exercises/solutions/ex07/LearningAndPlanning.ipynb

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   "source": [
    "# Exercise 7) Learning and Planning"
   ]
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   "source": [
    "In this exercise, we will again investigate the inverted pendulum from the `gym` environment. We want to check, which benefits the implementation of planning offers.\n",
    "\n",
    "Please note that the parameter $n$ has a different meaning in the context of planning (number of planning steps per actual step) than in the context of n-step learning."
   ]
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   "source": [
    "import numpy as np\n",
    "import gym\n",
    "gym.logger.set_level(40)\n",
    "import random\n",
    "import time\n",
    "from tqdm.notebook import tqdm\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-talk')"
   ]
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   "source": [
    "We will reuse the discretization routine from the previous exercise:"
   ]
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   "source": [
    "d_T = 15\n",
    "d_theta = 15\n",
    "d_omega = 15\n",
    "\n",
    "def discretize_state(states):   \n",
    "    limits = [1, 1, 8]\n",
    "    nb_disc_intervals = [d_theta, d_theta, d_omega]\n",
    "    \n",
    "    # bring to value range [-1, 1]\n",
    "    norm_states = [state / limit for state, limit in zip(states, limits)]\n",
    "    interval_lengths = [2 / d for d in nb_disc_intervals]\n",
    "    disc_state = [(norm_state + 1) // interval_length for norm_state, interval_length in zip(norm_states, interval_lengths)]\n",
    "    disc_state = [(state - 1) if state == d else state for state, d in zip(disc_state, nb_disc_intervals)] # ensure that disc_state < d\n",
    "    \n",
    "    return np.array(disc_state)\n",
    "    \n",
    "\n",
    "    \n",
    "    \n",
    "def continualize_action(disc_action):    \n",
    "    limit = 2\n",
    "    interval_length = 2 / (d_T-1)\n",
    "    norm_action = disc_action * interval_length\n",
    "    cont_action = (norm_action - 1) * limit\n",
    "    return np.array(cont_action).flatten()"
   ]
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   "source": [
    "## 1) Dyna-Q"
   ]
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   "source": [
    "Write a Dyna-Q algorithm to solve the inverted pendulum. Check the quality of the result for different number of episodes, number of steps per episode and number of planning steps per interaction.\n",
    "\n",
    "Make sure that the total number of learning steps stays the same for different n, such that comparisons are fair:\n",
    "\n",
    "$\\text{episodes} \\cdot \\text{steps} \\cdot (1+n) = \\text{const.}$\n",
    "\n",
    "Interesting metrics for a comparison could be e.g. the execution time (the tqdm loading bar shows execution time of loops, alternatively you can use the time.time() command to get the momentary system time in seconds) and training stability. \n",
    "\n",
    "![](DynaQ_Algo.png)"
   ]
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   "source": [
    "## Solution 1)"
   ]
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   "source": [
    "The solution code is given below.\n"
   ]
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   "source": [
    "def pendulumDynaQ(alpha, gamma, epsilon, n, nb_episodes, nb_steps):\n",
    "\n",
    "    env = gym.make('Pendulum-v0')\n",
    "    env = env.unwrapped\n",
    "\n",
    "    action_values = np.zeros([d_theta, d_theta, d_omega, d_T])\n",
    "    pi = np.zeros([d_theta, d_theta, d_omega])\n",
    "\n",
    "    model = {} # dictionary\n",
    "\n",
    "    cumulative_reward_history = [] # we can use this to figure out how well the learning worked\n",
    "\n",
    "    for j in tqdm(range(nb_episodes), position=0, leave=True):\n",
    "        \n",
    "        ### BEGIN SOLUTION\n",
    "\n",
    "        rewards = [] # this time, this list is only for monitoring\n",
    "\n",
    "        state = env.reset() # initialize x_0\n",
    "        state = tuple(discretize_state(state).astype(int))\n",
    "\n",
    "        for k in range(nb_steps):\n",
    "\n",
    "            # sample experiences for the model\n",
    "            if np.random.uniform(0, 1) < epsilon:\n",
    "                action = np.random.choice(d_T) # explorative action\n",
    "            else:\n",
    "                action = pi[state].astype(int) # exploitative action        \n",
    "\n",
    "            cont_action = continualize_action(action)\n",
    "            next_state, reward, done, _ = env.step(cont_action)\n",
    "            next_state = tuple(discretize_state(next_state).astype(int))\n",
    "\n",
    "            # learn from the momentary experience\n",
    "            action_values[state][action] += alpha * (reward \n",
    "                                                          + gamma * np.max(action_values[next_state])\n",
    "                                                          - action_values[state][action]\n",
    "                                                         )\n",
    "            pi[state] = np.argmax(action_values[state])\n",
    "            model[state, action] = (next_state, reward) # update the model accoring to the latest experience\n",
