4_ReinforcementLearning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ddcd727a",
   "metadata": {},
   "source": [
    "### Reinforcement Learning Mechanisms "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92b61ac9",
   "metadata": {},
   "source": [
    "This notebook is based on Aurelion Geron's \n",
    "Hands-On Machine Learning with Scikit-Learn & Tensorflow, Chapter 18. Includes notes made during my own study of the material and it accompanies my article: https://t.co/9k9jwKYaPc \n",
    "\n",
    "His notebook: https://github.com/ageron/handson-ml2/blob/3cffb49fffb4d79db5e68de1fc5f91d5e74262e8/18_reinforcement_learning.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "ec98ef5b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: gym in /Users/tdubon/opt/anaconda3/lib/python3.9/site-packages (0.22.0)\n",
      "Requirement already satisfied: importlib-metadata>=4.10.0 in /Users/tdubon/opt/anaconda3/lib/python3.9/site-packages (from gym) (4.11.1)\n",
      "Requirement already satisfied: gym-notices>=0.0.4 in /Users/tdubon/opt/anaconda3/lib/python3.9/site-packages (from gym) (0.0.4)\n",
      "Requirement already satisfied: cloudpickle>=1.2.0 in /Users/tdubon/opt/anaconda3/lib/python3.9/site-packages (from gym) (2.0.0)\n",
      "Requirement already satisfied: numpy>=1.18.0 in /Users/tdubon/opt/anaconda3/lib/python3.9/site-packages (from gym) (1.19.5)\n",
      "Requirement already satisfied: zipp>=0.5 in /Users/tdubon/opt/anaconda3/lib/python3.9/site-packages (from importlib-metadata>=4.10.0->gym) (3.6.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install gym"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "b1f328b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: pygame in /Users/tdubon/opt/anaconda3/lib/python3.9/site-packages (2.1.2)\r\n"
     ]
    }
   ],
   "source": [
    "!pip install pygame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3b8228e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import gym"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cf1ffc5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f1ea2c27",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pygame"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a738dfb5",
   "metadata": {},
   "source": [
    "Create the environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2f3996b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make(\"CartPole-v1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "000698aa",
   "metadata": {},
   "source": [
    "Initialize the simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fa24c55f",
   "metadata": {},
   "outputs": [],
   "source": [
    "obs = env.reset()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e275f65e",
   "metadata": {},
   "source": [
    "Return 1D numpy array of observations: \n",
    "cart's horizontal position, \n",
    "velocity, \n",
    "angle of the pole, \n",
    "angular velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "094f3df7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.01484308, -0.02171928,  0.03367683, -0.0356262 ], dtype=float32)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b5fad9c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.render()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29d6b436",
   "metadata": {},
   "source": [
    "What actions are possible? Discrete(2) means poss. actions are 0 (accelerating left) and 1 (accelerating right)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "946c691b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Discrete(2)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.action_space"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "897fdd9a",
   "metadata": {},
   "source": [
    "env.step executes the action. Accelerate to the right since pole is leaning right. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b8e98ac8",
   "metadata": {},
   "outputs": [],
   "source": [
    "action = 1\n",
    "obs, reward, done, info = env.step(action)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "19f4a56a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.01440869,  0.17290395,  0.03296431, -0.31749642], dtype=float32)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#new observations\n",
    "obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2b8c9549",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#reward of 1 at every step\n",
    "reward"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be4adfd4",
   "metadata": {},
   "source": [
    "If this value=True, the episode is over and the env must be reset as the pole is too tilted to move forward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e5002ef1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "done"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf5d7d54",
   "metadata": {},
   "source": [
    "Defining base policy "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2c0c8e5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def basic_policy(obs):\n",
    "    angle = obs[2]\n",
    "    return 0 if angle < 0 else 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d6fdf081",
   "metadata": {},
   "outputs": [],
   "source": [
    "totals = []\n",
    "for episode in range(500):\n",
    "    episode_rewards = 0\n",
