'->#\n",
    "            next_state, reward, done, info = env.step(action)\n",
    "            #<-Add reward to score->#\n",
    "            score += reward\n",
    "            #<-Update values->#\n",
    "            Q[state][action] = update_Q(Q[state][action], np.max(Q[next_state]), \\\n",
    "                                                  reward, alpha, gamma)        \n",
    "            state = next_state\n",
    "            #<-Until S is terminal->#\n",
    "            if done:\n",
    "                #Append score\n",
    "                tmp_scores.append(score)\n",
    "                break\n",
    "        if (i_episode % plot_every == 0):\n",
    "            scores.append(np.mean(tmp_scores))\n",
    "    ###<-Plot performance->###\n",
    "    plt.plot(np.linspace(0,num_episodes,len(scores),endpoint=False),np.asarray(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(scores))\n",
    "    return Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cell below tests the implementation and visualize the estimated optimal policy and the corresponding state-value function.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 5000/5000"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccda55c550>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Average Reward over 100 Episodes:  -13.0\n",
      "\n",
      "Estimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 0  0  1  1  1  0  1  2  3  2  1  2]\n",
      " [ 0  1  1  1  0  0  1  1  0  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 0x7fccda55ca20>"
      ]
     },
     "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",
    "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 4: TD Control: Expected Sarsa\n",
    "\n",
    "In this section, I have coded an implementation of the Expected Sarsa control algorithm.\n",
    "\n",
    "The 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`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_sarsa(env, num_episodes, alpha, gamma=1.0):\n",
    "    ###<-Initialize action-value function (empty dictionary of arrays)->###\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\n",
    "    ###<-Initialize performance monitor->###\n",
    "    plot_every = 100\n",
    "    tmp_scores = deque(maxlen=plot_every)\n",
    "    scores = deque(maxlen=num_episodes)\n",
    "    ###<-Loop over episodes->###\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",
    "        ##<-Initialize score->##\n",
    "        score = 0\n",
    "        ##<-Begin an episode->##\n",
    "        state = env.reset()\n",
    "        ##<-Get epsilon-greedy action probabilities->##\n",
    "        policy_s = epsilon_greedy_probs(env, Q[state], i_episode, 0.005)\n",
    "        while True:\n",
    "            #<-Pick next action->#\n",
    "            action = np.random.choice(np.arange(env.nA), p=policy_s)\n",
    "            #<-Take action A, observe R, S'->#\n",
    "            next_state, reward, done, info = env.step(action)\n",
    "            #<-Add reward to score->#\n",
    "            score += reward\n",
    "            #<-Get epsilon-greedy action probabilities (for S')->#\n",
    "            policy_s = epsilon_greedy_probs(env, Q[next_state], i_episode, 0.005)\n",
    "            #<-Update values->#\n",
    "            Q[state][action] = update_Q(Q[state][action], np.dot(Q[next_state], policy_s), \\\n",
    "                                                  reward, alpha, gamma)        \n",
    "            state = next_state\n",
    "            #<-Until S is terminal->#\n",
    "            if done:\n",
    "                #Append score\n",
    "                tmp_scores.append(score)\n",
    "                break\n",
    "        if (i_episode % plot_every == 0):\n",
    "            scores.append(np.mean(tmp_scores))\n",
    "    ###<-Plot performance->###\n",
    "    plt.plot(np.linspace(0,num_episodes,len(scores),endpoint=False),np.asarray(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(scores))\n",
    "    return Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cell below tests the implementation and visualize the estimated optimal policy and the corresponding state-value function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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 0x7fccda4596d8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Average Reward over 100 Episodes:  -13.0\n",
      "\n",
      "Estimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[ 0  1  3  1  1  1  1  1  1  1  1  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 0x7fccda3bdeb8>"
      ]
     },
     "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",
    "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)])"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}