SARSAmethod.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Temporal-Difference Methods: SARSA\n",
    "\n",
    "In this notebook you will write your own implementation of SARSA method.\n",
    "\n",
    "---\n",
    "\n",
    "### Part 0: Explore CliffWalkingEnv\n",
    "\n",
    "We begin by importing the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import gym\n",
    "import numpy as np\n",
    "from collections import defaultdict\n",
    "import matplotlib.pyplot as plt\n",
    "import random\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.\n",
    "\n",
    "_**Note**: You can safely ignore the values of the cliff \"states\" as these are not true states from which the agent can make decisions.  For the cliff \"states\", the state-value function is not well-defined._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "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": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def epsilon_greedy(Q, state, nA, eps):\n",
    "    \"\"\"Selects epsilon-greedy action for supplied state.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "        Q (dictionary): action value function, Q[s][a] is the estimated \n",
    "                        action value corresponding to state s and action a.\n",
    "        state (int): current state of the CliffWalkingEnv\n",
    "        nA (int): number of possible actions in the environment\n",
    "        eps(float): epsilon\n",
    "    \"\"\"\n",
    "    \n",
    "    if random.random() > eps:\n",
    "        return np.argmax(Q[state])\n",
    "    else:\n",
    "        return random.choice(np.arange(nA))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    alpha, gamma (float): parameters from the formula defining SARSA method\n",
    "    Q (dictionary): action value function, Q[s][a] is the estimated \n",
    "                    action value corresponding to state s and action a.\n",
    "    state (int): current state S_t\n",
    "    action (int): current action A_t\n",
    "    reward (int): reward R_{t+1}\n",
    "    next_state (int) : next state S_{t+1}\n",
    "    next_action (int): next_action A_{t+1}\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    # Estimate in Q-table (for current state, action pair) Q(S_t,A_t)\n",
    "    current = Q[state][action] \n",
    "    # Get value of state, action pair at next time step Q(S_{t+1},A_{t+1})\n",
    "    Qsa_next = Q[next_state][next_action] if next_state is not None else 0\n",
    "    # Construct TD target R_{t+1} + gamma * Q(S_{t+1},A_{t+1})\n",
    "    target = reward + (gamma * Qsa_next)\n",
    "    # Get updated value Q(S_t,A_t) + alpha * (R_{t+1} + gamma * Q(S_{t+1},A_{t+1}) - Q(S_t,A_t))\n",
    "    new_value = current + alpha * (target - current)\n",
    "    \n",
    "    return new_value\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sarsa(env, num_episodes, alpha, gamma=1.0):\n",
    "    # initialize action-value function (empty dictionary of arrays)\n",
    "    nA = env.action_space.n\n",
    "    Q = defaultdict(lambda: np.zeros(nA))\n",
    "    # initialize performance monitor\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",
    "        \n",
    "        ## ---> COMPLETE THE FUNCTION <---\n",
    "        # Set epsilon\n",
    "        eps = 1.0 / i_episode\n",
    "        # Initialize score\n",
    "        score = 0\n",
    "        # Observe S_0: the initial state is #36\n",
    "        state = env.reset()\n",
    "        # Choose action A_0 using policy derived from Q (e.g., eps-greedy)\n",
    "        action = epsilon_greedy(Q, state, nA, eps)\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",
    "                # Choose action A_{t+1} using policy derived from Q (e.g., eps-greedy)\n",
    "                next_action = epsilon_greedy(Q, next_state, nA, eps) \n",
    "                # Update Q\n",
    "                Q[state][action] = update_Q_sarsa(alpha, gamma, Q, state, action, \n",
    "                                                  reward, next_state, next_action)\n",
    "                # Update state and action\n",
    "                state = next_state     # S_t <- S_{t+1}\n",
    "                action = next_action   # A_t <- A_{t+1}\n",
    "            if done:\n",
    "                Q[state][action] = update_Q_sarsa(alpha, gamma, Q, \n",
    "                                                  state, action, reward)\n",
    "                break \n",
    "    \n",
    "    return Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 500/500\n",
      " best action: 0 \n",
      " action values: [-2.55483932 -2.55805957 -7.54982841 -2.56856832]\n",
      "\n",
      " [[ 3  1  1  1  1  2  3  1  0  2  1  0]\n",
      " [ 1  0  2  0  2  2  1  3  0  0  0  2]\n",
      " [ 3  0  3  3  3  1  0  3  3  0  1  2]\n",
      " [ 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1]]\n"
     ]
    }
   ],
   "source": [
    "# Little test \n",
    "# UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3\n",
    "Q_sarsa = sarsa(env, 500, .01)\n",
    "state_number = 33 # pick a value between 0 and 36\n",
    "print(\"\\n best action:\",np.argmax(Q_sarsa[state_number]),\"\\n action values:\", Q_sarsa[state_number])\n",
    "\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(\"\\n\",policy_sarsa)"
   ]
  },
  {
   "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": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 5000/5000"
     ]
    },
    {
     "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  3  1  2  1  1  1  1  1  1  2]\n",
      " [ 0  2  2  3  1  2  3  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 -1]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "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": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}