    "    obs = env.reset()\n",
    "    for step in range(1000):\n",
    "        action = basic_policy(obs)\n",
    "        obs, reward, done, info = env.step(action)\n",
    "        episode_rewards += reward\n",
    "        if done:\n",
    "            break\n",
    "    totals.append(episode_rewards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b39ce55f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(41.564, 9.19879905205022, 24.0, 68.0)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(totals), np.std(totals), np.min(totals), np.max(totals)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d8c33f7",
   "metadata": {},
   "source": [
    "Using a neural network policy: Take an observation as input, outputs action to be taken. In this environment, each observation contains the environment's full state so past actions and observations can be ignored. This would not be the case if we had hidden states or if observations would be noisy, in which case we'd use several observations to estimate the current state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "57406ea2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "c49db7be",
   "metadata": {},
   "outputs": [],
   "source": [
    "# To get smooth animations\n",
    "import matplotlib.animation as animation\n",
    "mpl.rc('animation', html='jshtml')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "64f6a74a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a base model -- sequential, functional, or subclass.\n",
    "keras.backend.clear_session()\n",
    "tf.random.set_seed(42)\n",
    "np.random.seed(42)\n",
    "\n",
    "n_inputs = 4 # == env.observation_space.shape[0]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "aa140691",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = keras.models.Sequential([\n",
    "    keras.layers.Dense(5, activation=\"elu\", input_shape=[n_inputs]),\n",
    "    keras.layers.Dense(1, activation=\"sigmoid\")])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a37610e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "#run one episode\n",
    "def render_policy_net(model, n_max_steps=200, seed=42):\n",
    "    frames = []\n",
    "    env = gym.make(\"CartPole-v1\")\n",
    "    env.seed(seed)\n",
    "    np.random.seed(seed)\n",
    "    obs = env.reset()\n",
    "    for step in range(n_max_steps):\n",
    "        frames.append(env.render(mode=\"rgb_array\"))\n",
    "        left_proba = model.predict(obs.reshape(1, -1))\n",
    "        action = int(np.random.rand() > left_proba)\n",
    "        obs, reward, done, info = env.step(action)\n",
    "        if done:\n",
    "            break\n",
    "    env.close()\n",
    "    return frames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "84a3b178",
   "metadata": {},
   "outputs": [],
   "source": [
    "#set up to visualize one episode\n",
    "env.seed(42)\n",
    "\n",
    "frames = []\n",
    "\n",
    "obs = env.reset()\n",
    "for step in range(200):\n",
    "    img = env.render(mode=\"rgb_array\")\n",
    "    frames.append(img)\n",
    "    action = basic_policy(obs)\n",
    "\n",
    "    obs, reward, done, info = env.step(action)\n",
    "    if done:\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "0628dd08",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_scene(num, frames, patch):\n",
    "    patch.set_data(frames[num])\n",
    "    return patch,\n",
    "\n",
    "def plot_animation(frames, repeat=False, interval=40):\n",
    "    fig = plt.figure()\n",
    "    patch = plt.imshow(frames[0])\n",
    "    plt.axis('off')\n",
    "    anim = animation.FuncAnimation(\n",
    "        fig, update_scene, fargs=(frames, patch),\n",
    "        frames=len(frames), repeat=repeat, interval=interval)\n",
    "    plt.close()\n",
    "    return anim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "70de8f48",
   "metadata": {},
   "outputs": [
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       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"animd0b1d82534af4f3e97f5c6450938e369.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"animd0b1d82534af4f3e97f5c6450938e369.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"animd0b1d82534af4f3e97f5c6450938e369.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"animd0b1d82534af4f3e97f5c6450938e369.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_selectd0b1d82534af4f3e97f5c6450938e369\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_d0b1d82534af4f3e97f5c6450938e369\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio1_d0b1d82534af4f3e97f5c6450938e369\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_d0b1d82534af4f3e97f5c6450938e369\"\n",
       "             >\n",
       "      <label for=\"_anim_radio2_d0b1d82534af4f3e97f5c6450938e369\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_d0b1d82534af4f3e97f5c6450938e369\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_d0b1d82534af4f3e97f5c6450938e369\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_imgd0b1d82534af4f3e97f5c6450938e369\";\n",
       "    var slider_id = \"_anim_sliderd0b1d82534af4f3e97f5c6450938e369\";\n",
       "    var loop_select_id = \"_anim_loop_selectd0b1d82534af4f3e97f5c6450938e369\";\n",
       "    var frames = new Array(32);\n",