    "            state = next_state\n",
    "\n",
    "            rewards.append(reward)     \n",
    "\n",
    "\n",
    "            # learn from the model, IMPORTANT: USE DIFFERENT VARIABLES HERE\n",
    "            for i in range(n):\n",
    "                # sample a random key from the dict: this state action combination has surely been taken in the past\n",
    "                x, u = random.sample(model.keys(), 1)[0]\n",
    "                x_1, r = model[x, u]\n",
    "                action_values[x][u] += alpha * (r \n",
    "                                                + gamma * np.max(action_values[x_1])\n",
    "                                                - action_values[x][u]\n",
    "                                               )\n",
    "                pi[x] = np.argmax(action_values[x])\n",
    "\n",
    "            if done:\n",
    "                break\n",
    "                \n",
    "\n",
    "        cumulative_reward_history.append(np.sum(rewards))\n",
    "\n",
    "    env.close()\n",
    "    \n",
    "    ### END SOLUTION\n",
    "    \n",
    "    return cumulative_reward_history, pi\n",
    "\n"
   ]
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   "source": [
    "Function to evaluate and render the measurement using the gym environment:"
   ]
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   "source": [
    "def experiment(pi,nb_steps = 300):\n",
    "# Runs the inverted pendulum experiment using policy pi for nb_steps steps\n",
    "\n",
    "\n",
    "    env = gym.make('Pendulum-v0')\n",
    "    env = env.unwrapped\n",
    "\n",
    "\n",
    "    state = env.reset() # initialize x_0\n",
    "    disc_state = tuple(discretize_state(state).astype(int)) # only tuples of integers can be used as index \n",
    "    disc_action = pi[disc_state].astype(int)\n",
    "\n",
    "    for k in range(nb_steps):\n",
    "\n",
    "        cont_action = continualize_action(disc_action)\n",
    "        env.render() # comment out for faster execution\n",
    "        state, reward, done, _ = env.step(cont_action)\n",
    "        disc_state = tuple(discretize_state(state).astype(int))\n",
    "\n",
    "        if done:\n",
    "            break\n",
    "\n",
    "        disc_action = pi[disc_state].astype(int) # exploitative action\n",
    "\n",
    "    env.close()"
   ]
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   "source": [
    "Let's use nb_episodes = 5000, nb_steps = 500, n = 0 as a first try. This is effectively Q learning.\n",
    "\n",
    "\\begin{align}\n",
    "5000 \\cdot 500 \\cdot (0+1) &= 2.5 \\cdot 10^6\n",
    "\\end{align}\n",
    "\n",
    "The resulting policy is satisfactory.\n",
    "\n"
   ]
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run without planning\n"
     ]
    },
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       "HBox(children=(FloatProgress(value=0.0, max=5000.0), HTML(value='')))"
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     "name": "stdout",
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     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "### train \n",
    "print(\"Run without planning\")\n",
    "no_planning_history, no_planning_pi = pendulumDynaQ(alpha = 0.1, gamma = 0.9, epsilon = 0.1, n = 0, nb_episodes = 5000, nb_steps = 500)"
   ]
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   "cell_type": "code",
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   },
   "outputs": [],
   "source": [
    "### run and render the experiment\n",
    "experiment(no_planning_pi,nb_steps = 300)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Now let's try $n=9$ with the same nb_steps = 500:\n",
    "\n",
    "\\begin{align}\n",
    "\\text{nb_episodes} &= \\frac{2.5 \\cdot 10^6}{500 \\cdot (9+1)} = 500\n",
    "\\end{align}\n",
    "\n",
    "The resulting policy also looks good.\n",
    "\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
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    "scrolled": true
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run with planning\n"
     ]
    },
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       "HBox(children=(FloatProgress(value=0.0, max=500.0), HTML(value='')))"
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "### train\n",
    "print(\"Run with planning\")\n",
    "with_planning_history, with_planning_pi = pendulumDynaQ(alpha = 0.1, gamma = 0.9, epsilon = 0.1, n = 9, nb_episodes = 500, nb_steps = 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
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   },
   "outputs": [],
   "source": [
    "### run and render the experiment\n",
    "experiment(with_planning_pi,nb_steps = 300)"
   ]
  },
  {
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   },
   "source": [
    "Now lets compare the cumulative rewards:\n"
   ]
  },
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    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 748.8x514.8 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(no_planning_history)\n",
    "plt.plot(with_planning_history)\n",
    "plt.xlabel(\"episode\")\n",
    "plt.ylabel(r\"$\\sum R$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-de1462d7fe9bdbed",
     "locked": false,
     "points": 0,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "\n",
