Chapter18.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f0d423d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "import sklearn\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import os\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "mpl.rc('animation', html='jshtml')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "91d54998",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.0461906 , -0.02063419,  0.04314876,  0.00705948], dtype=float32)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import gym\n",
    "env = gym.make(\"CartPole-v1\")\n",
    "obs = env.reset()\n",
    "obs\n",
    "####각각 카트 수평위치, 카트 속도, 막대 각도, 막대 각속도"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "940b57b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_environment(env, figsize=(5,4)):\n",
    "    plt.figure(figsize=figsize)\n",
    "    img = env.render(mode=\"rgb_array\")\n",
    "    plt.imshow(img)\n",
    "    plt.axis(\"off\")\n",
    "    return img"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "66e5102a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot_environment(env)\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7a572387",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\hjhhi\\anaconda3\\envs\\python3.6.8\\lib\\site-packages\\pyglet\\image\\codecs\\wic.py:289: UserWarning: [WinError -2147417850] 스레드 모드가 설정된 후에는 바꿀 수 없습니다\n",
      "  warnings.warn(str(err))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(400, 600, 3)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img = env.render(mode=\"rgb_array\")\n",
    "img.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c15674fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Discrete(2)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.action_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "72f120c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00559216,  0.17431584,  0.04849188, -0.30695853], dtype=float32)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "action=1\n",
    "obs, reward, done, info = env.step(action)\n",
    "obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6995f28a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2474637e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "done"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "476a1029",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5b256a5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def basic_policy(obs):\n",
    "    angle = obs[2]\n",
    "    return 0 if angle < 0 else 1\n",
    "totals=[]\n",
    "for episode in range(500):\n",
    "    episode_rewards = 0\n",
    "    obs = env.reset()\n",
    "    for step in range(200):\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": 12,
   "id": "79f1a0ed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "41.214 8.574858832657247 24.0 68.0\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(totals), np.std(totals), np.min(totals), np.max(totals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "62759e0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "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": 5,
   "id": "b1bdc850",
   "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": 15,
   "id": "17ed74ac",
   "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, Mircosoft 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_img2fe277e18047446492375e52c15e1d61\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider2fe277e18047446492375e52c15e1d61\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim2fe277e18047446492375e52c15e1d61.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" onclick=\"anim2fe277e18047446492375e52c15e1d61.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" onclick=\"anim2fe277e18047446492375e52c15e1d61.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" onclick=\"anim2fe277e18047446492375e52c15e1d61.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" onclick=\"anim2fe277e18047446492375e52c15e1d61.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" onclick=\"anim2fe277e18047446492375e52c15e1d61.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" onclick=\"anim2fe277e18047446492375e52c15e1d61.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" onclick=\"anim2fe277e18047446492375e52c15e1d61.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" onclick=\"anim2fe277e18047446492375e52c15e1d61.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" onclick=\"anim2fe277e18047446492375e52c15e1d61.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select2fe277e18047446492375e52c15e1d61\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_2fe277e18047446492375e52c15e1d61\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio1_2fe277e18047446492375e52c15e1d61\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_2fe277e18047446492375e52c15e1d61\"\n",