       "    \n",
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       "gg==\\\n",
       "\"\n",
       "  frames[1] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "\"\n",
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       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        animd0b1d82534af4f3e97f5c6450938e369 = new Animation(frames, img_id, slider_id, 40.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x7fbb2146c1c0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frames = render_policy_net(model)\n",
    "plot_animation(frames)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f52e7405",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 4999, Loss: 0.150"
     ]
    }
   ],
   "source": [
    "#try again with 50 different environment in parallel, for 5000 iterations\n",
    "n_environments = 50\n",
    "n_iterations = 5000\n",
    "\n",
    "envs = [gym.make(\"CartPole-v1\") for _ in range(n_environments)]\n",
    "for index, env in enumerate(envs):\n",
    "    env.seed(index)\n",
    "np.random.seed(42)\n",
    "observations = [env.reset() for env in envs]\n",
    "optimizer = keras.optimizers.RMSprop()\n",
    "loss_fn = keras.losses.binary_crossentropy\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    # if angle < 0, we want proba(left) = 1., or else proba(left) = 0.\n",
    "    target_probas = np.array([([1.] if obs[2] < 0 else [0.])\n",
    "                              for obs in observations])\n",
    "    with tf.GradientTape() as tape:\n",
    "        left_probas = model(np.array(observations))\n",
    "        loss = tf.reduce_mean(loss_fn(target_probas, left_probas))\n",
    "    print(\"\\rIteration: {}, Loss: {:.3f}\".format(iteration, loss.numpy()), end=\"\")\n",
    "    grads = tape.gradient(loss, model.trainable_variables)\n",
    "    optimizer.apply_gradients(zip(grads, model.trainable_variables))\n",
    "    actions = (np.random.rand(n_environments, 1) > left_probas.numpy()).astype(np.int32)\n",
    "    for env_index, env in enumerate(envs):\n",
    "        obs, reward, done, info = env.step(actions[env_index][0])\n",
    "        observations[env_index] = obs if not done else env.reset()\n",
    "\n",
    "for env in envs:\n",
    "    env.close()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "1c5bc580",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img6c594f24c9d74cc0bf47a6ff7d0ca0e5\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider6c594f24c9d74cc0bf47a6ff7d0ca0e5\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim6c594f24c9d74cc0bf47a6ff7d0ca0e5.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim6c594f24c9d74cc0bf47a6ff7d0ca0e5.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim6c594f24c9d74cc0bf47a6ff7d0ca0e5.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim6c594f24c9d74cc0bf47a6ff7d0ca0e5.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim6c594f24c9d74cc0bf47a6ff7d0ca0e5.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim6c594f24c9d74cc0bf47a6ff7d0ca0e5.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim6c594f24c9d74cc0bf47a6ff7d0ca0e5.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim6c594f24c9d74cc0bf47a6ff7d0ca0e5.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim6c594f24c9d74cc0bf47a6ff7d0ca0e5.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim6c594f24c9d74cc0bf47a6ff7d0ca0e5.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select6c594f24c9d74cc0bf47a6ff7d0ca0e5\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_6c594f24c9d74cc0bf47a6ff7d0ca0e5\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio1_6c594f24c9d74cc0bf47a6ff7d0ca0e5\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_6c594f24c9d74cc0bf47a6ff7d0ca0e5\"\n",
       "             >\n",
       "      <label for=\"_anim_radio2_6c594f24c9d74cc0bf47a6ff7d0ca0e5\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_6c594f24c9d74cc0bf47a6ff7d0ca0e5\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_6c594f24c9d74cc0bf47a6ff7d0ca0e5\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img6c594f24c9d74cc0bf47a6ff7d0ca0e5\";\n",
       "    var slider_id = \"_anim_slider6c594f24c9d74cc0bf47a6ff7d0ca0e5\";\n",
       "    var loop_select_id = \"_anim_loop_select6c594f24c9d74cc0bf47a6ff7d0ca0e5\";\n",
       "    var frames = new Array(36);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "gg==\\\n",
       "\"\n",
       "  frames[1] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "AgZASgIGQEoCBkBKAgZASv8D2QEoNuwWXeUAAAAASUVORK5CYII=\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim6c594f24c9d74cc0bf47a6ff7d0ca0e5 = new Animation(frames, img_id, slider_id, 40.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x7fbb258b1a30>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frames = render_policy_net(model)\n",
    "plot_animation(frames)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9ac444d",
   "metadata": {},
   "source": [
    "## Policy Gradients <br> \n",
    "#### Implementing variant of the REINFORCE algo <br>\n",
    "1. NN plays several games. Compute gradients at each step <br>\n",
    "2. After several episodes, compute each actions score <br>\n",
    "3. If score is positive, apply the gradients by multiplying <br> \n",