    "The cumulative reward over the episodes both seems to have high variance.\n",
    "\n",
    "So why should we prefer the planning method?\n",
    "### Planning leads to the agent interacting less often with the \"real\" environment, such that in the end fewer interaction time is needed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-2810aacf498563db",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "## 2) Simulation-based planning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-eb709d007371a52d",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Although it can be useful for small state spaces, building a system model by storing large amounts of state transitions like in task (1) is rarely feasible in engineering. As engineers, we are capable of a more efficient way of system modeling that we can utilize here: differential equations.\n",
    "\n",
    "Using a state-space model allows to efficiently integrate existing pre-knowledge into the Dyna-Q algorithm we already used. To do so, write a class `pendulum_model` that implements a model of the pendulum. This class should work similar to `gym`: it should at least have a `step` and a `reset` method. In the step method, make use of forward Euler integration to simulate the system dynamics. In the reset method, allow to pass an optional initial state to the model, such that we can easily compare model and environment. If no initial state is passed to the `reset` function, a random initial state should be determined.\n",
    "\n",
    "Integrate this model into a Dyna-Q algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-4f43d13fe3da4001",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Model of the pendulum in differential-equation form for change of the angular frequency $\\omega$ and the angle $\\theta$ depending on the torque $T_\\mathrm{u}$:\n",
    "\n",
    "\\begin{align}\n",
    "\\dot{\\omega} &= -\\frac{3 g}{2 l} \\text{sin}(\\theta +\\pi) + \\frac{1}{J} T_\\mathrm{u}\n",
    "\\\\\n",
    "\\dot{\\theta} &= \\omega\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "\n",
    "Parameters (gravity constant $g$, mass $m$, length  $l$ and intertia $J$ of the pendulum):\n",
    "\n",
    "\\begin{align}\n",
    "g&=10 \\, \\frac{\\text{m}}{\\text{s}^2}\n",
    "&\n",
    "m&=1 \\, \\text{kg}\n",
    "&\n",
    "l&=1 \\, \\text{m}\n",
    "&\n",
    "J&=\\frac{1}{3} m l^2\n",
    "\\end{align}\n",
    "\n",
    "Forward Euler integration:\n",
    "\n",
    "\\begin{align}\n",
    "\\dot{x}(k T_S) \\approx \\frac{x[k+1] - x[k]}{T_S}\n",
    "\\end{align}\n",
    "\n",
    "with sampling time $T_S = 0.05 \\, \\text{s}$\n",
    "\n",
    "Reward function:\n",
    "\n",
    "\\begin{align}\n",
    "r_{k+1} = -(\\theta^2[k] + 0.1 \\, \\text{s}^2 \\cdot \\omega^2[k] + 0.001 \\frac{1}{(\\text{N}\\text{m})^2} \\cdot T_\\mathrm{u}^2[k])\n",
    "\\end{align}\n",
    "\n",
    "Limitations of state and action space:\n",
    "\\begin{align}\n",
    "\\theta &\\in [-\\pi, \\pi]\n",
    "&\n",
    "\\omega &\\in [-8  \\, \\frac{1}{\\text{s}}, 8  \\, \\frac{1}{\\text{s}}]\n",
    "&\n",
    "T_\\mathrm{u} &\\in [-2 \\, \\text{N}\\text{m}, 2 \\, \\text{N}\\text{m}]\n",
    "\\end{align}\n",
    "\n",
    "And of course input and output space:\n",
    "\\begin{align}\n",
    "\\text{action}&=T_\\mathrm{u}\n",
    "&\n",
    "\\text{state}&=\n",
    "\\begin{bmatrix}\n",
    "\\text{cos}(\\theta)\\\\\n",
    "\\text{sin}(\\theta)\\\\\n",
    "\\omega\n",
    "\\end{bmatrix}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-5b01fba780d2909f",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "## Solution 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-5d0c5a3e7a69720d",
     "locked": false,
     "points": 0,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "Model-based planning does not necessarily run faster than experience-based planning. However, experience-based planning fails to cover the whole state space especially in the earlier episodes when there are too few experiences. On the other hand, model-based planning can, of course, only be performed if a state-space model with accurate parametrization is available. In order to overcome parametric deviations between state-space model and environment, one could even use the measurements from the actual environment in order to identify the parameters of the model during runtime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-11f8cac7e03b7f81",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "class pendulum_model:\n",
    "    def __init__(self, dt=0.05, m=1, g=10, l=1):\n",
    "        \n",
    "        ### BEGIN SOLUTION\n",
    "        \n",
    "        self.max_speed  = 8\n",
    "        self.max_torque = 2\n",
    "\n",
    "        self.dt = dt # sampling time in s\n",
    "        self.g  =  g # gravity in m / s^2\n",
    "        self.m  =  m # mass in kg\n",
    "        self.l  =  l # length in m\n",
    "        \n",
    "        self.J = 1 / 3 * m * l ** 2 # pedulums moment of inertia in kg * m^2\n",
    "        \n",
    "        ### END SOLUTION\n",
    "    \n",
    "    def reset(self, state=None):\n",
    "        \n",
    "        ### BEGIN SOLUTION\n",
    "        \n",
    "        # if no state is give, set randomly\n",
    "        if np.any(state == None):\n",
    "            self.theta = np.random.uniform(-np.pi, +np.pi)\n",