       "             >\n",
       "      <label for=\"_anim_radio2_2fe277e18047446492375e52c15e1d61\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_2fe277e18047446492375e52c15e1d61\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_2fe277e18047446492375e52c15e1d61\">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_img2fe277e18047446492375e52c15e1d61\";\n",
       "    var slider_id = \"_anim_slider2fe277e18047446492375e52c15e1d61\";\n",
       "    var loop_select_id = \"_anim_loop_select2fe277e18047446492375e52c15e1d61\";\n",
       "    var frames = new Array(55);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "AZCSgAGQkoABkJKAAZCSgAGQkoABkJKAAZCSgAGQ0n8AFqCecuBjYGQAAAAASUVORK5CYII=\\\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",
       "        anim2fe277e18047446492375e52c15e1d61 = 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 0x1683ccc2668>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_animation(frames)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "67af3e87",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_inputs = 4\n",
    "model = keras.models.Sequential([\n",
    "    keras.layers.Dense(5, activation=\"elu\", input_shape=[n_inputs]),\n",
    "    keras.layers.Dense(1, activation=\"sigmoid\")\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e822078",
   "metadata": {},
   "source": [
    "# 정책 그래디언트 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "90c30b9f",
   "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, 2]) > left_proba)\n",
    "        y_target = tf.constant([[1.]]) - tf.cast(action, tf.float32)\n",
    "###### tf,reduce_mean은 텐서의 특정 축 값을 전부 더해서 len(원소 수)로 나눠줌 없을 시 모든 원소 합함\n",
    "        loss = tf.reduce_mean(loss_fn(y_target, left_proba))\n",
    "    grads = tape.gradient(loss, model.trainable_variables)\n",
    "    obs, reward, done, info = env.step(int(action[0, 0].numpy()))\n",
    "    return obs, reward, done, grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3275227e",
   "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": 8,
   "id": "19cb0788",
   "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": 20,
   "id": "13c87bd8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-22, -40, -50])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "discount_rewards([10, 0, -50], 0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7e1ad1bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([-0.28435071, -0.86597718, -1.18910299]),\n",
       " array([1.26665318, 1.0727777 ])]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "discount_and_normalize_rewards([[10, 0, -50], [10, 20]], 0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "b076665e",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_iteration=150\n",
    "n_episodes_per_update = 10\n",
    "n_max_steps = 200\n",
    "discount_rate = 0.95"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0c175e91",
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = keras.optimizers.Adam(lr=0.01)\n",
    "loss_fn = keras.losses.binary_crossentropy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "89c8782d",
   "metadata": {},
   "outputs": [],
   "source": [
    "for iteration in range(n_iteration):\n",
    "    all_rewards, all_grads = play_multiple_episodes(\n",
    "    env, n_episodes_per_update, n_max_steps, model, loss_fn)\n",
    "    all_final_rewards = discount_and_normalize_rewards(all_rewards, discount_rate)\n",
    "    \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))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "3afecd70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000.0"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(all_rewards).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "1540e9a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(model.trainable_variables)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "3015dd52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<tf.Tensor: shape=(4, 5), dtype=float32, numpy=\n",
       " array([[-1.5531044e-03,  2.1297160e-04,  8.0465317e-05,  2.4752435e-03,\n",
       "         -2.4279431e-04],\n",
       "        [ 2.2489647e-03, -8.2624890e-04, -8.7316614e-03, -1.0000690e-02,\n",
       "          4.0723683e-04],\n",
       "        [-1.6719729e-04,  1.6218566e-04,  7.2579016e-04,  5.5940379e-04,\n",
       "         -3.4279226e-05],\n",
       "        [-1.2299070e-03,  7.0141745e-04,  4.0113018e-03,  4.1992427e-03,\n",
       "         -2.1142617e-04]], dtype=float32)>,\n",
