Temporal_Difference.ipynb

{
 "cells": [
  {
   "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": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import gym\n",
    "import numpy as np\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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def epsilon_greedy_action(state, Q, epsilon):\n",
    "    p = np.random.rand()  # Generate random float between 0 and 1\n",
    "    if p > epsilon: # Pick the optimal action\n",
    "        action = np.argmax(Q[state]) # Pick the best action to date for the given state\n",
    "    else:\n",
    "        action = env.action_space.sample()  # Pick a random action for the policy\n",
    "    return action\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see epsilon in action:\n",
    "https://observablehq.com/@katnoria/visualising-epsilon-decay#:~:text=In%20Reinforcement%20Learning%2C%20epsilon%20an,over%20the%20number%20of%20episodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Visualise explore / exploit balance, tune parameters\n",
    "# num_episodes = 50_000\n",
    "# epsilon = 0.5\n",
    "# decay = 0.9995\n",
    "# e_graph = np.zeros(shape = (num_episodes), dtype=float) # Empty numpy array\n",
    "# step = int(num_episodes/100)\n",
    "# for i_episode in range(1, (num_episodes+1), step):\n",
    "#     e_graph[(i_episode)] = epsilon*(decay**(i_episode-1))\n",
    "# print(\"Terminal epsilon = \", epsilon*(decay**(num_episodes)))\n",
    "# plt.plot(e_graph)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# epsilon = 0.5\n",
    "# num_episodes = 10\n",
    "# explore_fraction = 0.1\n",
    "# for i_episode in range(1,num_episodes+1):\n",
    "#     epsilon_episode = epsilon * (1 - (i_episode-1)/(num_episodes*explore_fraction))\n",
    "#     print(epsilon_episode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def 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",
    "    for state in range(0, env.nS):  # for each possible state\n",
    "        for action in range(0, env.nA):  # and for each possible action\n",
    "            # Initialise all to zero, including the terminal state\n",
    "            Q[state][action] = 0\n",
    "        # TODO can test with all but terminal state large, terminal state zero - remember notes\n",
    "\n",
    "\n",
    "    # loop over episodes\n",
    "    for i_episode in range(1, num_episodes+1):\n",
    "        # monitor progress\n",
    "        if i_episode % 1_000 == 0:\n",
    "            print(\"\\rEpisode {:,}/{:,}\".format(i_episode, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "\n",
    "        # TODO: complete the function\n",
    "        # Allow random exploration, balance exploration with exploitation\n",
    "        # explore_fraction = 0.5 # first % of steps to use higher epsilon\n",
    "        # epsilon = 0.8  # Pick epsilon between 0.05 and 0.1 normally.  This is the start epsilon\n",
    "        # if (i_episode-1)/(num_episodes*explore_fraction) < 0.9: # Hunt for global optima for first xx% of iterations\n",
    "        #     epsilon_episode = epsilon * (1 - (i_episode-1)/(num_episodes*explore_fraction)) # Linearly decrease epsilon\n",
    "        # else:\n",
    "        #     epsilon_episode = 0.01   # Exclusively exploit to converge policy to optimum.  This may not be zero\n",
    "\n",
    "\n",
    "\n",
    "        # epsilon = 0.5 # Pick epsilon between 0.05 and 0.1 normally\n",
    "        # decay = 0.9995\n",
    "        # epsilon_episode = epsilon*(decay**(i_episode-1))\n",
    "        epsilon_episode = 1/i_episode\n",
    "        state_t = env.reset()  # Observe State 0 - state_t is now state zero\n",
    "        # Choose Action 0 based on policy from Q\n",
    "        action_t = epsilon_greedy_action(\n",
    "            state_t, Q, epsilon_episode)  # action_t is now action zero\n",
    "        # Initialise loop\n",
    "        done = False\n",
    "        # Now loop until terminal state is reached\n",
    "        while not done:  # Until terminal state is reached\n",
    "            # Take Action(t), observe R(t+1), S(t+1)\n",
    "            state_t_plus_one, reward_t_plus_one, done, info = env.step(\n",
    "                action_t)\n",
    "            # Choose Action(t+1) using policy derived from Q\n",
    "            action_t_plus_one = epsilon_greedy_action(\n",
    "                state_t_plus_one, Q, epsilon_episode)\n",
    "            Q[state_t][action_t] += alpha * (reward_t_plus_one + gamma * (\n",
    "                Q[state_t_plus_one][action_t_plus_one]) - (Q[state_t][action_t]))\n",
    "            action_t = action_t_plus_one\n",
    "            state_t = state_t_plus_one\n",
    "         \n",
    "\n",
    "    return Q\n"
   ]
  },
  {
   "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": {},
   "outputs": [
    {
     "data": {