    "each gradient vector by the corresponding actions score <br>\n",
    "If score is negative apply opposite gradients to make action less likely <br>\n",
    "4. Compute average of all gradient vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "1591fa7b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def play_one_step(env, obs, model, loss_fn):\n",
    "    with tf.GradientTape() as tape:\n",
    "        left_proba = model(obs[np.newaxis])\n",
    "        action = (tf.random.uniform([1, 1]) > left_proba)\n",
    "        y_target = tf.constant([[1.]]) - tf.cast(action, tf.float32) #target prob\n",
    "        loss = tf.reduce_mean(loss_fn(y_target, left_proba)) #loss function\n",
    "    grads = tape.gradient(loss, model.trainable_variables) #gradient\n",
    "    obs, reward, done, info = env.step(int(action[0, 0].numpy()))\n",
    "    return obs, reward, done, grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "d93616b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def play_multiple_episodes(env, n_episodes, n_max_steps, model, loss_fn):\n",
    "    all_rewards = []\n",
    "    all_grads = []\n",
    "    for episode in range(n_episodes):\n",
    "        current_rewards = []\n",
    "        current_grads = []\n",
    "        obs = env.reset()\n",
    "        for step in range(n_max_steps):\n",
    "            obs, reward, done, grads = play_one_step(env, obs, model, loss_fn)\n",
    "            current_rewards.append(reward)\n",
    "            current_grads.append(grads)\n",
    "            if done:\n",
    "                break\n",
    "        all_rewards.append(current_rewards)\n",
    "        all_grads.append(current_grads)\n",
    "    return all_rewards, all_grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "52311fc6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def discount_rewards(rewards, discount_rate):\n",
    "    discounted = np.array(rewards)\n",
    "    for step in range(len(rewards) - 2, -1, -1):\n",
    "        discounted[step] += discounted[step + 1] * discount_rate\n",
    "    return discounted\n",
    "\n",
    "def discount_and_normalize_rewards(all_rewards, discount_rate):\n",
    "    all_discounted_rewards = [discount_rewards(rewards, discount_rate)\n",
    "                              for rewards in all_rewards]\n",
    "    flat_rewards = np.concatenate(all_discounted_rewards)\n",
    "    reward_mean = flat_rewards.mean()\n",
    "    reward_std = flat_rewards.std()\n",
    "    return [(discounted_rewards - reward_mean) / reward_std\n",
    "            for discounted_rewards in all_discounted_rewards]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "6d7dc442",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-22, -40, -50])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "discount_rewards([10, 0, -50], discount_rate=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "7c96b4ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([-0.28435071, -0.86597718, -1.18910299]),\n",
       " array([1.26665318, 1.0727777 ])]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "discount_and_normalize_rewards([[10, 0, -50], [10, 20]], discount_rate=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "004d6b9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_iterations = 150\n",
    "n_episodes_per_update = 10\n",
    "n_max_steps = 200\n",
    "discount_rate = 0.95"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "d65ddf61",
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = keras.optimizers.Adam(learning_rate=0.01)\n",
    "loss_fn = keras.losses.binary_crossentropy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "4591e399",
   "metadata": {},
   "outputs": [],
   "source": [
    "keras.backend.clear_session()\n",
    "np.random.seed(42)\n",
    "tf.random.set_seed(42)\n",
    "\n",
    "model = keras.models.Sequential([\n",
    "    keras.layers.Dense(5, activation=\"elu\", input_shape=[4]),\n",
    "    keras.layers.Dense(1, activation=\"sigmoid\"),\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f406474b",
   "metadata": {},
   "source": [
    "Algorithm runs the policy and at each step calculates the tensors and stores the values. Multiply each gradient vector by action score. Standardizes gradients and computes the average of the tweaked gradients. Feeds the resulting gradients back to the optimizer. One placeholder per gradient vector. Apply updated gradients using .apply_gradients that takes gradient vector, variable pairs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "3519980d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration: 149, mean rewards: 199.6"
     ]
    }
   ],
   "source": [
    "env = gym.make(\"CartPole-v1\")\n",
    "env.seed(42);\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    all_rewards, all_grads = play_multiple_episodes(\n",
    "        env, n_episodes_per_update, n_max_steps, model, loss_fn)\n",
    "    total_rewards = sum(map(sum, all_rewards))                     # Not shown in the book\n",
    "    print(\"\\rIteration: {}, mean rewards: {:.1f}\".format(          # Not shown\n",
    "        iteration, total_rewards / n_episodes_per_update), end=\"\") # Not shown\n",
    "    all_final_rewards = discount_and_normalize_rewards(all_rewards,\n",