       " <tf.Tensor: shape=(5,), dtype=float32, numpy=\n",
       " array([-0.00202173,  0.00198197,  0.00947445,  0.00987856, -0.000351  ],\n",
       "       dtype=float32)>,\n",
       " <tf.Tensor: shape=(5, 1), dtype=float32, numpy=\n",
       " array([[ 0.00053823],\n",
       "        [-0.00275461],\n",
       "        [-0.00134186],\n",
       "        [-0.00223923],\n",
       "        [ 0.00329582]], dtype=float32)>,\n",
       " <tf.Tensor: shape=(1,), dtype=float32, numpy=array([-0.00556229], dtype=float32)>]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_mean_grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c5525c64",
   "metadata": {},
   "outputs": [],
   "source": [
    "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": 27,
   "id": "ea1e124e",
   "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, Mircosoft 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_img0ad84b90996d4db39279d7dbe2205d53\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider0ad84b90996d4db39279d7dbe2205d53\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim0ad84b90996d4db39279d7dbe2205d53.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" onclick=\"anim0ad84b90996d4db39279d7dbe2205d53.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" onclick=\"anim0ad84b90996d4db39279d7dbe2205d53.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" onclick=\"anim0ad84b90996d4db39279d7dbe2205d53.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" onclick=\"anim0ad84b90996d4db39279d7dbe2205d53.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" onclick=\"anim0ad84b90996d4db39279d7dbe2205d53.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" onclick=\"anim0ad84b90996d4db39279d7dbe2205d53.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" onclick=\"anim0ad84b90996d4db39279d7dbe2205d53.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" onclick=\"anim0ad84b90996d4db39279d7dbe2205d53.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" onclick=\"anim0ad84b90996d4db39279d7dbe2205d53.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select0ad84b90996d4db39279d7dbe2205d53\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_0ad84b90996d4db39279d7dbe2205d53\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio1_0ad84b90996d4db39279d7dbe2205d53\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_0ad84b90996d4db39279d7dbe2205d53\"\n",
       "             >\n",
       "      <label for=\"_anim_radio2_0ad84b90996d4db39279d7dbe2205d53\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_0ad84b90996d4db39279d7dbe2205d53\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_0ad84b90996d4db39279d7dbe2205d53\">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_img0ad84b90996d4db39279d7dbe2205d53\";\n",
       "    var slider_id = \"_anim_slider0ad84b90996d4db39279d7dbe2205d53\";\n",
       "    var loop_select_id = \"_anim_loop_select0ad84b90996d4db39279d7dbe2205d53\";\n",
       "    var frames = new Array(170);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
       "bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsT\\\n",
       "AAALEwEAmpwYAAAHPklEQVR4nO3dzWtddR7H8e9JbpO0vTbxToh3EHXAB4QZUVy50I0rkS66dzF/\\\n",
       "RaH/gWDXhf4Ps8l6hln5QFFbZwTBqAMWNY3Shj7EtknTHBczDJQM2GTMOf3cvF67++PenE8W4Z2b\\\n",
       "3Js0bdsWAKSZ6nsAAOyHgAEQScAAiCRgAEQSMAAiCRgAkQQMgEgCBkAkAQMgkoABEEnAAIgkYABE\\\n",
       "EjAAIgkYAJEEDIBIAgZAJAEDIJKAARBJwACIJGAARBIwACIJGACRBAyASAIGQCQBAyCSgAEQScAA\\\n",
       "iCRgAEQSMAAiCRgAkQQMgEgCBkAkAQMgkoABEGnQ94AOtX0PAHgENX0P2C/PwACIJGAARBIwACIJ\\\n",
       "GACRBAyASAIGQCQBAyCSgAEQScAAiCRgAEQSMAAiCRgAkQQMgEgCBkAkAQMgkoABEEnAAIgkYABE\\\n",
       "EjAAIgkYAJEEDIBIAgZAJAEDIJKAARBJwACIJGAARBIwACIJGACRBAyASAIGQCQBAyCSgAEQScAA\\\n",
       "iCRgAEQSMAAiCRgAkQQMgEgCBkAkAQMgkoABEEnAAIgkYABEEjAAIgkYAJEEDIBIAgZAJAEDIJKA\\\n",
       "ARBJwACIJGAARBIwACIJGACRBAyASAIGQCQBAyCSgAEQScAAiCRgAEQSMAAiCRgAkQQMgEgCBkAk\\\n",
       "AQMgkoABEEnAAIgkYABEEjAAIgkYAJEEDIBIAgZAJAEDIJKAARBJwACIJGAARBIwACIJGACRBAyA\\\n",
       "SAIGQCQBAyCSgAEQScAAiCRgAEQSMAAiCRgAkQQMgEgCBkAkAQMgkoABEEnAAIgkYABEEjAAIgkY\\\n",
       "dOju9bW6tfpV7dzf7nsKxBv0PQAOkx8//1tdXfmwhuPna2r6319+M8NRPf3GO9U0vp+EvRAw6Frb\\\n",
       "1saVr/57c25h3OMYyOVbPgAiCRgAkQQMgEgCBkAkAQMgkoABEEnAAIgkYABEEjAAIgkYAJEEDDqy\\\n",
       "s32vtu/+vOv8yLGF7sfABBAw6MjWxrW6fvkfu86X/vRmVTWd74F0AgaPgKYRMNgrAQMgkoABEEnA\\\n",
       "AIgkYABEEjAAIgkYAJEEDIBIAgZAJAEDIJKAARBJwKAj6998XNW2D5w104OaGsz0tAiyCRh05Pa1\\\n",
       "73edHVt8uh578sUe1kA+AYNeNf6QL+yTgAEQScAAiCRgAEQSMAAiCRgAkQQMgEgCBkAkAQMgkoAB\\\n",
       "EEnAAIgkYNCBzZtX6876D7vOF/7wSvdjYEIIGHTg3u0btXXr6q7z4RPP9rAGJoOAARBJwACIJGAA\\\n",
       "RBIwACIJGACRBAyASAIGQCQBAyCSgAEQScAAiCRgAEQSMOjArdUvd53Nzj9RM8PHe1gDk0HAoAM3\\\n",