    "            self.omega = np.random.uniform(-self.max_speed, +self.max_speed)\n",
    "                        \n",
    "        # else set initial state as given    \n",
    "        else:\n",
    "            self.theta = np.arctan2(state[1], state[0])\n",
    "            self.omega = state[2]\n",
    "            \n",
    "        state = np.array([np.cos(self.theta), np.sin(self.theta), self.omega])\n",
    "        \n",
    "        ### END SOLUTION\n",
    "        \n",
    "        return state\n",
    "    \n",
    "    def step(self, T_u):\n",
    "        \n",
    "        ### BEGIN SOLUTION\n",
    "        \n",
    "        T_u = np.clip(T_u, -self.max_torque, +self.max_torque)[0]\n",
    "        \n",
    "        reward = -(self.angle_normalize(self.theta)** 2 + 0.1 * self.omega ** 2 + 0.001 * (T_u ** 2))\n",
    "        \n",
    "        # differential-equations for state values\n",
    "        self.omega = self.omega + self.dt * (-3 * self.g/(2 * self.l) * np.sin(self.theta + np.pi) + 1 / self.J * T_u)\n",
    "        self.theta = self.theta + self.dt * self.omega\n",
    "        \n",
    "        self.omega = np.clip(self.omega, -self.max_speed, +self.max_speed)\n",
    "                \n",
    "        state = np.array([np.cos(self.theta), np.sin(self.theta), self.omega])\n",
    "        \n",
    "        ### END SOLUTION\n",
    "        \n",
    "        return state, reward\n",
    "    \n",
    "    def angle_normalize(self, theta):\n",
    "        # usage of this helper function is optional\n",
    "        return (((theta+np.pi) % (2*np.pi)) - np.pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-21f127639f04da34",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "The following cell is for debugging of the `pendulum_model` class. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-1c1d572fbaded77d",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.04729206 -0.9988811  -0.48690693]\n",
      "state: [ 0.04729206 -0.9988811  -0.48690693]\n",
      "model: [ 0.04729206 -0.9988811  -0.48690693]\n",
      "\n",
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    {
     "name": "stdout",
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      "\n",
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      "\n",
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      "state: [ 0.48394513  0.87509834 -3.06394093]\n",
      "model: [-0.80445268  0.59401673 -5.45924434]\n",
      "\n",
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      "state: [ 0.58639508  0.81002519 -2.4288783 ]\n",
      "model: [-0.63190895  0.77504263 -5.01479485]\n",
      "\n",
      "reward difference: 6.117535983032454, env_reward:-1.4845667908435618, model_reward:-7.602102773876015\n",
      "state: [ 0.64759727  0.76198279 -1.5565137 ]\n",
      "model: [-0.44663448  0.89471652 -4.42027059]\n",
      "\n",
      "reward difference: 5.097338265683195, env_reward:-0.9942726507273916, model_reward:-6.091610916410587\n",
      "state: [ 0.69077669  0.72306816 -1.1627145 ]\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-44-779f4446fd2d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"state: {state}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"model: {m_state}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/core/arrayprint.py\u001b[0m in \u001b[0;36m_array_str_implementation\u001b[0;34m(a, max_line_width, precision, suppress_small, array2string)\u001b[0m\n\u001b[1;32m   1504\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0m_guarded_repr_or_str\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__getitem__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1505\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1506\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0marray2string\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax_line_width\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprecision\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msuppress_small\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m' '\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1507\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1508\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/core/arrayprint.py\u001b[0m in \u001b[0;36marray2string\u001b[0;34m(a, max_line_width, precision, suppress_small, separator, prefix, style, formatter, threshold, edgeitems, sign, floatmode, suffix, **kwarg)\u001b[0m\n\u001b[1;32m    710\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0;34m\"[]\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    711\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 712\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0m_array2string\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moptions\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseparator\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprefix\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    713\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    714\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/core/arrayprint.py\u001b[0m in \u001b[0;36mwrapper\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    482\u001b[0m             \u001b[0mrepr_running\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    483\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 484\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    