temporal-difference/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": 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": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6920a53c18>"
      ]
     },
     "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 get_greedy_action(Q, state):\n",
    "    # if there are two or more actions for which Q[s][a] is maximized, choose uniformly between them\n",
    "    greedy_actions = np.argwhere(Q[state] == np.amax(Q[state]))\n",
    "    greedy_actions = greedy_actions.flatten()\n",
    "    return np.random.choice(greedy_actions)\n",
    "\n",
    "def get_random_action(Q, state):\n",
    "    return np.random.choice(np.arange(Q[state].size))\n",
    "\n",
    "def eps_greedy_policy(Q, state, eps):\n",
    "    return get_random_action(Q, state) if np.random.uniform() <= eps \\\n",
    "        else get_greedy_action(Q, state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sarsa(env, num_episodes, alpha, gamma=1.0, eps=1, final_eps=0.1, stop_eps_after=0.5):\n",
    "    # initialize action-value function (empty dictionary of arrays)\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\n",
    "    \n",
    "    # eps will decrease linearly and reach final_eps in episode stop_eps_at_episode\n",
    "    final_eps = min(eps, final_eps)\n",
    "    stop_eps_at_episode = num_episodes * stop_eps_after - 1\n",
    "    eps_delta = (eps - final_eps) / stop_eps_at_episode\n",
    "    \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",
    "        S_t = env.reset()  # get initial state S_t\n",
    "        A_t = eps_greedy_policy(Q, S_t, eps)  # choose initial action A_t\n",
    "        \n",
    "        while True:\n",
    "            \n",
    "            S_t1, R_t1, done, _ = env.step(A_t)  # execute A_t, get R_t+1, S_t+1\n",
    "            \n",
    "            if done:\n",
    "                # if the episode is completed, update Q[S_t][A_t] using an estimated return of zero\n",
    "                Q[S_t][A_t] += alpha * (R_t1 - Q[S_t][A_t])\n",
    "                break\n",
    "            \n",
    "            A_t1 = eps_greedy_policy(Q, S_t1, eps)  # choose action A_t+1\n",
    "            \n",
    "            # update Q[S_t][A_t] using the estimated return from Q[S_t+1][A_t+1]\n",
    "            Q[S_t][A_t] += alpha * (R_t1 + gamma * Q[S_t1][A_t1] - Q[S_t][A_t])\n",
    "            \n",
    "            S_t = S_t1\n",
    "            A_t = A_t1\n",
    "        \n",
    "        eps -= eps_delta\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": 7,
   "metadata": {},
   "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",
      "[[ 3  2  0  2  2  2  1  1  1  1  2  3]\n",
      " [ 0  3  1  1  1  1  1  1  1  2  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 0x7f6920a532e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# obtain the estimated optimal policy and corresponding action-value function\n",
    "Q_sarsa = sarsa(env, 5000, .01, eps=0.01)  # eps=.1 safe path, eps = .01 optimal path\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": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def q_learning(env, num_episodes, alpha, gamma=1.0, eps=1, final_eps=0.1, stop_eps_after=0.5):\n",
    "    # initialize empty dictionary of arrays\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\n",
    "\n",
    "    # eps will decrease linearly and reach final_eps in episode stop_eps_at_episode\n",
    "    stop_eps_at_episode = num_episodes * stop_eps_after - 1\n",
    "    eps_delta = (eps - final_eps) / stop_eps_at_episode\n",
    "    \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",
    "        S_t = env.reset()  # get initial state S_t\n",
    "        \n",
    "        done = False\n",
    "        while not done:\n",
    "            \n",
    "            A_t = eps_greedy_policy(Q, S_t, eps)  # choose action A_t according to the behaviour policy\n",
    "            S_t1, R_t1, done, _ = env.step(A_t)  # execute A_t, get R_t+1, S_t+1\n",
    "            \n",
    "            A_max = get_greedy_action(Q, S_t1)  # choose A_max according to the target policy\n",
    "            # update Q[S_t][A_t] using the estimated return from Q[S_t+1][A_max]\n",
    "            Q[S_t][A_t] += alpha * (R_t1 + gamma * Q[S_t1][A_max] - Q[S_t][A_t])\n",
    "            \n",
    "            S_t = S_t1\n",
    "        \n",
    "        eps -= eps_delta\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": 9,
   "metadata": {},
   "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  3  1  1  0  1  0  1  0  1  1  2]\n",
      " [ 2  2  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 0x7f691e91ebe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# obtain the estimated optimal policy and corresponding action-value function\n",
    "Q_sarsamax = q_learning(env, 5000, .01, eps=0.1)\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": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_estimated_return_for_eps_greedy_policy(Q, state, eps):\n",
    "    prob = np.ones(Q[state].shape) * (eps / Q[state].size)  # pi(a|s) = eps/|A(s)|  else\n",
    "    prob[np.argmax(Q[state])] = 1 - eps + eps / Q[state].size  # pi(a|s) = 1 - eps + eps/|A(s)|  for greedy\n",
    "    return np.dot(prob, Q[state])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_sarsa(env, num_episodes, alpha, gamma=1.0, eps=1, final_eps=0.1, stop_eps_after=0.5):\n",
    "    # initialize empty dictionary of arrays\n",
    "    Q = defaultdict(lambda: np.zeros(env.nA))\n",
    "    \n",
    "    # eps will decrease linearly and reach final_eps in episode stop_eps_at_episode\n",
    "    stop_eps_at_episode = num_episodes * stop_eps_after - 1\n",
    "    eps_delta = (eps - final_eps) / stop_eps_at_episode\n",
    "    \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",
    "        S_t = env.reset()  # get initial state S_t\n",
    "\n",
    "        done = False\n",
    "        while not done:\n",
    "            \n",
    "            A_t = eps_greedy_policy(Q, S_t, eps)  # choose action A_t according to the behaviour policy\n",
    "            S_t1, R_t1, done, _ = env.step(A_t)  # execute A_t, get R_t+1, S_t+1\n",
    "            \n",
    "            G = get_estimated_return_for_eps_greedy_policy(Q, S_t1, eps)\n",
    "            Q[S_t][A_t] += alpha * (R_t1 + gamma * G - Q[S_t][A_t])  # update Q[S_t][A_t] using G\n",
    "            \n",
    "            S_t = S_t1\n",
    "        \n",
    "        eps -= eps_delta\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": 12,
   "metadata": {},
   "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",
      "[[ 1  1  1  1  1  1  0  1  1  3  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 0x7f691e9814e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# obtain the estimated optimal policy and corresponding action-value function\n",
    "Q_expsarsa = expected_sarsa(env, 5000, 0.5, eps=0.01, final_eps=0.001)  # higher alpha but lower eps\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": []
  }
 ],
 "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
}