       "vvti19ncwrhmhqMe1sBkEDAAIgkYAJEEDIBIAgZAJAEDIJKAARBJwACIJGAARGratu17Q1cOzSfK\\\n",
       "wVtZWakzZ8489P3//NpCPfX4zIMf48fN+sulG7/62Lm5uTp//nzNz8/veSc8hKbvAfs16HsAJFpf\\\n",
       "X6/l5eWHvv/bz52qpRPP/OdWWzNTd+vKlSu1vPzXX33scDiszc3N/Q2FCSZg0IF/bbxcaz+9VVVV\\\n",
       "Te3US/MfVlvf9jsKwvkdGByw8WhY27Mv1P32SN1vj9R2O1v/vP56ffKNZ1Xw/xAwOGC/Hz9bi6Mn\\\n",
       "Hzjb3pmuv1/6tp9BMCEEDA7YY4PrdXSw8cDZ7NSdmm7u97QIJoPfgcEBu715r+rmR3V149X63Ymj\\\n",
       "deLYoP544v06On2r72kQTcDggH26slqX3nu32mrqlefG9cx4vj5o27p2807f0yDaoQnY2bNn+57A\\\n",
       "BLl8+fKe7r/TtlXV1mdfr9ZnX6/u6bFbW1t17ty5Gg6He3ocPIzTp0/3PWHfDs0bmdfW1g7HJ0on\\\n",
       "Ll68WCdPnuzkWsePH68LFy7U4uJiJ9fjcBmPx97I/Kgbj8d9T2CCjEajzq7VNE0tLS3V0tJSZ9eE\\\n",
       "BF6FCEAkAQMgkoABEEnAAIgkYABEOjSvQoTf0mg0qlOnTnVyrbm5uZqdne3kWpDk0LwPrPxDS4D/\\\n",
       "JfZ9YH6ECEAkAQMgkoABEEnAAIgkYABEEjAAIgkYAJEEDIBIAgZAJAEDIJKAARBJwACIJGAARBIw\\\n",
       "ACIJGACRBAyASAIGQCQBAyCSgAEQScAAiCRgAEQSMAAiCRgAkQQMgEgCBkAkAQMgkoABEEnAAIgk\\\n",
       "YABEEjAAIgkYAJEEDIBIAgZAJAEDIJKAARBJwACIJGAARBIwACIJGACRBAyASAIGQCQBAyCSgAEQ\\\n",
       "ScAAiCRgAEQa9D2gQ03fAwD47XgGBkAkAQMgkoABEEnAAIgkYABEEjAAIgkYAJEEDIBIAgZAJAED\\\n",
       "IJKAARBJwACIJGAARBIwACIJGACRBAyASAIGQCQBAyCSgAEQScAAiCRgAEQSMAAiCRgAkQQMgEgC\\\n",
       "BkAkAQMgkoABEEnAAIgkYABEEjAAIgkYAJEEDIBIAgZAJAEDIJKAARDpF2W0uBR9QGaQAAAAAElF\\\n",
       "TkSuQmCC\\\n",
       "\"\n",
       "  frames[1] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "\"\n",
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       "\"\n",
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       "Ui4QgFMAAAAASUVORK5CYII=\\\n",
       "\"\n",
       "  frames[169] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "/hhjmT1ja96BAazMteM74+DF1fHy8NoY48vZc05NwABW5sef7owxfh1j7Ixbt45nzzm11QTs5s2b\\\n",
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       "EjAAkgQMgCQBAyBJwABIEjAAkgQMgCQBAyDpX/y9bSPYDf5CAAAAAElFTkSuQmCC\\\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",
       "        anim0ad84b90996d4db39279d7dbe2205d53 = 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 0x16be4c73668>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frames = render_policy_net(model)\n",
    "plot_animation(frames)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "781b9ec7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200.0"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(all_rewards[9]).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af310ba0",
   "metadata": {},
   "source": [
    "# Q 가치"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "86c640ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "transition_probabilities = [[[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",
    "                        \n",
    "rewards = [[[+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",
    "    \n",
    "possible_actions = [[0, 1, 2], [0, 2], [1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "22bd9d35",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_values = np.full((3, 3), -np.inf)\n",
    "for state, actions in enumerate(possible_actions):\n",
    "    Q_values[state, actions] = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "560bfccb",
   "metadata": {},
   "outputs": [],
   "source": [
    "gamma = 0.9\n",
    "\n",
    "for iteration in range(50):\n",
    "    Q_prev = Q_values.copy()\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] * (rewards[s][a][sp] + gamma * np.max(Q_prev[sp]))\n",
    "            for sp in range(3)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "13da9a94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[18.91891892, 17.02702702, 13.62162162],\n",
       "       [ 0.        ,        -inf, -4.87971488],\n",
       "       [       -inf, 50.13365013,        -inf]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f1ab01be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1], dtype=int64)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(Q_values, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3bb3032a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 [0, 1, 2]\n",
      "1 [0, 2]\n",
      "2 [1]\n"
     ]
    }
   ],
   "source": [
    "for state, actions in enumerate(possible_actions):\n",
    "    print(state,actions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f3c8fe40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.02702702452192"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum([transition_probabilities[0][1][sp] * (rewards[0][1][sp] + gamma * np.max(Q_prev[sp]))\n",
    "            for sp in range(3)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7644706",
   "metadata": {},
   "source": [