485\u001b[0m             \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    486\u001b[0m                 \u001b[0mrepr_running\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiscard\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/core/arrayprint.py\u001b[0m in \u001b[0;36m_array2string\u001b[0;34m(a, options, separator, prefix)\u001b[0m\n\u001b[1;32m    508\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    509\u001b[0m     \u001b[0;31m# find the right formatting function for the array\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 510\u001b[0;31m     \u001b[0mformat_function\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_get_format_function\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    511\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    512\u001b[0m     \u001b[0;31m# skip over \"[\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/core/arrayprint.py\u001b[0m in \u001b[0;36m_get_format_function\u001b[0;34m(data, **options)\u001b[0m\n\u001b[1;32m    441\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mformatdict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'longfloat'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    442\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 443\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mformatdict\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'float'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    444\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0missubclass\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdtypeobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_nt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcomplexfloating\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    445\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0missubclass\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdtypeobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_nt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclongfloat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/core/arrayprint.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m()\u001b[0m\n\u001b[1;32m    380\u001b[0m         \u001b[0;34m'int'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mlambda\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mIntegerFormat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    381\u001b[0m         \u001b[0;34m'float'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mlambda\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 382\u001b[0;31m             \u001b[0mFloatingFormat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfmode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msupp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msign\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlegacy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlegacy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    383\u001b[0m         \u001b[0;34m'longfloat'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mlambda\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    384\u001b[0m             \u001b[0mFloatingFormat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfmode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msupp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msign\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlegacy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlegacy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/core/arrayprint.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, precision, floatmode, suppress_small, sign, **kwarg)\u001b[0m\n\u001b[1;32m    879\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlarge_exponent\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    880\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 881\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfillFormat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    882\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    883\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfillFormat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/core/arrayprint.py\u001b[0m in \u001b[0;36mfillFormat\u001b[0;34m(self, data)\u001b[0m\n\u001b[1;32m    936\u001b[0m                                        sign=self.sign == '+')\n\u001b[1;32m    937\u001b[0m                     for x in finite_vals)\n\u001b[0;32m--> 938\u001b[0;31m             \u001b[0mint_part\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfrac_part\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'.'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstrs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    939\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_legacy\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'1.13'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    940\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpad_left\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlstrip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'-+'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mint_part\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/core/arrayprint.py\u001b[0m in \u001b[0;36m<genexpr>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m    936\u001b[0m                                        sign=self.sign == '+')\n\u001b[1;32m    937\u001b[0m                     for x in finite_vals)\n\u001b[0;32m--> 938\u001b[0;31m             \u001b[0mint_part\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfrac_part\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'.'