      "text/plain": "defaultdict(<function __main__.sarsa.<locals>.<lambda>()>,\n            {0: array([-10.8319362 , -10.83138918, -10.8309906 , -10.83231652]),\n             1: array([-10.35400376, -10.35434369, -10.35412628, -10.35508401]),\n             2: array([-9.71923606, -9.7192016 , -9.71924827, -9.71917399]),\n             3: array([-9.01050848, -9.01000056, -9.01090235, -9.01140463]),\n             4: array([-8.26073649, -8.26006211, -8.26097082, -8.2615024 ]),\n             5: array([-7.48810866, -7.48635664, -7.48643876, -7.48661684]),\n             6: array([-6.69936477, -6.6981871 , -6.69843631, -6.69959963]),\n             7: array([-5.90366366, -5.9030053 , -5.90362099, -5.90299422]),\n             8: array([-5.10900587, -5.10736809, -5.10752658, -5.10773915]),\n             9: array([-4.31929985, -4.31874898, -4.31895924, -4.31929138]),\n             10: array([-3.55161036, -3.55069746, -3.55081653, -3.55116629]),\n             11: array([-2.84798043, -2.84694085, -2.84681448, -2.84716414]),\n             12: array([-11.27045877, -11.27022726, -11.27188995, -11.27157289]),\n             13: array([-10.60498982, -10.60493964, -10.605688  , -10.60514923]),\n             14: array([-9.84523563, -9.84450318, -9.84445573, -9.84550278]),\n             15: array([-9.04080788, -9.04073363, -9.04147972, -9.04144641]),\n             16: array([-8.21141028, -8.21136797, -8.21188527, -8.21199826]),\n             17: array([-7.36508877, -7.36471339, -7.36527529, -7.36516279]),\n             18: array([-6.50605429, -6.50505352, -6.50541736, -6.50599687]),\n             19: array([-5.63426501, -5.63386719, -5.63392888, -5.63469144]),\n             20: array([-4.7517866 , -4.75061247, -4.75052005, -4.75114123]),\n             21: array([-3.85442238, -3.85317099, -3.85313982, -3.85353907]),\n             22: array([-2.93858247, -2.93769818, -2.93774917, -2.93871909]),\n             23: array([-1.99837873, -1.99919606, -1.99754789, -1.99760558]),\n             24: array([-12.00042117, -12.        , -12.00454804, -12.00117084]),\n             25: array([-11.00051519, -11.        , -11.37039964, -11.00197859]),\n             26: array([-10.00043331, -10.        , -10.03812345, -10.00539986]),\n             27: array([-9.00044736, -9.        , -9.13118571, -9.00029063]),\n             28: array([-8.00179462, -8.        , -8.02333928, -8.0006232 ]),\n             29: array([-7.00190577, -7.        , -7.10470375, -7.00118042]),\n             30: array([-6.00259637, -6.        , -6.03686476, -6.00209586]),\n             31: array([-5.00106554, -5.        , -5.00014343, -5.00186517]),\n             32: array([-4.00273067, -4.        , -4.08921301, -4.00478367]),\n             33: array([-3.00302528, -3.        , -3.06179101, -3.00286833]),\n             34: array([-2.00066688, -2.        , -2.2572932 , -2.00786665]),\n             35: array([-1.00012235, -1.00158261, -1.        , -1.00247528]),\n             36: array([-13.        , -13.20303364, -13.00287942, -13.0034344 ]),\n             37: array([0., 0., 0., 0.]),\n             38: array([0., 0., 0., 0.]),\n             39: array([0., 0., 0., 0.]),\n             40: array([0., 0., 0., 0.]),\n             41: array([0., 0., 0., 0.]),\n             42: array([0., 0., 0., 0.]),\n             43: array([0., 0., 0., 0.]),\n             44: array([0., 0., 0., 0.]),\n             45: array([0., 0., 0., 0.]),\n             46: array([0., 0., 0., 0.]),\n             47: array([0., 0., 0., 0.])})"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_sarsa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 500,000/500,000\n",
      "Estimated Optimal Policy (UP = 0, RIGHT = 1, DOWN = 2, LEFT = 3, N/A = -1):\n",
      "[[2 0 3 1 1 1 1 3 1 1 1 2]\n",
      " [1 1 2 1 1 1 1 1 2 2 1 2]\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 0]]\n"
     ]
    },
    {
     "data": {
      "text/markdown": "**<span style=\"color: green;\">PASSED</span>**",
      "text/plain": "<IPython.core.display.Markdown object>"
     },
     "metadata": {
      "transient": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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   "source": [
    "# obtain the estimated optimal policy and corresponding action-value function\n",
    "Q_sarsa = sarsa(env, 500_000, .001)\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)"
   ]
  },
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   "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._)"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def q_learning(env, num_episodes, alpha, gamma=1.0):\n",
    "    # initialize empty dictionary of arrays\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\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",
    "        ## TODO: complete the function\n",
    "        \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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def expected_sarsa(env, num_episodes, alpha, gamma=1.0):\n",
    "    # initialize empty dictionary of arrays\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\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",
    "        ## TODO: complete the function\n",
    "        \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": null,
   "metadata": {},
   "outputs": [],
   "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)])"
   ]
  }
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