    "### 할인계수 0.95"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "7e8dac7d",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_values = np.full((3, 3), -np.inf) # 불가능한 행동에 대해서는 -np.inf\n",
    "for state, actions in enumerate(possible_actions):\n",
    "    Q_values[state, actions] = 0.0  # 모든 가능한 행동에 대해서"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "6129356c",
   "metadata": {},
   "outputs": [],
   "source": [
    "gamma = 0.95  # 할인 계수\n",
    "\n",
    "history1 = []\n",
    "for iteration in range(50):\n",
    "    Q_prev = Q_values.copy()\n",
    "    history1.append(Q_prev)\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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "afd411d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[21.73304188, 20.63807938, 16.70138772],\n",
       "       [ 0.95462106,        -inf,  1.01361207],\n",
       "       [       -inf, 53.70728682,        -inf]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "2006079e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 1], dtype=int64)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(Q_values, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "222c62b8",
   "metadata": {},
   "source": [
    "# 시간차 학습, Q러닝"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "03575a0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def step(state, action):\n",
    "    probas = transition_probabilities[state][action]\n",
    "######random.choice -> 첫번쨰 인자를 list로 줄 시 원소의 값을 균등분포로 출력 p매개변수에 값을 넣어 각각의 확률 지정가능\n",
    "    next_state = np.random.choice([0, 1, 2], p=probas)\n",
    "    reward = rewards[state][action][next_state]\n",
    "##### next_state와 reward는 각각 s -> s'에서 s의 전이확률에 맞춘 s'와 그로 향할떄의 보상을 반환한다\n",
    "    return next_state, reward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7740a6d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def exploration_policy(state):\n",
    "###### 얘는 균등분포이므로 그냥 가능한 선택지에서 랜덤하게 뽑는다\n",
    "    return np.random.choice(possible_actions[state])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "5a49810a",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q_values = np.full((3, 3), -np.inf)\n",
    "for state, actions in enumerate(possible_actions):\n",
    "    Q_values[state, actions] = 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "a6aefb90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.,   0.,   0.],\n",
       "       [  0., -inf,   0.],\n",
       "       [-inf,   0., -inf]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "b5d68b18",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha0 = 0.05\n",
    "decay = 0.005\n",
    "gamma = 0.90\n",
    "state=0\n",
    "history2 = []\n",
    "\n",
    "for iteration in range(10000):\n",
    "    history2.append(Q_values.copy())\n",
    "    action = exploration_policy(state)\n",
    "    next_state, reward = step(state, action)\n",
    "    next_value = np.max(Q_values[next_state])\n",
    "    alpha = alpha0 / (1 + iteration * decay)\n",
    "##### 이전Q가치를 감소시키는 역활\n",
    "    Q_values[state, action] *= 1 - alpha\n",
    "##### Q가치 함수에 alpha적용\n",
    "    Q_values[state, action] += alpha * (reward + gamma * next_value)\n",
    "    state = next_state\n",
    "    \n",
    "history2 = np.array(history2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "53cf530a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[17.8808603 , 15.40440483, 12.29549146],\n",
       "       [ 0.        ,        -inf, -9.38073531],\n",
       "       [       -inf, 48.36326377,        -inf]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "95280625",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "true_Q_value = history1[-1, 0, 0]\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 4), sharey=True)\n",
    "axes[0].set_ylabel(\"Q-Value$(s_0, a_0)$\", fontsize=14)\n",
    "axes[0].set_title(\"Q-Value Iteration\", fontsize=14)\n",
    "axes[1].set_title(\"Q-Learning\", fontsize=14)\n",
    "for ax, width, history in zip(axes, (50, 10000), (history1, history2)):\n",
    "    ax.plot([0, width], [true_Q_value, true_Q_value], \"k--\")\n",
    "    ax.plot(np.arange(width), history[:, 0, 0], \"b-\", linewidth=2)\n",
    "    ax.set_xlabel(\"Iterations\", fontsize=14)\n",
    "    ax.axis([0, width, 0, 24])\n",
    "    \n",
    "### 그래프를 Q_가치반복의 마지막 a0 -> a0를 목표로 잡았는데 이게 목표로 적당한건가?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5e849d7",
   "metadata": {},
   "source": [
    "# 탐험 정책 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5e5715a8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "python3.6.8",
   "language": "python",
   "name": "python3.6.8"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}