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstrs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    939\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_legacy\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'1.13'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    940\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpad_left\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlstrip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'-+'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mint_part\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.7/site-packages/numpy/core/arrayprint.py\u001b[0m in \u001b[0;36m<genexpr>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m    935\u001b[0m                                        \u001b[0munique\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0munique\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtrim\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtrim\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    936\u001b[0m                                        sign=self.sign == '+')\n\u001b[0;32m--> 937\u001b[0;31m                     for x in finite_vals)\n\u001b[0m\u001b[1;32m    938\u001b[0m             \u001b[0mint_part\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfrac_part\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'.'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstrs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    939\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_legacy\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'1.13'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "env = gym.make('Pendulum-v0')\n",
    "env = env.unwrapped # removes a builtin time limit of k_T = 200, we want to determine the time limit ourselves\n",
    "\n",
    "model = pendulum_model()\n",
    "\n",
    "state = env.reset()\n",
    "print(state)\n",
    "m_state = model.reset(state) # model is set to state of env\n",
    "\n",
    "for _ in range(10000):    \n",
    "    print(f\"state: {state}\")\n",
    "    print(f\"model: {m_state}\")\n",
    "    print()\n",
    "    \n",
    "    action = env.action_space.sample()\n",
    "    \n",
    "    state, reward, done, _ = env.step(action) # take action on env\n",
    "    m_state, m_reward = model.step(action) # take the same action on model\n",
    "    \n",
    "    print(f\"reward difference: {reward- m_reward}, env_reward:{reward}, model_reward:{m_reward}\")\n",
    "    \n",
    "env.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-48d9727d1bcf9cba",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Using $-\\mathrm{sin}(\\theta)$ instead of $\\mathrm{sin}(\\theta +\\pi)$ makes no difference when assuming analytical precision, but due to numeric errors these formulations will still yield different results in numpy, mainly because $\\pi$ is represented with finite (float) precision. In order to yield the same numbers as in `gym`, we will still make use of the (more cumbersome) $\\mathrm{sin}(\\theta +\\pi)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-0a63f527a46b3115",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Write a function for the Dyna-Q algorithm, which uses the model we defined above: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-ab054c945a614362",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def pendulumModelDynaQ(alpha, gamma, epsilon, n, nb_episodes, nb_steps):\n",
    "\n",
    "    env = gym.make('Pendulum-v0')\n",
    "    env = env.unwrapped\n",
    "    model = pendulum_model()\n",
    "\n",
    "    action_values = np.zeros([d_theta, d_theta, d_omega, d_T])\n",
    "    pi = np.zeros([d_theta, d_theta, d_omega])\n",
    "\n",
    "    cumulative_reward_history = [] # we can use this to figure out how well the learning worked\n",
    "\n",
    "    for j in tqdm(range(nb_episodes), position=0, leave=True):\n",
    "        \n",
    "        ### BEGIN SOLUTION\n",
    "\n",
    "        rewards = [] # this time, this list is only for monitoring\n",
    "\n",
    "        state = env.reset() # initialize x_0\n",
    "        state = tuple(discretize_state(state).astype(int))\n",
    "\n",
    "        for k in range(nb_steps):\n",
    "\n",
    "            # sample experiences for the model\n",
    "            if np.random.uniform(0, 1) < epsilon:\n",
    "                action = np.random.choice(d_T) # explorative action\n",
    "            else:\n",
    "                action = pi[state].astype(int) # exploitative action        \n",
    "\n",
    "            cont_action = continualize_action(action)\n",
    "            next_state, reward, done, _ = env.step(cont_action)\n",
    "            next_state = tuple(discretize_state(next_state).astype(int))\n",
    "\n",
    "            # learn from the momentary experience\n",
    "            action_values[state][action] += alpha * (reward \n",
    "                                                          + gamma * np.max(action_values[next_state])\n",
    "                                                          - action_values[state][action]\n",