    "                                                       discount_rate)\n",
    "    all_mean_grads = []\n",
    "    for var_index in range(len(model.trainable_variables)):\n",
    "        mean_grads = tf.reduce_mean(\n",
    "            [final_reward * all_grads[episode_index][step][var_index]\n",
    "             for episode_index, final_rewards in enumerate(all_final_rewards)\n",
    "                 for step, final_reward in enumerate(final_rewards)], axis=0)\n",
    "        all_mean_grads.append(mean_grads)\n",
    "    optimizer.apply_gradients(zip(all_mean_grads, model.trainable_variables))\n",
    "\n",
    "env.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "178a0fc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "frames = render_policy_net(model)\n",
    "plot_animation(frames)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "792f4699",
   "metadata": {},
   "source": [
    "### Markov Chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d24606c9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "States: 0 0 3 \n",
      "States: 0 1 2 1 2 1 2 1 2 1 3 \n",
      "States: 0 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 3 \n",
      "States: 0 3 \n",
      "States: 0 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 3 \n",
      "States: 0 1 3 \n",
      "States: 0 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 ...\n",
      "States: 0 0 3 \n",
      "States: 0 0 0 1 2 1 2 1 3 \n",
      "States: 0 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 3 \n"
     ]
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "\n",
    "transition_probabilities = [ # shape=[s, s']\n",
    "        [0.7, 0.2, 0.0, 0.1],  # from s0 to s0, s1, s2, s3\n",
    "        [0.0, 0.0, 0.9, 0.1],  # from s1 to ...\n",
    "        [0.0, 1.0, 0.0, 0.0],  # from s2 to ...\n",
    "        [0.0, 0.0, 0.0, 1.0]]  # from s3 to ...\n",
    "\n",
    "n_max_steps = 50\n",
    "\n",
    "def print_sequence():\n",
    "    current_state = 0\n",
    "    print(\"States:\", end=\" \")\n",
    "    for step in range(n_max_steps):\n",
    "        print(current_state, end=\" \")\n",
    "        if current_state == 3:\n",
    "            break\n",
    "        current_state = np.random.choice(range(4), p=transition_probabilities[current_state])\n",
    "    else:\n",
    "        print(\"...\", end=\"\")\n",
    "    print()\n",
    "\n",
    "for _ in range(10):\n",
    "    print_sequence()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25509c62",
   "metadata": {},
   "source": [
    "## Decision Process and Q-Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4b52e103",
   "metadata": {},
   "outputs": [],
   "source": [
    "#used to calculate Q-Values\n",
    "transition_probabilities = [ # shape=[s, a, s']\n",
    "        [[0.7, 0.3, 0.0], [1.0, 0.0, 0.0], [0.8, 0.2, 0.0]],\n",
    "        [[0.0, 1.0, 0.0], None, [0.0, 0.0, 1.0]],\n",
    "        [None, [0.8, 0.1, 0.1], None]]\n",
    "rewards = [ # shape=[s, a, s']\n",
    "        [[+10, 0, 0], [0, 0, 0], [0, 0, 0]],\n",
    "        [[0, 0, 0], [0, 0, 0], [0, 0, -50]],\n",
    "        [[0, 0, 0], [+40, 0, 0], [0, 0, 0]]]\n",
    "possible_actions = [[0, 1, 2], [0, 2], [1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3d1555e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "#initializing q-values\n",
    "Q_values = np.full((3, 3), -np.inf) # -np.inf for impossible actions\n",
    "for state, actions in enumerate(possible_actions):\n",
    "    Q_values[state, actions] = 0.0  # for all possible actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "70c2dc65",
   "metadata": {},
   "outputs": [],
   "source": [
    "gamma = 0.90  # the discount factor\n",
    "\n",
    "history1 = [] # Not shown in the book (for the figure below)\n",
    "for iteration in range(50):\n",
    "    Q_prev = Q_values.copy()\n",
    "    history1.append(Q_prev) # Not shown\n",
    "    for s in range(3):\n",
    "        for a in possible_actions[s]:\n",
    "            Q_values[s, a] = np.sum([\n",
    "                    transition_probabilities[s][a][sp]\n",
    "                    * (rewards[s][a][sp] + gamma * np.max(Q_prev[sp]))\n",
    "                for sp in range(3)])\n",
    "\n",
    "history1 = np.array(history1) # Not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "33901e1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[18.91891892, 17.02702702, 13.62162162],\n",
       "       [ 0.        ,        -inf, -4.87971488],\n",
       "       [       -inf, 50.13365013,        -inf]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e65226b",
   "metadata": {},
   "source": [
    "##### The optimal policy for this MDP, when using a discount factor of 0.90, is to choose action a0 when in state s0, and choose action a0 when in state s1, and finally choose action a1 (the only possible action) when in state s2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "faccb922",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(Q_values, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "739aecad",
   "metadata": {},
   "source": [
    "### Q-Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "804d7567",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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