    "                                                         )\n",
    "            pi[state] = np.argmax(action_values[state])\n",
    "            # no model update is needed\n",
    "            state = next_state\n",
    "\n",
    "            rewards.append(reward)     \n",
    "\n",
    "\n",
    "            # learn from the model, IMPORTANT: USE DIFFERENT VARIABLES HERE\n",
    "            for i in range(n):\n",
    "                x = model.reset() # if no state is passed to the model, state is initialized randomly\n",
    "                u_d = np.random.choice(d_T)\n",
    "                                       \n",
    "                x_d = tuple(discretize_state(x).astype(int))\n",
    "                u = continualize_action(u_d)\n",
    "                \n",
    "                x_1, r = model.step(u)\n",
    "                x_1_d = tuple(discretize_state(x_1).astype(int))\n",
    "                action_values[x_d][u_d] += alpha * (r \n",
    "                                                    + gamma * np.max(action_values[x_1_d])\n",
    "                                                    - action_values[x_d][u_d]\n",
    "                                                    )\n",
    "                pi[x_d] = np.argmax(action_values[x_d])\n",
    "\n",
    "            if done:\n",
    "                break\n",
    "               \n",
    "\n",
    "        cumulative_reward_history.append(np.sum(rewards))\n",
    "       \n",
    "    env.close()\n",
    "    \n",
    "    ### END SOLUTION\n",
    "    \n",
    "    return cumulative_reward_history, pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-6f4a8238fb568bf1",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Use the following cell to compare the learing from experience from 1) to the learning using the defined model: (Beware, nb_steps = 10000 can take some time)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-55a20ee55df4b168",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Run with planning from experience\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f37e922335fb48baa58e845411591000",
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       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=30.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Run with planning from model\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "66b22229ef1c4ef59b0979adcef80620",
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       "HBox(children=(FloatProgress(value=0.0, max=30.0), HTML(value='')))"
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 748.8x514.8 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### train both setups once\n",
    "print(\"Run with planning from experience\")\n",
    "exp_planning_history, exp_planning_pi = pendulumDynaQ(alpha = 0.1, gamma = 0.9, epsilon = 0.1, n = 19, nb_episodes = 30, nb_steps = 10000)\n",
    "\n",
    "print(\"Run with planning from model\")\n",
    "model_planning_history, model_planning_pi = pendulumModelDynaQ(alpha = 0.1, gamma = 0.9, epsilon = 0.1, n = 19, nb_episodes = 30, nb_steps = 10000)\n",
    "    \n",
    "\n",
    "\n",
    "plt.plot(exp_planning_history)\n",
    "plt.plot(model_planning_history)\n",
    "plt.xlabel(\"episode\")\n",
    "plt.ylabel(r\"$\\sum R$\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-1a7bfac51c16c83f",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "Use the following cell to execute the policy we got using the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-05c7abf525fbaa40",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "experiment(model_planning_pi,nb_steps = 300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-54c9b97a5d245359",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "### Extra-task:\n",
    "Change the model parameters (e.g. $g$, $m$, $l$) so that our model differs from the \"real world\" (we got from gym).\n",
    "What do you observe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-ce6069a5b3db12d1",
     "locked": true,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "source": [
    "By changing the parameters our model differs from the \"real world\". Depending on the amount of difference, the learing curve looks worse than the one with the correct values. \n",
    "The experiment result is also depending on the random starting position. \n",
    "Depending on the parameter difference, the experiment can not be executed successfully any more. \n",
    "\n",
    "Try to change the parameters on your own."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": true,
     "grade_id": "cell-35f013c58ce9bdca",
     "locked": false,
     "points": 0,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "The Following learning curve results from a parameter change using $g =20 \\, \\frac{\\text{m}}{\\text{s}^2}, m = 5 \\, \\text{kg and } l = 2 \\, \\text{m}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "cell-27a52b7e54657710",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 748.8x514.8 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(exp_planning_history, label=\"exp\")\n",
    "plt.plot(model_planning_history, label=\"model\")\n",
    "plt.xlabel(\"episode\")\n",
    "plt.ylabel(r\"$\\sum R$\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Create Assignment",
  "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}